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By using the substitution, x = 2sin(y) find the exact value of integral sqrt(1/3(4-x^2)) dx with limits 0 and 1.

In order to calculate this integral we must use the sustitution provided. x=2siny. Firtsly I will differentiate to find the dx component of the integral, so dx/dy=2cosy hence, dx=2cosydy. Now for the limits ...
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Answered by Sara S. • Maths tutor
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Show that the line y = x - 7 does not meet the circle (x + 2)^2 + y^2 = 33.

To find potential points of intersection between the line and the circle, we need to solve the equations simultaneously. So, we substitute y = x - 7 into the equation of the circle: (x + 2) 2 + y 2 = 33 (x +...
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Answered by Anastasios I. • Maths tutor
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Find x for: x^2 + 5x = 5

x 2 + 5x = 5 Make equal to 0. x 2 +5x - 5 = 0 Recognise that you need to use the quadratic equation. (-b ± sqrt(b 2 -4ac))/2 sub in. (-5 ± sqrt(5 2 -4 1 -5))/2 (-5 ± sqrt(45))/2 x = (-5 + 6.7)/2, x = (-5 - 6...
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Answered by Lewis C. • Maths tutor
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Why is the inverse of a gradient -1/x?

Because the value, x and its inverse, -1/x should multiply together to give -1. This is proof that two lines are perpendicular (or having the same magnitude of gradient but opposite signs +/- ).
SR
Answered by Sherin R. • Maths tutor
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Work out area of shaded region in terms of pi. (https://prnt.sc/hqfbsl) [Question link]

Area of square : Base x Height. Area of Circle : π x (Radius) 2 . Looking at the diagram we are given the dimensions of the base or height of the cube (as all sides are equal in a square) and the diameter of...
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Answered by Mohammed A. • Maths tutor
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