332354 + Interview Questions in Secondary School in Math

1.	solve the questions...find govind purchased 15 kg ghee for rs 300 then he sold the ghee for rs 23.50 per kg. the percentage of profit is
Answer» ong>ANSWER: COST price 15kg=300 rs 1kg=300/15 1kg=20rs now SELLING price 1kg=23.5 rs profit=23.5-20 =3.5 profit percentage *profit 100/selling price 3.5100/23.5* *0.15100 15% Step-by-step explanation:**

1.

solve the questions...find govind purchased 15 kg ghee for rs 300 then he sold the ghee for rs 23.50 per kg. the percentage of profit is

Answer»

ong>ANSWER:

COST price

15kg=300 rs

1kg=300/15

1kg=20rs

now SELLING price

1kg=23.5 rs

profit=23.5-20

=3.5

profit percentage

profit *100/selling price

3.5*100/23.5

0.15*100

15%

Step-by-step explanation:

Discussion

2.	Write order of rotation and angle ofrotation of :(i) Equilateral triangle(ii) Circle(iii) Regular hexagonp
Answer» ONG>Answer: circle Step-by-step explanation: ANGLE of ROTATION and order of rotation suitable for circle

2.

Write order of rotation and angle ofrotation of :(i) Equilateral triangle(ii) Circle(iii) Regular hexagonp

Answer» ONG>Answer:

circle

Step-by-step explanation:

ANGLE of ROTATION and order of rotation suitable for circle

Discussion

3.	Neetu saves Rs 500 from her salary. Ifthis is 8% of her salary. What is hersalary? give ans with explanation
Answer» ONG>ANSWER: chkfhkfgjdjgdugdfjxjgxkgxgfh

Discussion

4.	Which is greater of the followingi) 2/3,3/2ii) -2/3,-3/2
Answer» ONG>Answer: 2/3 3/2 Step-by-step EXPLANATION: because they are POSITIVE

4.

Which is greater of the followingi) 2/3,3/2ii) -2/3,-3/2

Answer» ONG>Answer:

2/3 3/2

Step-by-step EXPLANATION:

because they are POSITIVE

Discussion

5.	From a point P which is a distance of 13 cm from the centre o of a circle of radius 5 cm a tangent PQ is drawn to the circle.Find the length of PQ
Answer» ONG>Answer: 12 cm Step-by-step EXPLANATION: See the PIC we will be using phythagorous theorem.

5.

From a point P which is a distance of 13 cm from the centre o of a circle of radius 5 cm a tangent PQ is drawn to the circle.Find the length of PQ

Answer» ONG>Answer:

12 cm

Step-by-step EXPLANATION:

See the PIC

we will be using phythagorous theorem.

Discussion

6.	A/ax-1 + b/bx-1 =a+b slove by factorization
Answer» ONG>Step-by-step explanation: Given: aax−1+bbx−1=a+b Subtract aax−1+bbx−1 from both SIDES to get: 0=a+b−aax−1−bbx−1 Multiply through by (ax−1)(bx−1) to get: 0=(a+b)(ax−1)(bx−1)−a(bx−1)−b(ax−1) 0=(a+b)(abx2−(a+b)X+1)−a(bx−1)−b(ax−1) 0=(a+b)(abx2−(a+b)x)+

6.

A/ax-1 + b/bx-1 =a+b slove by factorization

Answer» ONG>Step-by-step explanation:

Given:

aax−1+bbx−1=a+b

Subtract aax−1+bbx−1 from both SIDES to get:

0=a+b−aax−1−bbx−1

Multiply through by (ax−1)(bx−1) to get:

0=(a+b)(ax−1)(bx−1)−a(bx−1)−b(ax−1)

0=(a+b)(abx2−(a+b)X+1)−a(bx−1)−b(ax−1)

0=(a+b)(abx2−(a+b)x)+

Discussion

7.	Write the approximate measurement for the following things.
Answer» ONG>Answer: 7 8 2.5 2 2 1.5 4 6 4 20 10 30 4.5

7.

Write the approximate measurement for the following things.

Answer» ONG>Answer:

7

8

2.5

2

1.5

4

6

4

20

10

30

4.5

Discussion

8.	So, -1/2 would be marked at a pointhalf the distance between 0 and –1.Now represent the following rationals on number lines.(i) 3/5 (ii) -4/7 (iii) 2/3
Answer» ong>ANSWER: This is NUMBER line h XD prepare a Presentation on the TOPIC: Effects of the CoviD-19 Pandemic the on Indian economy.about 400 WORD

8.

So, -1/2 would be marked at a pointhalf the distance between 0 and –1.Now represent the following rationals on number lines.(i) 3/5 (ii) -4/7 (iii) 2/3

Answer»

ong>ANSWER:

This is NUMBER line h XD

prepare a Presentation

on the TOPIC:

Effects of the CoviD-19 Pandemic

the on

Indian economy.about 400 WORD

Discussion

9.	8. A man walking at a speed of 10 km/hr takes 12 minutes to complete one round of the park. Find the distance covered by him.
Answer» ong>Answer: He covered 2 km of DISTANCE. Step-by-step explanation: Given that: A man walking at a SPEED of 10 km/hr. Time taken to complete one round of park is 12 minutes. To Find: The distance covered by him. First converting the time in hours: We know that. ⇒ 1 MINUTE = 1/60 hours ⇒ 12 minutes = 12/60 hours ⇒ 12 minutes = 0.2 hours Finding the distance covered by him: FORMULA: Distance = Speed × Time ⟶ Distance = 10 × 0.2 ⟶ Distance = 2 ∴ The distance covered by him = 2 km

9.

