Top answers

Solve the equation 2ln2x = 1 + ln3. Give your answer correct to 2dp.

LHS: because alnx = lnx a , 2ln2x = ln(2x) 2 = ln4x 2 Now, because ln and e are inverse functions, we take both sides to the power of e. Therefore: e ln4x^2 = e 1 + ln3 4x 2 = e 1 + ln3 x 2 = (e 1 + ln3 ) / ...
SS
Answered by Shiv S. • Maths tutor
5289 Views

The number of uniform spherical balls that can be produced from a given mass of lead is inversely proportional to the radius of the ball cubed. If 2744 balls can be made when the radius is 1mm, how many balls can be made when the radius is 1.4mm ?

So first we need to write down the proportionality relationship the question states. If we let n be the number of balls and r be the radius of the balls we can say n (proportional symbol) 1/r 3 . We can turn...
TC
Answered by Tabraiz C. • Maths tutor
3699 Views

Integrate ⌠( xcos^2(x))dx

We must first use trigonometric identities to simplify cos 2 (x). We can use the formula cos(A+B) = cos(A)cos(B) - sin(A)sin(B) , where A=x and B=x , so that we get cos(2x) = cos 2 (x) - sin 2 (x) = 2cos 2 (...
DA
Answered by Daniel A. • Maths tutor
11120 Views

A curve C has equation y = (2 - x)(1 + x) + 3 . A line passes through the point (2, 3) and the point on C with x-coordinate 2 + h . Find the gradient of the line, giving your answer in its simplest form.

First we find the y coordinate which is a function of x: x = 2+ h so y = (2 - 2 - h)(1 + 2 + h) + 3 = -h 2 - 3h + 3 Now for the gradient, the line passes through points (2,3) and (2 + h, -h 2 - 3h + 3) dx = ...
RS
Answered by Ricardo S. • Maths tutor
4821 Views

Solve 4x - 6 < 2x + 5

4x - 6 &lt; 2x + 5 is an inequality. It means &quot;4x - 6 is smaller than 2x + 5&quot;. An inequality can be solved just like an equation: whatever you do to one side, you also do to the other. Firstly, add...
LS
Answered by Laura S. • Maths tutor
9145 Views