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Let y=arcsin(x-1), 0<=x<=2 (where <= means less than or equal to). Find x in terms of y, and show that dx/dy=cos(y).

First, the question asks us to find x in terms of y, or in other words, rearrange the equation to be in the form ' x= ' , rather than ' y= ', as it is currently. We start with y=acrsin(x-1) , as given in the...
KM
Answered by Kalina M. • Maths tutor
7910 Views

The line l is a tangent to the circle x^2 + y^2 = 40 at the point A. A is the point (2, 6). The line l crosses the x-axis at the point P. Work out the area of triangle OAP.

This will involve drawing a diagram to aid your answer. Where O is the origin, A is a point on the circle and P is a point on the x-axis. OA is the radius of the circle. Line l crosses through point A and me...
TD
Answered by Tutor51285 D. • Maths tutor
34159 Views

A ball is thrown vertically upwards with a speed of 24.5m/s. For how long is the ball higher than 29.4m above its initial position? Take acceleration due to gravity to be 9.8m/s^2.

To find how much time the ball spends above 29.4m, we need to find the times at which the ball is at 29.4m above its starting point, and then calculate the difference between these times. Acceleration is con...
SB
Answered by Sherry B. • Maths tutor
12564 Views

What is the difference between permutations and combinations?

The main difference is that order of objects matters for permutations. Both involve choosing k objects from a group of size n. Permutations are used to calculate the amount of possible ways a group can be ma...
OP
Answered by Oliver P. • Maths tutor
5154 Views

F ind all values of x in the range 0° <= x <= 180° satisfying tan(x+45°)= 8tan(x)

tan(x)+tan(45)/1-tan(x)tan(45) = 8tan(x) 8tan 2 (x)-7tan(x)+1=0 tan(x)=0.6952 or 0.1798 x = arctan(0.6952) = 34.8070 deg and arctan(0.1798) = 10.1932 deg
TM
Answered by Tomos M. • Maths tutor
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