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A curve has equation y=x^2 + (3k - 4)x + 13 and a line has equation y = 2x + k, where k is constant. Show that the x-coordinate of any point of intersection of the line and curve satisfies the equation: x^2 + 3(k - 2)x + 13 - k = 0

When we deal with points of interception, this immediately indicates that these two equations have to equal. Therefore, begin by equaling these two equations: x^2 + (3k - 4)x + 13 = 2x + k Bring all figur...

Answered by Helena W. • Maths tutor

12094 Views

Solve 5x - 6 = 3x + 7

Rearrange the equation so that both x's are on the same side of the equation, making sure that you change the sign of the number you bring across: 5x - 3x = 7 + 6 Now simplify: 2x = 13 Divide by 2: x = 13...

Answered by Helena W. • Maths tutor

8093 Views

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

The key is start out by working out the number of widgets per minute that a single machine makes. If it takes five minutes for five machines to produce five widgets then, on average, it takes five machine...

Answered by Hamza A. • Maths tutor

100863 Views

How can I calculate the value of a number raised to the power of a fraction, e.g., 9^(3/2)?

In order to calculate the value of a number raised to the power of a fraction, you first find the root of the number according to the value of the denominator (bottom number of the fraction).

In th...

Answered by Elsa A. • Maths tutor

11887 Views

Outline the various ways that you can differentiate a function

The ways to differentiate a function depend on the function itself. If there is only one x value in the function you can differentiate as normal (hard to explain on a computer), yet if the function contai...

Answered by Barnaby N. • Maths tutor

4701 Views