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theta = arctan(5x/2). Using implicit differentiation, find d theta/dx.

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec2(θ)dθ/dx = 5 Use identity sin2(θ) + cos2(θ) = 1, dividing through by cos

CW
Answered by Callum W. • Maths tutor
3869 Views

Bob sprints down a 100 metre track as fast as he can and as he arrives at the finish, a light gate cuts a timer that has been active since Bob began his sprint. It reads 12.45 seconds. calculate Bobs average speed during the sprint.

s=distance/time = 100/12.45 =8.03m/s

RW
Answered by Richard W. • Maths tutor
2427 Views

f(x) = x^3 + 3x^2 + 5. Find f'(x) and f''(x).

With differentitaion you multiply the fatcor it's raised by and minus one from the order

e.g. y = x^n so y' = nx^(n-1)

So f'(x) = 3x^2 + 6x and f''(x) = 6x + 6

NS
Answered by Nikita S. • Maths tutor
8999 Views

Solve the equation (2x + 3 / x - 4) - (2x - 8 / 2x + 1) = 1

     Solve the equation  (2x + 3 / x - 4) - (2x - 8 / 2x + 1) = 1 

Answer

To start off, we must find the common denominator between the two fractions.

When dealing with complex...

JB
Answered by Jonathan B. • Maths tutor
10838 Views

What is the equation of the tangent to the circle (x-5)^2+(y-3)^2=9 at the points of intersection of the circle with the line 2x-y-1=0

Teh points of intersection can be found by subbing in y=2x-1 to the equation of the circle. (x-5)2+(2x-1-3)2=5x2-26x+33=9 so we have 5x2-26x+24=0. Solving the q...

TD
Answered by Tutor67416 D. • Maths tutor
2863 Views

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