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Find the turning point of the line y = -2x^2 +5x -9

The first step in finding any turning point is to differentiate. To do this, we muiltiply x by its power and drop the power by 1. so in this senario we multiply the -2x by 2 giving us -4x and the power be...

Answered by Felix B. • Maths tutor

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The polynomial p(x) is given by p(x) = x^3 – 5x^2 – 8x + 48 (a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). [2 marks] (ii) Express p(x) as a product of three linear factors. [3 marks]

(a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x).

The Factor Theorem is derived from the remainder theorem. We know from the remainder theorem that by doing p(x)/(x – a) then w...

Answered by Mustafa A. • Maths tutor

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Susan is researching the population growth of a city. She proposes that x, the number of people in the city, t years after 2017 is given by x=250,000e^(0.012t) A.population in 2017 B.population in 2020 C.During which year would the population have doubled

A. t=0 ; x=250,000 B. 2020, so t=3. plug in to equation > x=250,000e^(0.012)3 = 259,163 (people so cannot round up) C. Population to double so 500,000 = 250,000e^(0.012)t -> 1/0.012(ln2) = t t= 57.7...

Answered by James G. • Maths tutor

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Find an equation of the circle with centre C(5, -3) that passes through the point A(-2, 1) in the form (x-a)^2 + (y-b)^2 = k

step 1 remember than the a and b terms locate the centre of the circle on the axis so we can substitute in the centre values for a and b. (x-5)^2 + (y-(-3))^2 = k. (x-5)^2 + (y+3)^2 = k.

Step 2. k ...

Answered by Tim W. • Maths tutor

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Given that y = 5x^(3) + 7x + 3, find dy/dx

(i): 15x^(2)+7 --- in order to arrive at this answer, we can divide the equation into 3 separate parts: 5x^(3) and 7x and 3. For the first part, you would multiply the first number, 5 by the power, in thi...

Answered by Angela P. • Maths tutor

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