8. A man walking at a speed of 10 km/hr takes 12 minutes to complete one round of the park. Find the distance covered by him.

Answer»

ong>Answer:

He covered 2 km of DISTANCE.

Step-by-step explanation:

Given that:

A man walking at a SPEED of 10 km/hr.
Time taken to complete one round of park is 12 minutes.

To Find:

The distance covered by him.

First converting the time in hours:

We know that.

⇒ 1 MINUTE = 1/60 hours

⇒ 12 minutes = 12/60 hours

⇒ 12 minutes = 0.2 hours

Finding the distance covered by him:

FORMULA: Distance = Speed × Time

⟶ Distance = 10 × 0.2

⟶ Distance = 2

∴ The distance covered by him = 2 km

Discussion

10.	O 00:45:40 GOVINDWAD SUJAL VYANKATQuestion 9 :FindÂ theÂ PrincipalÂ ValueÂ ofÂ sin 'ÂÂ (2
Answer» ong>ANSWER:HO 00:45:40 GOVINDWAD SUJAL VYANKAT Question 9 : FindÂ theÂ PrincipalÂ ValueÂ ofÂ sin 'Â Â ( 2 Step-by-step EXPLANATION:

10.

O 00:45:40 GOVINDWAD SUJAL VYANKATQuestion 9 :FindÂ theÂ PrincipalÂ ValueÂ ofÂ sin 'ÂÂ (2

Answer»

ong>ANSWER:HO 00:45:40

GOVINDWAD SUJAL VYANKAT

Question 9 :

FindÂ theÂ PrincipalÂ ValueÂ ofÂ sin 'Â

Â (

2

Step-by-step EXPLANATION:

Discussion

11.	If mean and median of given data x-a,x-b,x-c are equal find related between a,b,c.
Answer» ONG>Answer: 2b=a+c Step-by-step EXPLANATION: I have EXPLAINED it on paper. give me BRAINLIEST

11.

If mean and median of given data x-a,x-b,x-c are equal find related between a,b,c.

Answer» ONG>Answer:

2b=a+c

Step-by-step EXPLANATION:

I have EXPLAINED it on paper.

give me BRAINLIEST

Discussion

12.	The measure of angles of a quadrilateral are in the ratio 1:2:3:4 than find measures of each angles of quadrilateral
Answer» ong>Answer: 36°, 72°, 108° and 144° Step-by-step explanation: LET the ratio be x:2X:3x:4X. The sum of all four ANGLES of a quadrilateral is 360°. => x + 2x + 3x + 4x = 360° => 10x = 360° => x = 36° HENCE, the angles are 36°, 72°, 108° and 144°.

12.

The measure of angles of a quadrilateral are in the ratio 1:2:3:4 than find measures of each angles of quadrilateral

Answer»

ong>Answer:

36°, 72°, 108° and 144°

Step-by-step explanation:

LET the ratio be x:2X:3x:4X.

The sum of all four ANGLES of a quadrilateral is 360°.

=> x + 2x + 3x + 4x = 360°

=> 10x = 360°

=> x = 36°

HENCE, the angles are 36°, 72°, 108° and 144°.

Discussion

13.	Given four rational number equivalent to -7/5
Answer» ong>ANSWER: The four EQUIVALENT RATIONAL numbers to -7/5 are: -14/10 -21/15 -28/20 -35/25 -42/30

13.

Given four rational number equivalent to -7/5

Answer»

ong>ANSWER:

The four EQUIVALENT RATIONAL numbers to -7/5 are:

-14/10

-21/15

-28/20

-35/25

-42/30

Discussion

14.	____is graphical representation of continuous frequency distribution with rectangles
Answer» ong>Answer: Histogram a histogram or frequency histogram is a graphical representation of a frequency distribution in the form of RECTANGLES with class intervals as bases and HEIGHTS proportional to corresponding FREQUENCIES such there is no gap between any TWO successive rectangles

14.

____is graphical representation of continuous frequency distribution with rectangles

Answer»

ong>Answer:

Histogram a histogram or frequency histogram is a graphical representation of a frequency distribution in the form of RECTANGLES with class intervals as bases and HEIGHTS proportional to corresponding FREQUENCIES such there is no gap between any TWO successive rectangles

Discussion

15.	Write an a. p whose first term is 20 ans common difference is 8
Answer» ONG>Step-by-step explanation: i NEED help CALL me i need help 73688 30025

15.

Write an a. p whose first term is 20 ans common difference is 8

Answer» ONG>Step-by-step explanation:

i NEED help CALL me i need help 73688 30025

Discussion

16.	Construct ∆ whose semiperimeter is 5.5 cm and two base angles are 90° and 30° respectively.
Answer» ONG>ANSWER: kkgxulzyluydydyyyyydltdts Step-by-step EXPLANATION: dtkyydyydyssytospsylyylysyllyykydytyyyyl

16.

Construct ∆ whose semiperimeter is 5.5 cm and two base angles are 90° and 30° respectively.

Answer» ONG>ANSWER:

kkgxulzyluydydyyyyydltdts

Step-by-step EXPLANATION:

dtkyydyydyssytospsylyylysyllyykydytyyyyl

Discussion

17.	Question 17:The value of sec-1(-v2) ++ sec-1(v2)
Answer» ONG>ANSWER: ytn3ytl6ul63noko6263 bo626kenbo Step-by-step EXPLANATION: mark by BRAINLIST

17.

