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The function f is defined for all real values of x as f(x) = c + 8x - x^2, where c is a constant. Given that the range of f is f(x) <= 19, find the value of c. Given instead that ff(2) = 8, find the possible values of c.

We know -x^2 has a maximum point of 0 at x=0, and -x^2 dominates the behaviour of f. We complete the square on this eqn, so we have f(x) = -(x - 4)^2 + 16 + c. We note that g(x) = -(x - 4)^2 has a maximum...

Answered by Sanmay K. • Maths tutor

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A curve has equation y = 4x^2 + 5x + 3. A line has equation y = x + 2. What is the value of x?

First you as both equations are = to y you can make them equal to eachother.4x²+5x +3 = x+ 2.Then you rearrange the equation to gather all the terms on one side and make the equati...

Answered by Katherine H. • Maths tutor

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How do I solve a quadratic equation by competing the square?

How would you solve x²+8x+16=81Show that this can be factorised (x+4)²=9

Answered by • Maths tutor

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Solve ((x+2)/3x) + ((x-2)/2x) = 3

Multiple first fraction through by 2 and second fraction through by 3((2x+4)/6x) + ((3x-6)/6x) = (5x-2)/(6x) = 3Expand brackets and isolate x5x-2 = 18x13x = -2x = -2/13

Answered by Alex B. • Maths tutor

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Let X be a normally distributed random variable with mean 20 and standard deviation 6. Find: a) P(X < 27); and b) the value of x such that P(X < x) = 0.3015.

a) 27 is higher than the mean. So we can simply calculate the z value. z = (27 - 20)/6 ≈ 1.17. Using the table in the formula booklet, we find that P(Z < 1.17) = 0.8790, so P(X ...

Answered by Maximillian H. • Maths tutor

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