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Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.

In order to find the equation of the tangent to a curve at a point (x 1 , y 1 ), we use the equation y - y 1 = m(x - x 1 ), where m is the gradient of the curve at (x 1 , y 1 ). We already have x 1 = √3, so ...
BC
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log8(5) = b. Express log4(10) in terms of b

log 8 5=b using the base change rule log 8 5 = log 4 5/ log 4 8 log 4 8 can be solved: log 4 8 =x 4 x =8 2 2x = 2 3 2x=3 x= 3/ 2 Therefore we can write: log 8 5 = log 4 5/( 3/ 2) =b log 4 5 =( 3/ 2) b [1] To...
BM
Answered by Beatrice M. • Maths tutor
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Let f(x) = x * sin(2x). Find the area beneath the graph of y = f(x), bounded by the x-axis, the y-axis and the line x = π/2.

After short consideration, we see that we must integrate f(x) with respect to x, between 0 and π/2, using integration by parts. Taking the formula for integration by parts, we set u = x and dv/dx = sin(2x). ...
BC
Answered by Benjamin C. • Maths tutor
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Is there a difference between Law and Morality?

This question points to the clash between legal positivism and natural law theory. It can be interpreted in two different ways. The first interpretation would consider whether there is a requirement that all...
MS
Answered by Mohamed S. • LNAT tutor
5414 Views

How do I conjugate regular verbs in the present tense?

There are 3 types of regular verb in French ; verbs ending in -er , verbs ending in -ir , and verbs ending in -re . They each have their own set pattern when it comes to conjugating them in the present tense...
IW
Answered by Isabelle W. • French tutor
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