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Work out the points of intersection of the graphs of y= (x+2)(x-4) and y=3x+6.

3x+6=(x+2)(x-4) 3x+6 = x 2 -2x-8 x 2 -5x-14=0 (x-7)(x+2)=0 x=7 so y=27 and x=-2 so y=0
EL
Answered by Edward L. • Maths tutor
5263 Views

In a lottery, 6 numbered balls are drawn from a pool of 59. Calculate the probability of scoring a jackpot. There used to be 49 balls in the pool. Calculate by how much the addition of 10 balls has decreased the probability of scoring a jackpot

The question has to do with probability, and the branch of mathematics which models such situations is called probability theory. A jackpot is, of course, when we correctly predict all the numbers on the bal...
MM
Answered by Marcin M. • Maths tutor
13341 Views

How do you integrate by parts?

To integrate the product of two functions - say f(x) = xsinx, the product of g(x) = x and h(x) = sin(x) - the we use integration by parts. Since integration is the inverse of differentiation, we'll appeal to...
PK
Answered by Patrick K. • Maths tutor
6758 Views

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

First starting from the right hand side. A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1) Therefore the numerator = (A+2B)x+(3A+B) Equating this numorator with the Left hand side we are presented with t...
GD
Answered by George D. • Maths tutor
7316 Views

Use the Intermidiate Value Theorem to prove that there is a positive number c such that c^2 = 2.

This exercise is asking to prove the existance of the square root of 2. So let's consider the function f(x) = x^2. Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity). ...
DK
Answered by Dilyana K. • Maths tutor
9597 Views