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3 years ago

What is the product simplest form stat any restrictions on the variable 3g^5/10h^2 x h^5/10g^2

1 answer:

6 0

The restriction are that neither h nor g may equal zero as that would lead to division by zero.

The simplification after units cancel is:

(3(gh)^3)/100 or if you prefer

0.03(gh)^3

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Which is A Prime Number? A)7 B)33 C)27 D)63

Paraphin [41]

7 is a prime number because it is only divisible by 1 and itself which is 7.

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3 years ago

Read 2 more answers

Which of the following rotations around the origin of the triangle with

kramer

Answer:

Step-by-step explanation:

270 degrees

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3 years ago

Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i

jenyasd209 [6]

Answer:

If the limit that you want to find is $\lim_{x\to \infty}\dfrac{P(x)}{Q(x)}$ then you can use the following proof.

Step-by-step explanation:

Let $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ and $Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0}$ be the given polinomials. Then

$\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}$

Observe that

$\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}$

and

$\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}$

Then

$\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}$

3 0

2 years ago

Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 32 ft long. She wants to leave a uniform strip of floor aroun

Rainbow [258]

Answer:

The rug should be 15 ft wide and 28 ft long.

Step-by-step explanation:

I have attached a figure that represents the situation.

The the rug is $l$ by $h$ , the width of the strip of floor is $w$ .

We are told that Cynthia can only afford 420 square feet of carpeting; therefore, it must be that

$l*h=420$ (this says the area of the rug must be 420 square feet)

From the figure we see that

$l= 32-2w$

$h=19-2w$

Therefore,

$l*h=420\\\\(32-2w)(19-2w)=420$

We expand this equation and get:

$4w^2-102w+608=420\\\\4w^2-102w+188=0$

using the quadratic equation we get two solutions:

$w=2\\w=23.5$

since the second solution, namely $w=23.5$ , is larger than one of the dimensions of the room (is greater than 19 ft) it cannot be the width of the strip; therefore, we take $w=2$ to be our solution.

Now we find the dimensions of the rug:

$l=32-2(2)=28\\\\h=19-2(2)=15$

The rug is 15 ft wide and 28 ft long.

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3 years ago

What does the variable X equal

Ray Of Light [21]

The variable x always equals 1

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2 years ago