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Consider the unit hyperbola, whose equation is given by x^2 - y^2 = 1. We denote the origin, (0, 0) by O. Choose any point P on the curve, and label its reflection in the x axis P'. Show that the line OP and the tangent line to P' meet at a right angle.

We differentiate our equation with respect to x to find that 2x - 2y(dy/dx) = 0, and rearrange to find that dy/dx = x/y. We set P = (x, y). The slope of OP is given by y/x, and the slope of the tangent at...

Answered by Dylan C. • Maths tutor

3253 Views

Show that the volume of the solid formed by the curve y=cos(x/2), as it is rotated 360° around the x-axis between x= π/4 and x=3π/4, is of the form π^2/a. Find the constant a.

After sketching a diagram of the curve and the solid for clarity, we see that we need to use the formula V = π∫ y² dx (with upper and lower bounds of 3π/4 and π/4 respectively) to calculate the...

Answered by Nicholas C. • Maths tutor

3309 Views

Margret wants to share £36 in a ratio of 3:4 between her two grandchildren, Anna and Katie. How much money will Katie get?

36/12 = 33x4 = 12Katie gets £12

Answered by Martha N. • Maths tutor

3920 Views

Find and describe the stationary points of the curve y = x^2 + 2x - 8

Stationary points occur when the derivative is = 0Derivative: 2x + 2 = 0, so a stationary point occurs when x = -1y = 1 + 2 - 8 = -5Second derivative = 2Therefore, the stationary point (-1,2) is a minimum...

Answered by Martha N. • Further Mathematics tutor

2078 Views

Describe how to perform a flame test to identify an unknown compound.

The equipment needed is a bunsen burner, a wire loop, some HCl, and the compound being tested (usually in powder form). Set up the bunsen burner so that it is on a blue flame. Take the wire loop and dip i...

Answered by Martha N. • Chemistry tutor

3098 Views