Question 17:The value of sec-1(-v2) ++ sec-1(v2)

Answer» ONG>ANSWER:

ytn3ytl6ul63noko6263 bo626kenbo

Step-by-step EXPLANATION:

mark by BRAINLIST

Discussion

18.	Which is greater (i)2/ 3 ,3/2 (ii) -2/3 -3/2
Answer» ONG>ANSWER: 1) 2/3,3/2 this is answer

Discussion

19.	Write true or false(i) The cube can cast a shadow in theshape of a square.(ii) The cube can cast a shadow in theshape of a hexagon.
Answer» ONG>ANSWER: false true Step-by-step EXPLANATION: (✯ᴗ✯)(✯ᴗ✯)(✯ᴗ✯)

19.

Write true or false(i) The cube can cast a shadow in theshape of a square.(ii) The cube can cast a shadow in theshape of a hexagon.

Answer» ONG>ANSWER:

false
true

Step-by-step EXPLANATION:

(✯ᴗ✯)(✯ᴗ✯)(✯ᴗ✯)

Discussion

20.	How many natural numbers form 10 to 250 are divisible by 4?
Answer» ONG>Answer: 241 DIVIDED 5 Step-by-step EXPLANATION: the and of this DIVISION is the result of this ques

20.

How many natural numbers form 10 to 250 are divisible by 4?

Answer» ONG>Answer:

241 DIVIDED 5

Step-by-step EXPLANATION:

the and of this DIVISION is the result of this ques

Discussion

21.	Sum of two numbers is 50 and subtracting at this number is 10 find th number
Answer» the two numbers be x and y. According to the question, x + y = 50 ___ eq.(i) x - y = 10 ___ eq.(ii) By adding both the equation, we get 2x = 60 or, x = 60/2 = 30 By PUTTING the value of x in eq.(i), we get 30 + y = 50 or, y = 50 - 30 = 20 Answer: The two numbers are 30 and 20 RESPECTIVELY.

21.

Sum of two numbers is 50 and subtracting at this number is 10 find th number

Answer»

the two numbers be x and y.

According to the question,

x + y = 50 ___ eq.(i)

x - y = 10 ___ eq.(ii)

By adding both the equation, we get

2x = 60

or, x = 60/2 = 30

By PUTTING the value of x in eq.(i), we get

30 + y = 50

or, y = 50 - 30 = 20

Answer:

The two numbers are 30 and 20 RESPECTIVELY.

Discussion

22.	2.In the given figure ,if the exterior angle is 135º, then p isa)67.5° b)75°c)105° d)82.50
Answer» ong>Answer: P = 90° Step-by-step explanation: Given: = 135° PQ = PR >angle PRQ + EXT. angle = 180° ( since it is a STRAIGHT line) PRQ + 135° = 180° PRQ = 180° - 135° = 45° Now, angle Q = angle R = 45° (since PQ = PR) THEREFORE, >angle P + angle Q = ext. angle (since ext. angle is equal to the SUM of interior opposite angles) angle P + 45° = 135° angle P = 135° - 45° = 90°

22.

2.In the given figure ,if the exterior angle is 135º, then p isa)67.5° b)75°c)105° d)82.50

Answer»

ong>Answer:

P = 90°

Step-by-step explanation:

Given: = 135°

PQ = PR

>angle PRQ + EXT. angle = 180° ( since it is a STRAIGHT line)

PRQ + 135° = 180°

PRQ = 180° - 135° = 45°

Now, angle Q = angle R = 45° (since PQ = PR)

THEREFORE,

>angle P + angle Q = ext. angle (since

ext. angle is equal to the SUM of interior opposite angles)

angle P + 45° = 135°

angle P = 135° - 45° = 90°

Discussion

23.	(x- y)^2 = (x-y) (x+y) Is it true or false .
Answer» ONG>no it is FALSE (x^2-y^2)=(x+y) (x-y) this the CORRECT FORMULAE

23.

(x- y)^2 = (x-y) (x+y) Is it true or false .

Answer» ONG>no it is FALSE

(x^2-y^2)=(x+y) (x-y)

this the CORRECT FORMULAE

Discussion

24.	"(4)十 tteThe value of tantan"Gg2is
Answer» ONG>ANSWER: jahwhshskskwkw. wwjhsshsuekwii. iwiwyshiwis. iwiw9w9w. oqoooq9w9

Discussion

25.	B. Write all the integers between0 and -7
Answer» ong>ANSWER: -6,-5,-4,-3,-2,-1 this is the answer

25.

B. Write all the integers between0 and -7

Answer»

ong>ANSWER:

-6,-5,-4,-3,-2,-1

this is the answer

Discussion

26.	8. The equation of a straight line passing through the point (2,-7) and parallel to x-axis is(a) x = 2(c) y-7(b) x -7(d) y 2
Answer» Correct Statement is The equation of a straight line passing through the POINT (2,-7) and parallel to x-axis is (a) x = 2 (c) y = - 7 (b) x = 7 (d) y = 2 $\large\underline{\sf{<klux>GIVEN</klux>- }}$ A line passes through the point (2, - 7) and parallel to x- axis. $\large\underline{\sf{To\:Find - }}$ Equation of line. Concept USED :- Slope - point form of a line Let us assume a line which passes through the point (a, b) and having slope 'm', then equation of line is $\sf \: y - b \: = \: m(x - a)$ $\large\underline{\sf{Solution-}}$ Given that A line passes through the point (2, - 7) and parallel to x - axis. Since, Line is parallel to x- axis. $\rm :\implies\:m \: = \: 0$ Now, We know that Equation of line is given by $\rm :\longmapsto\:y - b \: = \: m(x - a)$ where, $\rm :\longmapsto\:a \: = \: 2$ $\rm :\longmapsto\:b \: = \: - \: 7$ $\rm :\longmapsto\:m \: = \: 0$ On substituting all these values in above equation, we get $\rm :\longmapsto\:y \: - \: ( - 7) = 0 \times (x - 2)$ $\rm :\longmapsto\:y + 7 = 0$ $\rm :\implies\:y \: = \: - \: 7$ $\overbrace{ \underline { \boxed { \rm \therefore The \: equation \: of \: line \: is \: y \: = \: - \: 7}}}$ ─━─━─━─━─━─━─━─━─━─━─━─━─ Additional Information Different forms of equations of a straight line 1. Equations of horizontal and vertical lines Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the POINTS on the line. Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line. 2. Point-slope form equation of line Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by y - b = m(x - a) 3. Slope-intercept form equation of line Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by y = mx + a. 4. Intercept Form of Line Consider a line L having x– intercept a and y– intercept b, then the line passes through X– axis at (a,0) and Y– axis at (0,b). Equation of line is given by x/a + y/b = 1. 5. Normal form of Line Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis. Then, equation of line is given by x cosβ + y sinβ = p.

