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Proof by Induction - "What's the point if we already know the answer?"

I'll try to use carefully chosen examples to explain the advantages/disadvantages of induction as a method of proof. My answer will go roughly as follows: Advantages: Sometimes the only obvious method of pro...
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Answered by Ruben H. • Maths tutor
4796 Views

An isosceles triangle has a base with length x+4 and the other two sides have length x+3. The perimeter of this isosceles triangle is 16cm. Find the area of the triangle.

First, we need to find the value of x. The perimeter of a shape is the sum of the length of all of its sides, so the perimeter of this isosceles is x + 4 + 2(x + 3) = x + 4 + 2x + 6 = 3x +10. We are told tha...
DM
Answered by Dominic M. • Maths tutor
4772 Views

Differentiate y = 15x^3 + 24x^2 + 6 with respect to x.

To differentiate y with respect to x, you have to multiply each x term by their respective power and then decrease their power by one. For example, 4x 2 differentiated is 2 x 4x 2-1 = 8x. So, splitting this ...
DM
Answered by Dominic M. • Maths tutor
4227 Views

What the integral of e^2x*x? (limits 0,1)

Whenever you see an integral with a product as the integrand, check if integration by parts works. That is, Int(v(x)*u'(x)) = u(x)v(x)-int(u(x) v'(x)) So you should see that its easier to call v(x)=x and u'(...
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Answered by Oliver O. • Maths tutor
4536 Views

A shop trying to sell a laptop reduces its price by 7% at the very end of each week, from an initial price of £600. If you have £365 to spend, how many weeks must you wait until you can buy the laptop?

This is a simple question, but it's important to not get confused when thinking about how the laptop's price gets reduced. We know the price starts at £600, and that it goes down by 7% each week. If somethin...
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Answered by Kiavash S. • Maths tutor
3546 Views