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Express (5-√ 8)(1+√ (2)) in the form a+b√2 , where a and b are integers

5 + 5√ 2 - √ 8 - √ 16 (Break up all terms in terms of square roots of 2) 5 + 5√ 2 - √ 8 - 4 5 + 5√ 2 - 2 √ 2 - 4 1 + 3√2
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Answered by Ignacio M. • Maths tutor
11348 Views

A rectangle has a shorter side with a length of x and a longer side with a length of x + 8, the perimeter of the rectangle is 80cm. Calculate the value of x.

For this question, one would sum the algebraic lengths of the rectangle, creating a result of 4x + 16. This is the algebraic perimeter of the rectangle which must be equated to the numerical value of the per...
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Answered by Ben S. • Maths tutor
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Differentiate "sin(2x)"

Sinx differentiates to give cosx. We then multiply this by the differential of "2x." Which equals 2. Our answer therefore is "2cos(2x)."
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Answered by Ciaran B. • Maths tutor
10258 Views

dy/dx = 10exp(2x) - 4; when x = 0, y = 6. Find the value of y when x = 2.

First, we must evaluate what is given in the question. As it can be seen, the expression indicates that the problem consists of a first-order differential equation. We are also given the values of x and thei...
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Answered by Girts L. • Maths tutor
2669 Views

Find the area between the curves y = x^2 and y = 4x - x^2.

First, we need to draw a diagram , to understand the question more clearly. y = x^2 is a common curve, but to sketch y = 4x - x^2, we should factorise it, to find where it inersects the x-axis. 4x - x^2 = x(...
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Answered by Lamisah M. • Maths tutor
9422 Views