26.

8. The equation of a straight line passing through the point (2,-7) and parallel to x-axis is(a) x = 2(c) y-7(b) x -7(d) y 2

Answer»

Correct Statement is

The equation of a straight line passing through the POINT (2,-7) and parallel to x-axis is

(a) x = 2

(c) y = - 7

(b) x = 7

(d) y = 2

$\large\underline{\sf{<klux>GIVEN</klux>- }}$

A line

passes through the point (2, - 7)

and

parallel to x- axis.

$\large\underline{\sf{To\:Find - }}$

Equation of line.

Concept USED :-

Slope - point form of a line

Let us assume a line which passes through the point (a, b) and having slope 'm', then equation of line is

$\sf \: y - b \: = \: m(x - a)$

$\large\underline{\sf{Solution-}}$

Given that

A line passes through the point (2, - 7) and parallel to x - axis.

Since,

Line is parallel to x- axis.

$\rm :\implies\:m \: = \: 0$

Now,

We know that

Equation of line is given by

$\rm :\longmapsto\:y - b \: = \: m(x - a)$

where,

$\rm :\longmapsto\:a \: = \: 2$

$\rm :\longmapsto\:b \: = \: - \: 7$

$\rm :\longmapsto\:m \: = \: 0$

On substituting all these values in above equation, we get

$\rm :\longmapsto\:y \: - \: ( - 7) = 0 \times (x - 2)$

$\rm :\longmapsto\:y + 7 = 0$

$\rm :\implies\:y \: = \: - \: 7$

$\overbrace{ \underline { \boxed { \rm \therefore The \: equation \: of \: line \: is \: y \: = \: - \: 7}}}$

─━─━─━─━─━─━─━─━─━─━─━─━─

Additional Information

Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the POINTS on the line.

Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line.

2. Point-slope form equation of line

Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by y - b = m(x - a)

3. Slope-intercept form equation of line

Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by y = mx + a.

4. Intercept Form of Line

Consider a line L having x– intercept a and y– intercept b, then the line passes through X– axis at (a,0) and Y– axis at (0,b). Equation of line is given by x/a + y/b = 1.

5. Normal form of Line

Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis. Then, equation of line is given by x cosβ + y sinβ = p.

Discussion

27.	I. If a 3i- j+ 4k, b= 2i+3j- k , c=-5i +2j +3k, then a (b xc)= (A) 100 (B) 101 (C) 110(D) 109
Answer» ONG>Answer: What INDICATES the below GIVEN PICTURE?

Discussion

28.	If the angles A and B differ by 90 degrees prove that tanA tanB equals negative 1
Answer» ONG>ANSWER: dhjfjejdjbdbdbnsjsjfhfh

Discussion

29.	Add:374kg 78g, 249kg 98g, 46kg 56g.
Answer» ONG>Answer: In c,a function that calls another function is known as CALLING function. And a function or MODULE which receives CONTROL from calling function is CALLED function

Discussion

30.	Tan-1 1/4+ cot-1 9/2
Answer» ong>ANSWER: the new year will you do with name in the line:'she launches in SEPTEMBER of wealth brainly was the only one of those that in fact had to be in and the m is the most powerful and powerful sta of the world of the SOUL of GOD in our society gotri is a VERY important PART in this society near eva and the m and its great place for us and our LIVES and the METHOD is a great place for the people to be in and out of our lives and to our mobi WORLD and the m is a VERY good to see

30.

Tan-1 1/4+ cot-1 9/2

Answer»

ong>ANSWER:

the new year will you do with name in the line:'she launches in SEPTEMBER of wealth brainly was the only one of those that in fact had to be in and the m is the most powerful and powerful sta of the world of the SOUL of GOD in our society gotri is a VERY important PART in this society near eva and the m and its great place for us and our LIVES and the METHOD is a great place for the people to be in and out of our lives and to our mobi WORLD and the m is a VERY good to see

Discussion

31.	Calculate teh mean deviation about the mean of the digits 3,5,10,8,7,12,9,18
Answer» ong>ANSWER: MEAN = 9 Step-by-step EXPLANATION: mean = 3+5+10+8+7+12+9+18 DIVIDE by 8 mean = 72 divide by 8 mean = 9

31.

Calculate teh mean deviation about the mean of the digits 3,5,10,8,7,12,9,18

Answer»

ong>ANSWER:

MEAN = 9

Step-by-step EXPLANATION:

mean = 3+5+10+8+7+12+9+18 DIVIDE by 8

mean = 72 divide by 8

mean = 9

Discussion

32.	Radius of circle is 13cm length of chord is 12cm find distance of chord from centre
Answer» ong>ANSWER: SINCE, the perpendicular from the centre of a CIRCLE to a chord bisects the chord. ⇒ OL = 12 cm. Hence, the distance of the chord from the centre is 12 cm.

32.

