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By integrating, find the area between the curve and x axis of y = x*exp(x) between x = 0 and x = 1

The area under a curve is found by integration.
Area = integral{xexp(x) dx} with limits 0 and 1
It's necessary to use integration by parts to find this integral as there are two x f...

Answered by Maths tutor
3162 Views

A shopkeeper compares the income from sales of a laptop in March and in April. The price in April was 1/5 more than in March. The number sold in April was 1/4 less than in March. By what fraction does income decrease from March to April?

Price in March = a Price in April = a x 1.2 = 1.2aNumber sold in March= b Number sold in April = b x 0.75 = 0.75bIncome = Price x Number soldIncome in March = abIncome in April = 0.9abDecrease is ...

RH
Answered by Robert H. Maths tutor
9307 Views

Solve the simultaneous equations: 5x + y = 21, x - 3y = 9

5x + y = 21x - 3y = 9First, multiply the equation one by 3 so we can cancel out the y's.15x + 3y = 63 (we've now multiplied this by 3)x - 3y = 9Now we can add the two equations together, thus adding 3 and...

SP
Answered by Sebastian P. Maths tutor
3326 Views

Solve 6x^2+8x-8 = 0 using factorisation.

Factorise using a suitable method (eg product and sum) to find (6x-4)(x+2) = 0Hence x = 4/6 and x = -2.

MS
Answered by Matthew S. Maths tutor
3586 Views

There are 35 people in a group. x(x+1) of them have a blue car, 5x of them have a red car, 4 have a blue and a red car and 4x-8 do not have car. Work out the probability that a person who has a blue car, has a red car as well.

We see this question is about conditional probability. Because a person chosen at random from the group satisfies a 1st condition: they have a blue car. And after we know this, they have to satisfy a 2nd ...

AP
Answered by Ana P. Maths tutor
2681 Views

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