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Solve the following simultaneous equations: 2x + 2y = 14; 4x - 2y = 10

By Elimination: We can add the equations together because +2y and -2y will cancel out: 2x + 4x = 14 + 10 This gives 6x = 24, so x = 4 We can put x back into one of the simultaneous equations: 2(4) + 2y = 14 ...
EB
Answered by Edward B. • Maths tutor
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A quadrilateral has a perimeter of 42cm. Three sides have equal length and the fourth side is longer by 6cm. What is the length of the fourth side?

We can call the sides of the equal lengths "x". We can then make an equation to satisfy the relationship between the perimeter and the length of the sides as follows: x + x + x + (x + 6) = 42 There...
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Answered by Edward B. • Maths tutor
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135 is 3/8 of a number. Work out the number.

Divide 135 by 3/8 OR multiply 135 by 8/3 135 * 8/3 = 360 You can do this in steps by starting with: 135/3 = 45, then multiply by 8. OR 135 * 8 = 1080, then divide by 3.
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Answered by Edward B. • Maths tutor
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How do I a differentiate a cosine function?

The differential is the slope of the graph at any point. So if we imagine a cosine in our heads, it starts at a peak and goes down to a negative peak. So in terms of the gradient (or slope) it starts at 0 an...
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Answered by Kieran H. • Maths tutor
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Define the derivative of a function f(x) and use this to calculate the derivative of f(x)=x^n for positive integer n.

f'(x)=lim(h->0) of [f(x+h)-f(x)]/h. In the case where f(x)=x^n, we have that f(x+h)-f(x)=h*nx^(n-1) + (h^2)*p(x) for a polynomial p(x), shown by binomially expanding f(x+h). Then dividing through by h and...
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Answered by Tutor302361 D. • Maths tutor
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