Radius of circle is 13cm length of chord is 12cm find distance of chord from centre

Answer»

ong>ANSWER:

SINCE, the perpendicular from the centre of a CIRCLE to a chord bisects the chord. ⇒ OL = 12 cm. Hence, the distance of the chord from the centre is 12 cm.

Discussion

33.	Factorise z^2-4z+3z-12
Answer» ong>ANSWER: (Z+3)(z-4) Step-by-step explanation: z²-4z+3z-12 = z(z-4)+3(z-4) = (z+3)(z-4)

33.

Factorise z^2-4z+3z-12

Answer»

ong>ANSWER:

(Z+3)(z-4)

Step-by-step explanation:

z²-4z+3z-12

= z(z-4)+3(z-4)

= (z+3)(z-4)

Discussion

34.	If the ratio of the mode and the median of certain data if 3:5, then find the ratio of its mean and median
Answer» ONG>ANSWER: ufjcjckgkcjcjcieififkfidifjfjdjd

Discussion

35.	Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2:3
Answer» AVE line segments JOINING A(-2,6) and B(3,-4) in the ratio 2:3 as: $\circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 2 \times 3+3 \times (-2) }{2+3} , \dfrac{2 \times (-4) + 3 \times 6}{2+3} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 6+(-6) }{5} , \dfrac{-8+18}{5} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 6-6 }{5} , \dfrac{10}{5} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 0 }{5} , 2 \right) }} \\ \\ \\ \colon\implies{\sf{ P = (0 , 2) }}$ ~Equation of line SEGMENT having gradient (m) = ${\sf{ \dfrac{3}{2} }}$ Line segment PASSES through P(0,2) x = 0 $\longrightarrow$ x - 0 = 0 y = 2 $\longrightarrow$ y - 2 = 0 $\dag \ {\pmb{\underline{\sf\green{ According \ to \ Equation: }}}} \\ \\ \colon\implies{\sf{ y-2 = \dfrac{3}{2} (x-0) }} \\ \\ \\ \colon\implies{\sf{ y-2 = \dfrac{3x-0}{2} }} \\ \\ \\ \colon\implies{\sf{ 2(y-2) = 3x }} \\ \\ \\ \colon\implies{\sf{ 2y-4 = 3x }} \\ \\ \\ \colon\implies{\sf{ 2y-3x = 4 }} \\$ Hence, ${\underline{\sf{The \ equation \ of \ the \ line \ is \ 2y-3x = 4 . }}}$

35.

Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2:3

Answer» AVE line segments JOINING A(-2,6) and B(3,-4) in the ratio 2:3 as:

$\circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 2 \times 3+3 \times (-2) }{2+3} , \dfrac{2 \times (-4) + 3 \times 6}{2+3} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 6+(-6) }{5} , \dfrac{-8+18}{5} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 6-6 }{5} , \dfrac{10}{5} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 0 }{5} , 2 \right) }} \\ \\ \\ \colon\implies{\sf{ P = (0 , 2) }}$

~Equation of line SEGMENT having gradient (m) = ${\sf{ \dfrac{3}{2} }}$

Line segment PASSES through P(0,2)

x = 0 $\longrightarrow$ x - 0 = 0
y = 2 $\longrightarrow$ y - 2 = 0

$\dag \ {\pmb{\underline{\sf\green{ According \ to \ Equation: }}}} \\ \\ \colon\implies{\sf{ y-2 = \dfrac{3}{2} (x-0) }} \\ \\ \\ \colon\implies{\sf{ y-2 = \dfrac{3x-0}{2} }} \\ \\ \\ \colon\implies{\sf{ 2(y-2) = 3x }} \\ \\ \\ \colon\implies{\sf{ 2y-4 = 3x }} \\ \\ \\ \colon\implies{\sf{ 2y-3x = 4 }} \\$

Hence,

${\underline{\sf{The \ equation \ of \ the \ line \ is \ 2y-3x = 4 . }}}$

Discussion

36.	Prove that : cosec2Ө + sec2Ө = cosec2Ө.sec2Ө
Answer» ONG>ANSWER: LH.S. = COSEC2 θ + SEC2 θ =1/sin^2Ө+1/cos^2Ө =cos^2Ө+sin^2Ө/sin^2Өcos^2Ө =1/sin^2Өcos^2Ө =(1/sin^2Ө)(1/cos^2Ө) = cosec2 θ sec2 θ = R.H.S

36.

Prove that : cosec2Ө + sec2Ө = cosec2Ө.sec2Ө

Answer» ONG>ANSWER:

LH.S. = COSEC2 θ + SEC2 θ

=1/sin^2Ө+1/cos^2Ө

=cos^2Ө+sin^2Ө/sin^2Өcos^2Ө

=1/sin^2Өcos^2Ө

=(1/sin^2Ө)(1/cos^2Ө)

= cosec2 θ sec2 θ

= R.H.S

Discussion

37.	Q. 2. Write the correct word in the space:(1) Rollingfriction
Answer» ONG>ANSWER: what do you MEAN ????????????????

Discussion

38.	Draw a number line and represent the rational number 1 2/5
Answer» ong>Step-by-step EXPLANATION: j8xejxb8xbiwbuvxuvxbwxubsx7bsxuibyxivysxivysx8yv svh 8ycexcgud ugcd,iye,8ycze8yvze8yvze8yvze97gez ezczeivez9vxei xe9 ehx igx xw8 x9ye ex9vy8wx8ygdei 28y97z3u3cdih3divediyed 2d 2dubd2i I wd9uv2du dev id id28y ihvd2 ihde7y edvd3 uhuv3fc8yd3 de 2ey8 ugd3 uhd39vu3r9uvd4i yv8d3i hf3ivud3 dedei 9vud3 jd3 i2dovu dih3ih d3i hd3 ihd3ovhdi3vih deih xeo j3div indeed 8u3dh delved xe9ui harish exit ih xw9u xw9 udeih xwih I hx9u d29u 9 ud2oh xwig xw dw ud2o ihdeigx oh2 udoh dh di d3voj ed1ih xw ex oobeuc1ibc4i e1cuvr1icb9rub1c8ycb8yed1yved1 is xe1 ex1ihbu9e1i 1exi harish di e1di hr1cih cr1h Craig drih 1i h1dih degi ug iyer UOP op FREE FIRE

38.

