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3 years ago

Given a circle with a radius of 22 inches, what is the circumference in terms of π?

Mathematics

2 answers:

Mars2501 [29]3 years ago

5 0

Answer:

$circumference = 2\pi \: r \\ = 2 \times \pi \times 22 \\ = 44\pi \: inches$

saw5 [17]3 years ago

3 0

Answer:

The circumference is 44 pi.

Step-by-step explanation:

You have to use the formula, C=2 Pi R but since it's in terms of pi, we can not include pi in the equation. 2 times r (radius) is 44, therefor the answer is 44 pi.

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3 years ago

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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3 years ago

Which inequality is represented by the graph y>-2/3x+1 y<-2/3x+1 y<-3/2x+1 y>-3/2x+1

soldi70 [24.7K]

Answer:

the 3rd one is the graph answer

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3 years ago