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G(x)=x^3 + 1, h(x)=3^x; solve G(h(a))=244

First combine the two functions so that we have an equation for a to solve: G(h(a)) = (3^x)^3 + 1 = 3^(3x) + 1 = 244 which gives 3^(3x) = 243 Now we can use logarithms in order to solve the equation log(3^(3...
JS
Answered by Josephine S. • Maths tutor
4950 Views

What does the term terminal velocity mean?

Terminal velocity is the constant speed (in a particular direction) a body reaches when the forces are balanced , i.e. acceleration = 0 m s -2 . An example of this is a ball bearing dropped in oil. ⬆ Resista...
DD
Answered by Daisy D. • Physics tutor
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A right-angled triangle has base 7cm and height 6cm. Find it's area.

Using the equation Area = 1/2 * base * height: Area = 1/2 * 7 * 6 Area = 21 units.
SB
Answered by Samuel B. • Maths tutor
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Find the tangent to the curve y = x^2 + 3x + 2 at x = 1

First, we differentiate y = x^2 + 3x + 2 to find the slope of the curve at any given x point: dy/dx = 2x + 3 So at x = 1, dy/dx = 2 + 3 = 5 We know that straight lines come in the form y = mx + c, and in thi...
SB
Answered by Samuel B. • Maths tutor
10460 Views

Differentiate: y = sin(2x).

Using the chain rule with u = 2x: y = sin(2x) becomes y = sin(u) dy/dx = dy/du * du/dx dy/du = cos(u) du/dx = 2 So dy/dx = dy/du * du/dx = 2 cos(u).
SB
Answered by Samuel B. • Maths tutor
19926 Views