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Distance covered= Perimeter of the track =80 m + π (14)m +80 m + π(14)m =80 m +44 m +80 m + 44 m =248 m

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Solution:-

1)To find mean proportion between 12 and 3we will multiply both12*3= 36 =√36= 6 will be the answer

2)

√50*8√40020 will be the mean proportion between 50and 8

Let the required no. be a and b.Therefore,14 is the mean proportional between a and b.a:14=14:bab= 196. eqn....1and, 112 is third proportional to a and ba:b=b:112b square=112 a. eqn....2From eqn.1;. ab=196. a=196/bsubstituting a =196/b in eqn ...2, we get:b square= 112*196/bb cube=112*196 and, b = 28therefore. a=196/b196/28. = 7therefore the required numbers are 28 and 7

Take any chord in a circle, say with endpoints AB. Let O be the center of the circle. Then segments AO and BO are radii of the circle. AOB is a triangle, and we know that the sum of the lengths of two sides of a triangle is always greater than or equal to the length of the third side. So:

|AB| ≤ |AO| + |BO|

(Here |AB| means length of AB.) Now the length of a diameter is twice the length of a radius, which is precisely equal to the quantity |AO| + |BO|.

Let x be the mean proportional. Then, 121/x = x/100=> x*x = 12100=> x = 110

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oh I got my mistake I was using a2c2 instead of acThnx bro

ratio of length : breath = 7 : 6 L 7--- = -----12 6so L = (12× 7)/6 = 14

We have to solve these equations(2,5)×(x,-3)= 2x- 6 + 5x -15=0 => 7x - 21 = 0 => x= 3

given equations are :

ax + by = 7..........(1)

bx + ay = 5 .........(2)

according to question, (3,1) is the point of intersection of given equations.

so, (3,1) will satisfy both of given equations.

put (3,1) in equation (1),

3a + b = 7 ........(3)

put (3,1) in equation (2),

3b + a = 5......... (4)

multiplying 3 with equation (3) and then subtracting equation (4),

3(3a + b) - (3b + a) = 3 × 7 - 5

9a + 3b - 3b - a = 21 - 5

8a = 16 => a = 2 , put it in equation (3)

b = 7 - 3a = 7 - 6 = 1

hence, a = 2 and b = 1

ax³ + 3x² - bx - 6

x = -1 , -2

put the values of x in Equation

we get,

a(-1)³ + 3(-1)² - b(-1) - 6 = 0

=> -a + 3 + b - 6 = 0

=> b - a = 3--------(1)

now x = - 2

a(- 2)³ + 3(-2)² - b(-2) - 6 = 0

=> -8a + 12 + 2b - 6 = 0

=> 2b - 8a + 6 = 0

=> b - 4a = -3--------(2)

from--(1) and -----(2)

b - a = 3b - 4a = -3(-)___(+)__(+)———————3a = 6

=> a = 2 put in --(1)

b - 3 = 2

=> b = 5 now put this value in Equation

ax³ + 3x² - bx - 6 = 0

=> 2x³ + 3x² - 5x - 6 = 0

two zeroes are given (-1 , -2)

(x + 1)(x + 2) = x² + 2x + x + 2 = 0

=> x² + 3x + 2 =0

x² + 3x + 2)2x³ + 3x² - 5x - 6(2x - 32x³ + 6x² + 4x- - -—————————-3x² - 9x - 6-3x² - 9x - 6+ + +—————————0 0 0

hence another zeroes is

2x - 3 = 0

=> x = 3/2

ax³ + 3x² - bx - 6

x = -1 , -2

put the values of x in Equation

we get,

a(-1)³ + 3(-1)² - b(-1) - 6 = 0

=> -a + 3 + b - 6 = 0

=> b - a = 3--------(1)

now x = - 2

a(- 2)³ + 3(-2)² - b(-2) - 6 = 0

=> -8a + 12 + 2b - 6 = 0

=> 2b - 8a + 6 = 0

=> b - 4a = -3--------(2)

from--(1) and -----(2)

b - a = 3b - 4a = -3(-)___(+)__(+)———————3a = 6

=> a = 2 put in --(1)

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b - 3 = 2

=> b = 5 now put this value in Equation

ax³ + 3x² - bx - 6 = 0

=> 2x³ + 3x² - 5x - 6 = 0

two zeroes are given (-1 , -2)

(x + 1)(x + 2) = x² + 2x + x + 2 = 0

=> x² + 3x + 2 =0

x² + 3x + 2)2x³ + 3x² - 5x - 6(2x - 32x³ + 6x² + 4x- - -—————————-3x² - 9x - 6-3x² - 9x - 6+ + +—————————0 0 0

hence another zeroes is

2x - 3 = 0

=> x = 3/2

x²+ 144=0x²=-144x=-√144x=+-12

you take x=1and ans is 6

answer is (-4x-1)(3x-1)

your question anwer is 18x

(4x-1)(3x-1) is the correct answer of the given question

1) x-2=7 x=2+7 x=94) (3/7)+x=(17/7) x=(17/7)-(3/7) x=14/7=27) 2x/3=182x=3×18x=3×9=27

1. 6+9 = 15

2 10+9 = 19

3. 10-6 = 4

4. 10-9 = 1

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x²=144x=✓144x=1212 is the right answer

999 answer of first question,1000 answer of second question.

1st answer=999 is right answer

(122/144)×100=(61/72)×100=6100/72=1525/18=84.7222

given,

a = xyp-1, b = xyq-1and c = xyr-1 here, x is first term and y is common ratio

as, G²= AH we ahve,

b²=ac

xyq-1

aq-r= xq-r* y(p-1)(q-r)

br-p = xr-p* y(q-1)(r-p)

cp-q= xp-q* y(p-q)(r-1)

multiply all 3 of them, we get RHS,

x⁰* y⁰= 1

henc proved.

Let one angle is x and other is 90-x Because they are complementary.

Difference is 10

x-(90-x)=10x-90+x=102x=100x=50

Other angle is 90-50=40

Larger angle is 50°

thanks

36*4/1= 36*4 = 144/1 nswers

Given division is 36 ÷ ¼ = 144.

5x-y-50=0*5Or 5x-y-50=0