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A square is placed in a circle of area (49π)cm^2 such that all four vertices of the square lie on the circumference of the circle. What is the area of the square?

It's always helpful to draw a diagram beforehand.Since we know the area of the circle is (49π)cm², we can work out the radius using A=πr². Rearranging, we get r = 7cm. Add this info...

Answered by Karnan S. • Maths tutor

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Make x the subject of the formula y=(4x+5)/x

xy=4x+5 xy-4x=5x(y-4)=5x=5/(y-4)

Answered by R P. • Maths tutor

4338 Views

The gradient of a curve is given by dy/dx = 3 - x^2. The curve passes through the point (6,1). Find the equation of the curve.

Since we differentiate a function to find the gradient of a curve at any point, we need to reverse that to find the equation of the curve. We do this by integrating with respect to x:If you have a constan...

Answered by Darya N. • Maths tutor

9431 Views

Points A and B have coordinates (–2, 1) and (3, 4) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as 5x +3 y = 10.

Formula for a straight line y-y₁=m(x-x₁), where m is the gradient substituting in the values given to find the gradient we get 4-1=m(3+2), therefore m= 3/5the midpoint of the two poi...

Answered by Paige M. • Maths tutor

7533 Views

Find the values of x for which f(x) is an increasing function given that f(x)=8x-2x^2

When a function is increasing, it’s derivative is positive. So first let us differentiate f(x). To differentiate xⁿwe multiply by n and then reduce the power by 1. So f’(x)=8-2*2x=8-4x. We wan...

Answered by Ruby L. • Maths tutor

10770 Views