Top answers

A spherical balloon of radius r cm has volume Vcm^3 , where V =4/3 * pi * r^3. The balloon is inflated at a constant rate of 10 cm^3 s^-1 . Find the rate of increase of r when r = 8.

We are being asked to find the rate of change of radius, dr/dt. We will need to use the chain rule to do this: dV/dt = dV/dr * dr/dt. We are given that dV/dt is 10cm^3 per second, and differentiating V = 4/3...
MA
Answered by Max A. • Maths tutor
14406 Views

Find the roots of y=x^{2}+2x+2

y=x 2 +2x-3 Can solve using quadratic equation. Using the square method to obtain for the square term and x term (x+1)(x+1) = x 2 +2x+1 Therefore (x+1)(x+1)-4=y To find roots equate to zero: (x+1)(x+1)-4=0 T...
HS
Answered by Harry S. • Maths tutor
6913 Views

How do you intergrate a function?

Increase the powers of all variables by one and then divide them by this number. For example, given 3x^3 + 5x^-0.5 - 8 , this would give 3/4x^4 + 10x^0.5 - 8x
DC
Answered by David C. • Maths tutor
3794 Views

given that angles A and B are such that, sec^2A-tanA = 13 and sinBsec^2B=27cosBcosec^2B

First of all key elements required for this question is the knowledge or retrival of these equations: tan 2 + 1 =sec 2 A tan(A-B) = (tanA-tanB)/(1+tanAtanB) so for the first equation sec 2 A - tanA =13 we su...
JM
Answered by Joshua M. • Maths tutor
11675 Views

Given that y=((4x+1)^3)sin2x. Find dy/dx.

To answer this we will need to use the product rule which is as follows: For y=uv , dy/dx=u'v+uv' where u' is the derivative of u and v' is the derivative of v. In this case, u= (4x+1)^3 and v= sin2x . u'= 3...
BG
Answered by Benjamin G. • Maths tutor
3762 Views