Draw a number line and represent the rational number 1 2/5

Answer»

ong>Step-by-step EXPLANATION:

j8xejxb8xbiwbuvxuvxbwxubsx7bsxuibyxivysxivysx8yv svh 8ycexcgud ugcd,iye,8ycze8yvze8yvze8yvze97gez ezczeivez9vxei xe9 ehx igx xw8 x9ye ex9vy8wx8ygdei 28y97z3u3cdih3divediyed 2d 2dubd2i I wd9uv2du dev id id28y ihvd2 ihde7y edvd3 uhuv3fc8yd3 de 2ey8 ugd3 uhd39vu3r9uvd4i yv8d3i hf3ivud3 dedei 9vud3 jd3 i2dovu dih3ih d3i hd3 ihd3ovhdi3vih deih xeo j3div indeed 8u3dh delved xe9ui harish exit ih xw9u xw9 udeih xwih I hx9u d29u 9 ud2oh xwig xw dw ud2o ihdeigx oh2 udoh dh di d3voj ed1ih xw ex oobeuc1ibc4i e1cuvr1icb9rub1c8ycb8yed1yved1 is xe1 ex1ihbu9e1i 1exi harish di e1di hr1cih cr1h Craig drih 1i h1dih degi ug iyer UOP op FREE FIRE

Discussion

39.	Belove IfA= {x-X is a multiple of 3&XE NXCTooB- (x:x is a multiple of 5, XN x 2100!the find the the value of"NA) () n (B) 1) n(A) NB) in(A-B
Answer» ONG>Step-by-step EXPLANATION: xjxjxxjxjxjxhsjKkakalakqjaajjszjjdjzjzjsjsjddjdjsjjdxjcicjsnakzlgnfzjiskekdjdjdjxjjxjx xjdjkdjdjs

Discussion

40.	Multiply(m3-2m+3) (m4 -2m2+3m+2)
Answer» $\sf\small\underline\red{Answer \: in \: the \: attachment.}$

40.

Multiply(m3-2m+3) (m4 -2m2+3m+2)

Answer»

$\sf\small\underline\red{Answer \: in \: the \: attachment.}$

Discussion

41.	-2/3, -3/2 which is greatest fraction
Answer» ONG>ANSWER: -2/3 is GREATEST FRACTION ....

Discussion

42.	Two circles of diameter 8.8cm and 6.6cm respectively touch each other internally. What is the distance between their centres? * a)2.2cmb)5.4cmc)1.1cmd)7.7cm
Answer» ong>Answer: a) 2.2 cm Step-by-step explanation: when TWO circles TOUCH each other INTERNALLY the distance between their center is difference between the bigger RADIUS and smaller radius therefore, 8.8-6.6= 2.2 cm hope it helps you :)

42.

Two circles of diameter 8.8cm and 6.6cm respectively touch each other internally. What is the distance between their centres? * a)2.2cmb)5.4cmc)1.1cmd)7.7cm

Answer»

ong>Answer:

a) 2.2 cm

Step-by-step explanation:

when TWO circles TOUCH each other INTERNALLY the distance between their center is difference between the bigger RADIUS and smaller radius therefore, 8.8-6.6= 2.2 cm hope it helps you :)

