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3 years ago

Make q the subject of the formula 2(q+p) = 1+5q. Give your answer in the form ap-b/c where a,b and c are all positive integers

Mathematics

1 answer:

musickatia [10]3 years ago

8 0

Answer:

$\frac{2p-1}{3}$

Step-by-step explanation:

Since you want to get q only and q appears in both side of the equation. Try to isolate q to one side.

1) Expand 2(q+p)

2q + 2p = 1 + 5q

2) Move all q terms to one side

5q - 2q = 2p - 1

3q = 2p - 1

3) Divide 3 on both side (to isolate q)

q = $\frac{2p-1}{3}$

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Step-by-step explanation:

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3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$