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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 differe...
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Answered by Ollie W. • Maths tutor
12705 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 fro...
OG
Answered by Octavian G. • Maths tutor
5635 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 % in order to get a . So a=b+b x% (the original price a equals the current price b + t...
AP
Answered by Aleksejs P. • Maths tutor
3910 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
RR
Answered by Riccardo R. • Maths tutor
7500 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)^3=2 >>> -3+1=2 >&g...
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Answered by Emma B. • Maths tutor
5330 Views