Discussion

43.	A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and36km downstream. Find the speed of the boat in still water and that of thestream.
Answer» align="absmiddle" alt="\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}" class="latex-formula" id="TexFormula1" SRC="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Chuge%7B%5Cgray%7B%5Ctt%7B%5Ctextbf%20Answer%20%3A-%7D%7D%7D%7D%7D" title="\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}"> ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Motorboat covers a distance of 16km upstream and 24km downstream in 6 hours In the same time it covers a distance of 12 km upstream and 36km downstream ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ The speed of the boat in still WATER The speed of STREAM ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Let the speed of boat in still water be 'B' Let the speed of stream be 'W' ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\underline{\purple{ \underline{\orange{\bold{\texttt{Speed in upstream :}}}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ B - W ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\underline{\purple{ \underline{\orange{\bold{\texttt{Speed in downstream :}}}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ B + W ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\rm{ \large{\pink{\underline\blue{Case \: I :}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ *We know that ,* ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf T = \dfrac { D } { S }$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Where , ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ T = Time TAKEN D = Distance travelled S = Speed ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Time taken in upstream ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ $\sf T_1 = \dfrac { 16} { B - W}$ ⚊⚊⚊⚊ ⓵ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Time taken in downstream ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ $\sf T_2 = \dfrac { 24} { B + W}$ ⚊⚊⚊⚊ ⓶ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ *Given that , Motorboat covers a distance of 16km upstream and 24km downstream in 6 hours* ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf T_1 + T_2 = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ From equation ⓵ & ⓶ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf \dfrac { 16} { B - W} + \dfrac { 24} { B + W} = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf \dfrac { 16(B + W) + 24(B - W)} { (B - W)(B + W)} = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf \dfrac { 16(B + W) + 24(B - W)} { B^2 - W^2 } = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 16B + 16W + 24B - 24W = 6B² - 6W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 40B - 8W = 6B² - 6W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 20B - 4W = 3B² - 3W² ⚊⚊⚊⚊ ⓷ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\rm{ \large{\pink{\underline\blue{Case \: II :}}}}$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ *We know that ,* ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ $\sf T = \dfrac { D } { S }$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Where , ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ T = Time taken D = Distance travelled S = Speed ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Time taken in upstream ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ $\sf T_3 = \dfrac { 12} { B - W}$ ⚊⚊⚊⚊ ⓸ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Time taken in downstream ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ➠ $\sf T_4 = \dfrac { 36} { B + W}$ ⚊⚊⚊⚊ ⓹ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ *Given that , Motorboat covers a distance of 12km upstream and 36km downstream in 6 hours* ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf T_3 + T_4 = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ From equation ⓸ & ⓹ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf \dfrac { 12} { B - W} + \dfrac { 36} { B + W} = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf \dfrac { 12(B + W) + 36(B - W)} { (B - W)(B + W)} = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ $\sf \dfrac { 12(B + W) + 36(B - W)} { B^2 - W^2 } = 6$ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 12B + 12W + 36B - 36W = 6B² - 6W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 48B - 24W = 6B² - 6W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 24B - 12W = 3B² - 3W² ⚊⚊⚊⚊ ⓺ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Clearly equation ⓷ = ⓺ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ So, ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 20B - 4W = 24B - 12W ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 12W - 4W = 24B - 20B ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 8W = 4B ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 2W = B ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ B = 2W ⚊⚊⚊⚊ ⓻ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ⟮ Putting B = 2W from ⓻ to ⓷ ⟯ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 20B - 4W = 3B² - 3W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 20(2W) - 4W = 3(2W)² - 3W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 40W - 4W = 12W² - 3W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 36W = 9W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 4W = W² ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ 4 = W ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : : ➨ W = 4 ⚊⚊⚊⚊ ⓼ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Hence the speed of stream is 4 km/hour ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ⟮ Putting W = 4 from ⓼ to ⓻ ⟯ ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ B = 2W ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : ➜ B = 2(4) ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ : : ➨ B = 8 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ Hence the speed of Boat in still water is 8 km/hour ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ ∴ The speed of Boat and stream are 8 km/hr & 4 km/hr respectively

43.

A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and36km downstream. Find the speed of the boat in still water and that of thestream.

Answer»

align="absmiddle" alt="\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}" class="latex-formula" id="TexFormula1" SRC="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Chuge%7B%5Cgray%7B%5Ctt%7B%5Ctextbf%20Answer%20%3A-%7D%7D%7D%7D%7D" title="\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}">

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Motorboat covers a distance of 16km upstream and 24km downstream in 6 hours
In the same time it covers a distance of 12 km upstream and 36km downstream

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

The speed of the boat in still WATER
The speed of STREAM

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Let the speed of boat in still water be 'B'
Let the speed of stream be 'W'

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\underline{\purple{ \underline{\orange{\bold{\texttt{Speed in upstream :}}}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

➠ B - W

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\underline{\purple{ \underline{\orange{\bold{\texttt{Speed in downstream :}}}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

➠ B + W

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\rm{ \large{\pink{\underline\blue{Case \: I :}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

We know that ,

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf T = \dfrac { D } { S }$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Where ,

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

T = Time TAKEN
D = Distance travelled
S = Speed

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Time taken in upstream

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

➠ $\sf T_1 = \dfrac { 16} { B - W}$ ⚊⚊⚊⚊ ⓵

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Time taken in downstream

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

➠ $\sf T_2 = \dfrac { 24} { B + W}$ ⚊⚊⚊⚊ ⓶

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Given that , Motorboat covers a distance of 16km upstream and 24km downstream in 6 hours

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf T_1 + T_2 = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

From equation ⓵ & ⓶

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf \dfrac { 16} { B - W} + \dfrac { 24} { B + W} = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf \dfrac { 16(B + W) + 24(B - W)} { (B - W)(B + W)} = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf \dfrac { 16(B + W) + 24(B - W)} { B^2 - W^2 } = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 16B + 16W + 24B - 24W = 6B² - 6W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 40B - 8W = 6B² - 6W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 20B - 4W = 3B² - 3W² ⚊⚊⚊⚊ ⓷

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\rm{ \large{\pink{\underline\blue{Case \: II :}}}}$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

We know that ,

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

$\sf T = \dfrac { D } { S }$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Where ,

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

T = Time taken
D = Distance travelled
S = Speed

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Time taken in upstream

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

➠ $\sf T_3 = \dfrac { 12} { B - W}$ ⚊⚊⚊⚊ ⓸

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Time taken in downstream

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

➠ $\sf T_4 = \dfrac { 36} { B + W}$ ⚊⚊⚊⚊ ⓹

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Given that , Motorboat covers a distance of 12km upstream and 36km downstream in 6 hours

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf T_3 + T_4 = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

From equation ⓸ & ⓹

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf \dfrac { 12} { B - W} + \dfrac { 36} { B + W} = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf \dfrac { 12(B + W) + 36(B - W)} { (B - W)(B + W)} = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ $\sf \dfrac { 12(B + W) + 36(B - W)} { B^2 - W^2 } = 6$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 12B + 12W + 36B - 36W = 6B² - 6W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 48B - 24W = 6B² - 6W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 24B - 12W = 3B² - 3W² ⚊⚊⚊⚊ ⓺

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Clearly equation ⓷ = ⓺

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

So,

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 20B - 4W = 24B - 12W

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 12W - 4W = 24B - 20B

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 8W = 4B

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 2W = B

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ B = 2W ⚊⚊⚊⚊ ⓻

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

⟮ Putting B = 2W from ⓻ to ⓷ ⟯

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 20B - 4W = 3B² - 3W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 20(2W) - 4W = 3(2W)² - 3W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 40W - 4W = 12W² - 3W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 36W = 9W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 4W = W²

