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By using the substitution x = tan(u), find the integral of [1 / (x^2+1) dx] between the limits 1 and 0

First we need to change the limits, and by plugging in 1 and 0 to our substitution we find that the limits for u are arctan(1) and arctan(0) (or pi/4 and 0). Then we need to substitute for dx, and by diff...

Answered by Ollie W. Maths tutor
10793 Views

Solve the equation (2X + 3) / (X-4) - (2X - 8) / (2X + 1) = 1

In order to solve this equation we need to find a common denominator for the 2 fractions. It is impossible to name the common denominator while working with unknown variables such as x,y etc. but we know ...

Answered by Octavian G. Maths tutor
4844 Views

Smartphones are on sale. A smartphone now costs only 80% of its original price. By how many per cent would we need to increase the current price of the smartphone in order to bring it back to the original price?

Let a be the original price, b - the current price, and x - the answer we are looking for, so we need to increase b by x

Answered by Aleksejs P. Maths tutor
2897 Views

In a sale the price of a shirt is reduced by 60%. The sale price is £7.98. What is the original price?

Reduced by 60%=4/5 Original price * 0.4=£7.98 Original price=7.98/0.4=19.95 ∴ Original price= £19.95 

Answered by Riccardo R. Maths tutor
6505 Views

Kelly is trying to work out the two values of w for which 3w-w^3=2. Her values are 1 and -1. Are her values correct?

Sub in her values to see if the LHS and the RHS of the equation equate:

w=1:  3(1)-(1)^3=2  >>>  3-1=2  >>>  2=2  ✅

Therefore 1 is a correct value.

w=-1: 3(-1)-(-1)^...

Answered by Emma B. Maths tutor
4120 Views

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