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9, 25, 31, 32, 33, 48, 5132 is the median

no this is not possible how do this? this is wrong

the answer would be 1458/625

the answer is 1458/625

the correct answer is 1458/625

cos6x=cos[2(3x)]=2cos^2(3x)-1 cos2x=2cos^2x-1

=2[cos(3x)]^2-1 cos3x=4cos^3x-3cosx

=2[4cos^3x-3cosx]^2-1 (a-b)^2=a^2+b^2-2ab

=2[16cos^6x+9cos^2x-24cos^4x]-1

=32cos^6x-48cos^4x+18cos^2x-1

extend the line EF and let it meet CD at Hthen in triangle FGH<FHG=180-p<GFH=180-q<FGH=rsum of angles in triangle is 180so,<FHG+<GFH+<FGH=180180-p+180-q+r=180p+q-r=180

The playfair axiom states that In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.

Axioms or Postulate is defined as a statement that is accepted as true and correct.Ex : Examples of axioms can be 2+2=4, 3 x 3=4 etc. In geometry, we have a similar statement that a line can extend to infinity. This is an Axiom because you do not need a proof to state its truth as it is evident in itself.

start with the 90 degree right angle JKL. If we continue to bend JK all the way down to a straight line, that would be twice of 90, or 180.

Continue bending JK all the way back to KL, and you have a complete circle, 360 degrees.

Now, why is there such an odd number as 360 degrees in a circle? Basically, because it was observed thousands of years ago (about 2400 BC) that it takes 360 days for the Sun to make one complete yearly cycle. A thousand years later, the Egyptians divided each day into 24 hours, and another thousand or so years later the Babylonians subdivided the hour into 60 minutes and the minutes into 60 seconds.

Obviously we know now that it actually takes 365 1/4 days for the earth to revolve around the sun. But I'm perfectly happy without 365 1/4 degrees in a circle.

As this graph is cutting the x axis 4 times so 4 zeroes are there

Which question?

4

Given : x + y = w + zTo prove : POQ is a line.Proof : We know that;x + y + w + z = 360०then, x + y + x + y = 360०(given)2x + 2y =360०2 (x + y) =360०x + y = 180०(linear pair)Therefore, POQ is a line. Hence, Proved!

4&5 solve

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An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma 'that which is thought worthy or fit' or 'that which commends itself as evident.

In geometry,Playfair's axiomis anaxiomthat can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.

TheCorresponding AnglesPostulatestatesthat, when two parallel lines are cut by a transversal , the resultingcorresponding anglesare congruent . The converse is also true; that is, if two lines and are cut by a transversal in such a way that thecorresponding anglesformed are congruent , then l ∥ m .

(5×5)+2-(14÷901)+(4000×1)=25+2-(0.0155)+4000=4026.98

good

Suppose we need to add X litres of alcohol to the solution.

So, overall quantity of alcohol = X + 20 litres.

But adding the alcohol increases volume of the solution also.So, total volume of solution = 60 + X

So, we have the following equation: X+20/(X+60) = 50/100=> 2X + 40 = X + 60=> X = 20 LTherefore, to get a solution of 50% alcohol, we need to add 20 L of alcohol.

20 l of alcohol is needed to get 50% solutions

20l of alcohol........

20 litre is right answer....

1) 52)83)04)n5)5(since it is 2+3)

thanks but can it be done with method

U need to find highest power term in an expressionIf the term contains more than one variable u need to add their powers to get their degree(like in 5th part)

Using Euler's formula

V - E + F = 2

where V is the number of vertices, E is the number of edges and F is the number of faces.

Given, V = 8 and F = 10 so the equation becomes

8 - E + 10= 2

18 - E = 2

E = 16

So number of edges in polyhedron are 16

f+v=e+2

10+8=e+218=e+2

e=18-2e=16

ii. is the correct answer

(i) If θ be the principal value of sin^−1 x then - π/2 ≤ θ ≤ π/2.

Therefore, If the principal value of sin^−1(-1/2) be θ then sin^−1(-1/2) = θ

⇒ sin θ = - 1/2 = sin (-π/6) [Since, - π/2 ≤ θ ≤ π/2]

Therefore, the principal value of sin^−1(-1/2) is (-π/6).

(ii) If the principal value of cos^−1 x is θ then we know, 0 ≤ θ ≤ π.

Therefore, If the principal value of cos^−1(- √3/2) be θ then cos^−1(- √3/2) = θ

⇒ cos θ = (- √3/2) = cos π/6 = cos (π - π/6) [Since, 0 ≤ θ ≤ π]

Therefore, the principal value of cos^−1(- √3/2) is π - π/6 = 5π/6.

I didn't understand first principal explain plz

Derivative by first principlerefers to using algebra to find a general expression for the slope of a curve. It is also known as the delta method. The derivative is a measure of the instantaneous rate of change, which is equal to

This expression is the foundation for the rest of differential calculus: every rule, identity, and fact, follows from this.

expression is which I have used in solving question

and what a function denote foe

what is use of h and x

which function.......

x is variable and h is limit for which we are solving

yes

thnx

what is limit

limit is h tending to zero

can u differentiate sin x by your method or easy and simple way

By first principle if f[x]=tanx

F'[x]= f[x+h]-f[x]/x+h-x at Lth tends to 0

F'(x) = tan(x+h)-tanx/h

By simple trigonometry

tan(x+h)=tanx+tanh/1-tanxtanh

Thus,

f'(x) =

tanx+tanh-tanx+tan^2xtanh/(1-tanxtanh) h

=tanh(1+tan^2x)/(1-tanxtanh) h

But Lt (tanx)/x. =1, 1+tan^2x=sec^2x

h~0

Hence f'(x) =sec^2x(1)/(1-tanxtanh)

= sec^2x

Thanks