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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 w...

Answered by Rebeka D. • Maths tutor

5687 Views

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

To simplify the fraction first notice (1-x²) = (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 ...

Answered by Ravinder H. • Maths tutor

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What is 7 to the power of 8? (

Rearrange to (7⁴)²= ((7²)²)²7²= 49(7²)² = 49² = (50-1)² = 50² - 2x50 + 1 = 24017<...

Answered by Michael H. • Maths tutor

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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
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Answered by Michael H. • Maths tutor
4275 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...

Answered by Jane Z. • Maths tutor

6150 Views