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A cone has a radius of 2 units and a height of 3 units. Devise a simplified equation to find the volume of the cone.

Vol = 1/3 pi r^2 h

r = 2n

h = 3n

Therefore

Vol = 1/3.pi.(2n)^2.3n

Vol = 1/3.pi.12n^3

Vol = 4.pi.n^3

TM
Answered by Toby M. Maths tutor
2742 Views

Prove by induction that the sum of the first n integers can be written as (1/2)(n)(n+1).

For n = 1, the sum is given by (1/2)(1)(1+1), which gives 1, the expected result. We now assume that the statement is true for some k. If we look at k+1, the sum is given by 1 + 2 + ... + k + (k+1). Since...

JS
2238 Views

Given the function f(x) = (x^2)sin(x), find f'(x).

The function f(x) is a product of 2 functions of x, so when we differentiate it, we need to use the product rule.

The product rule states that for a function f(x) = g(x)*h(x), f'(x) is given by g(x...

JS
Answered by Jason S. Maths tutor
9530 Views

A round cake is shared between Abi, Elvira and Tina. The angle cut at the centre of the cake for each piece is that person’s age multiplied by 10. Abi 9 years old and Elvira is 14 years old. How old is Tina?

The cake is in the shape of a circle. How many degrees in a circle?

Abi is 9 years old so the angle of her slice is 9 x 10 = 90°, Elvera is 14 years old so her angle is 14 x 10 = 140°. Total angle ...

VS
Answered by Varun S. Maths tutor
2579 Views

What is the enhanced greenhouse effect?

The enhanced greenhouse effect is the stronger impact caused by human emissions of greenhouse gases. Greenhouse gases include carbon dioxide, methane and water vapour and are often produced by burning fos...

IH
12512 Views

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