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.

sinclairdragon428 Jun 11, 2019

#1**+1 **

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=\(\boxed{193\pi}\)

.power27 Jun 11, 2019

#3**+2 **

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

CPhill Jun 11, 2019

#4**+2 **

\(\frac{2}{\sqrt[3]{4}+\sqrt[3]{32}} \) \(\frac{\sqrt[3]{A}}{B}\)

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 ( 2^{3}√2 - 4^{3}√2 + 8^{3}√2 ) 6^{3}√2 ^{ 3}√2

_______________________ = ______ = _____

36 18 3

A = 2 B = 3

And their sum is 5

CPhill Jun 11, 2019