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ 4 = W

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: : ➨ W = 4 ⚊⚊⚊⚊ ⓼

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Hence the speed of stream is 4 km/hour

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

⟮ Putting W = 4 from ⓼ to ⓻ ⟯

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ B = 2W

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: ➜ B = 2(4)

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

: : ➨ B = 8

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Hence the speed of Boat in still water is 8 km/hour

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

∴ The speed of Boat and stream are 8 km/hr & 4 km/hr respectively

Discussion

44.	(iv) তিনটি নিরেট ঘনক যাদের প্রত্যেকটি ধারের দৈর্ঘ্য যথাক্রমে 3 সেমি., 4 সেমি. এবং 5 সেমি.। ঘনক তিনটিকে গলিয়ে একটি নতুন নিরেট ঘনক তৈরি করা হলাে। নতুন ঘনকটির একটি ধারের দৈর্ঘ্যকত হবে তা লিখি।
Answer» ONG>Answer: Mitochondria are membrane-bound cell organelles (mitochondrion, SINGULAR) that generate most of the chemical ENERGY needed to power the cell's biochemical reactions. Chemical energy produced by the mitochondria is stored in a small molecule CALLED ADENOSINE triphosphate (ATP).

44.

(iv) তিনটি নিরেট ঘনক যাদের প্রত্যেকটি ধারের দৈর্ঘ্য যথাক্রমে 3 সেমি., 4 সেমি. এবং 5 সেমি.। ঘনক তিনটিকে গলিয়ে একটি নতুন নিরেট ঘনক তৈরি করা হলাে। নতুন ঘনকটির একটি ধারের দৈর্ঘ্যকত হবে তা লিখি।

Answer» ONG>Answer:

Mitochondria are membrane-bound cell organelles (mitochondrion, SINGULAR) that generate most of the chemical ENERGY needed to power the cell's biochemical reactions. Chemical energy produced by the mitochondria is stored in a small molecule CALLED ADENOSINE triphosphate (ATP).

Discussion

45.	3²×4³=12⁶Please answer
Answer» ONG>ANSWER: your answer is in the attachment Hope this HELPS you :)

45.

3²×4³=12⁶Please answer

Answer» ONG>ANSWER:

your answer is in the attachment

Hope this HELPS you :)

Discussion

46.	4) The radius of a circle is 15cm. The distance ofcentre O from M; theBmidpoint of chord AB isM9 cm. Find the length ofAchord AB
Answer» ong>Step-by-step explanation: is KE jesa he ye kar lena The radius of a circle is GIVEN as 15 cm and chord AB subtends an ANGLE of 131 ∘ at the centre C of the circle.Using TRIGONOMETRY ,calculate : (i) the length of AB ; (ii) the distance of AB from the centre C 1111888 Answer Open in answr app Given r=15 ∠AOB=13.1 AB=x AC=CB= 2 x ∠AOC=65.5 o sin65.5= 2×15 x As sin65.5=0.909 x=0.909×30=27.27 ∴ length of AB=27.27 OC=cos65−5×15 =0.414×15 OC=6.21cm ∴ length of chord AB=27.27cm distance between centre and the chord is 6.21 cm.

46.

4) The radius of a circle is 15cm. The distance ofcentre O from M; theBmidpoint of chord AB isM9 cm. Find the length ofAchord AB

Answer»

ong>Step-by-step explanation:

is KE jesa he ye kar lena

The radius of a circle is GIVEN as 15 cm and chord AB subtends an ANGLE of 131

∘

at the centre C of the circle.Using TRIGONOMETRY ,calculate :

(i) the length of AB ;

(ii) the distance of AB from the centre C

1111888

Answer

Open in answr app

Given r=15

∠AOB=13.1

AB=x

AC=CB=

2

x

∠AOC=65.5

o

sin65.5=

2×15

x

As sin65.5=0.909

x=0.909×30=27.27

∴ length of AB=27.27

OC=cos65−5×15

=0.414×15

OC=6.21cm

∴ length of chord AB=27.27cm

distance between centre and the chord is 6.21 cm.

Discussion

47.	Simplyfy this fastt please
Answer» ong>Answer: 8/30 Step-by-step explanation: we will TAKE out COMMON factors and we will get 8/30 if you LIKED my explanation PLS mark me as the BRAINLIEST

47.

Simplyfy this fastt please

Answer»

ong>Answer:

8/30

Step-by-step explanation:

we will TAKE out COMMON factors and we will get 8/30

if you LIKED my explanation PLS mark me as the BRAINLIEST

Discussion

48.	The area of a circle of diameter d is:
Answer» ong>ANSWER: Area of Circle Formula Suppose a circle has a RADIUS 'r' then the area of circle = πr2 or πd2/4 in SQUARE units, where π = 22/7 or 3.14, and d is the diameter. Area of circle can be calculated by USING the formulas: Area = π x r2, where 'r' is the radius.

48.

The area of a circle of diameter d is:

Answer»

ong>ANSWER:

Area of Circle Formula

Suppose a circle has a RADIUS 'r' then the area of circle = πr2 or πd2/4 in SQUARE units, where π = 22/7 or 3.14, and d is the diameter. Area of circle can be calculated by USING the formulas: Area = π x r2, where 'r' is the radius.

Discussion

49.	India celebrated its. 60th year of independence
Answer» ONG>ANSWER: what we have to do in this QUESTION?

Discussion

50.	4. Draw AB of length 7cm and find its axis of symmetry.
Answer» ONG>Answer: sorry I can't KNOW the answer

Discussion

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