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Solve simultaneously: 3x+2y=7 & x-2y=-3

Add the 2 eqns together to eliminate the y's to give: 4x=4. Divide by 4 to give x=1Now substitute x=1 into the first eqn: 3+2y=7. Subtract 3 from both sides -> 2y=4. Divide by 2 to give y=2.Now, check by ...
KL
Answered by Katie L. • Maths tutor
5605 Views

Find the coordinates of the turning point of the graph y=x^2 -x -12. Use it to sketch the graph on a set of x-y axis.

-Firstly we should check if the equation has the variables separated (x on one side and y on the other side of the equal sign), which they apear to are, therefore we can proceed to the next step. As it is kn...
IP
Answered by Ioanna P. • Maths tutor
7107 Views

solve 15x = 6x^3 + 8x^2

6x 3 + 8x 2 -15x = 0x(6x 2 + 8x - 15) = 0x=06x 2 + 8x - 15 = 0Quadratic formula ( can demonstrate in interview)x = 0 or x = 1.049 or x = -2.38
LL
Answered by Lewis L. • Maths tutor
3217 Views

The function f has domain (-∞, 0) and is defines as f(x) = (x^2 + 2)/(x^2 + 5) (here ^ is used to represent a power). Show that f'(x) < 0. What is the range of f?

First notice that f(x) = u/v. So f'(x) =[ v(u') - u(v')]/v 2 (the Quotient rule). After working it out, we find f'(x) = 6x/(x 2 + 5) 2 (the steps can be shown on the whiteboard). Since the denominator is alw...
CC
Answered by Chris C. • Maths tutor
3497 Views

Given that y = (1 + 3x^2)^(1/3) , use the chain rule to find dy/dx in terms of x.

Take u = 1+3x 2 , this gives that y = u 1/3 . By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u 1/3 with respect to u gives dy/du = (1/3)u -2/3 . By differentiating u = 1 + 3x 2 ...
JS
Answered by Jasmine S. • Maths tutor
5721 Views