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Solve the simultaneous equations: 2x + y = 12; x - y = 6

We add the two equations together (left-hand sides and right-hand sides separately). By doing this we get: 2x + y + (x - y) = 12 + 6. By rearranging and simplifying: 3x = 18.If we divide both sides by 3 we g...
RD
Answered by Rebeka D. • Maths tutor
6953 Views

Integrate(1+x)/((1-x^2)(2x+1)) with respect to x.

To simplify the fraction first notice (1-x 2 ) = (1-x)(1+x) so the common factor of (1+x) in the numerator and denominator can be cancelled. (1+x)/((1-x^2)(2x+1)) = 1/((1-x)(2x+1)), then we need to split thi...
RH
Answered by Ravinder H. • Maths tutor
4319 Views

What is 7 to the power of 8? (

Rearrange to (7 4 ) 2 = ((7 2 ) 2 ) 2 7 2 = 49(7 2 ) 2 = 49 2 = (50-1) 2 = 50 2 - 2x50 + 1 = 24017 8 = (7 4 ) 2 =((7 2 ) 2 ) 2 = 2401 2 = (2000 + 400 + 1) 2 = 5,764,801
MH
Answered by Michael H. • Maths tutor
5813 Views

The numbers a, b, c and d satisfy the following equations: a + b + 3c + 4d = k; 5a = 3b = 2c = d. What is the smallest value for k for which a, b, c and d are all positive integers

5a = 3b = 2c = d. d must be a multiple of 5, 3 and 2, therefore the smallest possible value for d is 30. This sets a = 6, b = 10 and c = 152) a + b + 3c + 4d = 6 + 10 + 3x15 + 4x30 = 181 k = 181
MH
Answered by Michael H. • Maths tutor
4932 Views

A class of pupils were asked about how they travelled to school on a particular day. 1/6 of the pupils were driven to school in a car. 2/5 of the pupils took the bus. The rest of the pupils walked to school. Calculate the fraction of pupils who walk

The total amount of student would be represented by 1 or 100%. The pupils are split into three categories meaning the total must add up to 1. Therefore to find the remaining pupils who walked to school we si...
JZ
Answered by Jane Z. • Maths tutor
7028 Views