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Given that x=ln(t) and y=4t^3,a) find an expression for dy/dx, b)and the value of t when d2y/dx2 =0.48. Give your answer to 2 decimal place.

a) Firstly, differentiate x and y with respect to t. 

Giving you dx/dt = 1/t       and dy/dt = 12t2

dy/dx is found using the chain rule:

dy/dx = dy/dt x dt/dx = 12t3

SW
Answered by Sara W. Maths tutor
3468 Views

solve the inequality 5x + 3> 3x - 6

5x +3 > 3x -6 2x +3 > -6 (-3x from both sides) 2x > -9 (-3 from both sides) x > -4.5 (divide by two on both sides)

AL
Answered by Anna L. Maths tutor
4751 Views

Calculate the gradient of the function y=x^2+6x when y=-9

-9=x^2+6x

0=x^2+6x+9

0=(x+3)(x+3)

when y=-9 x=3

dy/dx=2x+6

dy/dx=2(3)+6=12

HM
Answered by Hassan M. Maths tutor
5171 Views

Solve the following equation; 8x-2 > 4x +6

First of all we need to get all of the x's on one side and all the numbers on the other side. Therefore to do this firstly we should add 2 to both sides. 8x > 4x +8 Secondly we need to -4x from both si...

RD
Answered by Rory D. Maths tutor
5062 Views

What is 25% of 400?

25% = 0.25 or also one fourth of the total. Therefore if you divide 400 by 4, this equals 100. One fourth of 400 is 100. 

MM
Answered by Michelle M. Maths tutor
14116 Views

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