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1. If P=(-3,4) and Q=(9,-3) what is the number of units in the area of the circle with center at P and passing through Q? Express your answer in terms of pi.
2. Find the largest value of n such that 3x^2+nx+72 can be factored as the product of two linear factors with integer coefficients.
3.Rationalize the denominator of $\frac{2}{\sqrt[3]{4}+\sqrt[3]{32}}$. The answer can be written in the form of $\frac{\sqrt[3]{A}}{B}$, where A and B are positive integers. Find the minimum possible value of A+B.

Jun 11, 2019

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1. The radius of the circle is the discance between P and Q. Plug these into the distance formula:

$$radius=\sqrt{(-3-9)^2+(4--3)^2}$$

$$radius=\sqrt{(-12)^2+(7)^2}$$

$$radius=\sqrt{193}$$

The formula for the area of a circle is $$\pi r^2$$. Plug the radius into this to find the area.

$$\pi(\sqrt{193})^2$$

Area=$$\boxed{193\pi}$$

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Jun 11, 2019
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Thanks!

sinclairdragon428  Jun 11, 2019
#2
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hello hhh

hello,I hope you can understand me！

Jun 11, 2019
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2. Find the largest value of n such that 3x^2+nx+72 can be factored as the product of two linear factors with integer coefficients.

We need the  max sum of two factors that multiply to 72   and the same for two factors that multiply to 3

These are   1,72     and  1, 3

So......n will be maximized when we have

(3x + 1) (1x + 72)  =  3x^2 + 1x + 216x + 72  = 3x^2 + 217x + 72

n = 217

Jun 11, 2019
edited by CPhill  Jun 11, 2019
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Thank you!

sinclairdragon428  Jun 11, 2019
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$$\frac{2}{\sqrt[3]{4}+\sqrt[3]{32}}$$     $$\frac{\sqrt[3]{A}}{B}$$

Multiply the top/bottom  by   ( 3√[4^2] - 3√[4*32] + 3√[32]^2 )

2  ( 3√[4^2] - 3√[4*32] + 3√[32]^2 )

_____________________________________

(3√4 + 3√32) ( 3√[4^2] - 3√[4*32] + 3√[32]^2 )

This resolves the demoninator into  4 + 32 =  36

So we have

2 ( 23√2    -  43√2 + 83√2 )                    63√2           3√2

_______________________  =         ______  =   _____

36                                         18                3

A = 2     B = 3

And their sum is 5

Jun 11, 2019