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Find tan(A-B) sec^2(A) - 2tan(A) = 16 && sin(B)sec^2(B) = 64cos(B)cosec^2(B)

@tan(A) = 5, tan(B) =4, tan(A - B) = 1/21

@tan(A) = -3, tan(B) = 4, tan(A - B) = 7/11

I can demonstrate how the answers can be obtained during the session.

Answered by Fedor S. • Maths tutor

2815 Views

Differentiate with respect to x y=(x^3)ln2x

To be able to differentiate this we need to use the product rule as we want to differentiate two functions multiplied together. The product rule states that if y=uv, then : dy/dx= u dv/dx + v du/dx. Let u...

Answered by Jennifer P. • Maths tutor

11248 Views

The number of bacteria present in a culture at time t hours is modeled by the continuous variable N and the relationship N = 2000e^kt, where k is a constant. Given that when t = 3, N = 18 000, find (a) the value of k to 3 significant figures

putting in the conditions: 18000 = 2000e^3k .. ln(9) = 3k .. k=(1/3)ln(9)

Answered by Benjamin C. • Maths tutor

4525 Views

A circle has the equation x^2 + y^2 - 4x + 10y - 115 = 0. Express the equation in the form (x - a)^2 + (y - b)^2 = k, and find the centre and radius of the circle.

Rearrange the equation so that the x terms and y terms bracketed together, like so: (x^2 - 4x) + (y^2 + 10y) - 115 = 0. Complete the square on both sets of brackets, giving (x - 2)^2 - 4 + (y + 5)^2 - 25 ...

Answered by Joseph B. • Maths tutor

3318 Views

Find the indefinite integral of ( 32/(x^3) + bx) over x for some constant b.

To integrate (32/ x³ + bx) over x we can integrate each part separately. This is because addition of two integrals is the same as integrating the total of the elements.

So we integrate ...

Answered by Becky O. • Maths tutor

2669 Views