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Given that w=x * e^-w use implicit differentiation to show that dw/dx=1/(e^w + x)

Given that w=xe-w use implicit differentiation to show that dw/dx = 1/(ew+x)Answer:Use product rule to simplify:dw/dx = x(de-w/dx) + e-w(dx/dx)Use ...

Answered by Panagiota G. Maths tutor
1347 Views

The perimeter of a right angled triangle is 72cm. The length of its sides are in the ratio 3:4:5. Work out the area of the triangle.

Total perimeter - 72cm. Perimeter - (3+4+5)x -> 72=12x therefore x=6. The area of the triangle is 0.5(3x4x) (because 5x is the longest side) therefore the answer is 0.5(1824) = 216cm^2

Answered by Sam T. Maths tutor
2460 Views

Without expanding any brackets work out the exact solutions of 9(x+3)^2=4

Divide through by 9 giving:(x+3)2 = 4/9 Square root both sides remembering a square root is plus or minus the answer x+3 = +/-sqrt(4/9) sqrt(4/9)=2/3for the first solution x+3 = 2/3 or x = -7/3...

Answered by Thomas B. Maths tutor
11094 Views

A ball is thrown in the air. The height of the ball at time t is given by: h=5+4t-2t^2. What is its maximum height? At what time does the ball reach this height?

First, we find the derivative of h: dh/dt= 4-4t. To find the point(s) of interest, we solve dh/dt=0. This gives the answer t=1. In order to determine whether t=1 is a minimum point or maximum point we fin...

Answered by Debbie S. Maths tutor
3825 Views

Expand the brackets: (3a+3)(a+4)

To expand this, we must multiply each term in both brackets separately and then add all of these terms together. First, multiply the first term in each of the brackets: 3a x a = 3a^2. Next multiply the fi...

Answered by Luke B. Maths tutor
3204 Views

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