Top answers

A curve has equation y=(2-x)(1+x)+3, A line passes through the point (2,3) and the curve at a point with x coordinate 2+h. Find the gradient of the line. Then use that answer to find the gradient of the curve at (2,3), stating the value of the gradient

The gradient of the line is given by change in Y divided by change in X. To find the Y value of the point we must put 2+h into the y=(2-x)(1+x)+3. Doing this we get y=(2-(2+h))(1+(2+h))+3=(-h)(3+h)+3= -3h -h...
JC
3440 Views

Solve the following, giving your answers in terms of ln a: 7 sechx - tanhx =5

7sechx - tanhx = 5 7/coshx - sinhx/coshx = 5 7 - sinhx = 5 cosh x 7 - 0.5(e x - e -x ) = 2.5(e x + e -x ) 7 -0.5e x + 0.5e -x = 2.5e x + 2.5e -x 0 = 3e x - 7 + 2e -x 0 = 3e 2x - 7e x + 2 0 = (3e x - 1)(e x -...
AW
8257 Views

How would go about finding the set of values of x for which x+4 > 4 / (x+1)?

Whenever you see a problem involving an inequality (greater than or less than sign) it is really important to pause for a second before you go breaking any rules of mathematics. Inequalities do not always be...
TH
3005 Views

How can you divide an algebraic expression by another algebraic expression?

I would begin the session with checking a basic understanding of the methods of long division, as these will not have been taught very recently. Many students will have been using short division, as it is qu...
JH
3599 Views

Use algebra to find the set of values of x for which mod(3x^2 - 19x + 20) < 2x + 2.

The initial quadratic can be either positive or negative so we must solve for both possibilities. Solving for positive: 3x^2 - 19x + 20 &lt; 2x + 2 = 3x^2 - 21x + 18 &lt; 0 = x^2 - 7x + 6 &lt; 0 = (x - 6)(x ...
JM
11786 Views