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1 year ago

Triangle PQR has coordinates P (2, 4), Q (-2, 4), R (0,-6).

Mathematics

2 answers:

jok3333 [9.3K]1 year ago

7 0

Answer:dec I think

Step-by-step explanation:

alexdok [17]1 year ago

4 0

Answer: P’ (5,10) , Q’ (-5,10) , R’ ( 0,-15)

Step-by-step explanation:

Just multiply 2.5 by the x,y

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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

Explain how a personal budget relates to and takes into account your personal financial goals.

nexus9112 [7]

what? what subject is it

6 0

2 years ago

Read 2 more answers

The scale factor of a room for a scale drawing is 2.3. The actual length of a wall in the room is 46 feet and the actual width o

dimaraw [331]

Answer:

There's two ways to solve this.

Step-by-step explanation:

First way:

Let's divide the width and length by 2.3.

46÷2.3=20

69÷2.3=30

20×30

600 ft²

Second Way:

Let's find the area of the actual room.

46×69

3,174 ft²

Let's find the scale drawing squared.

2.3²=5.29

3,174÷5.29

600 ft²

3 0

2 years ago

Read 2 more answers

A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y de

strojnjashka [21]

Answer:

a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

a= μ-3.16*σ , b= μ+3.16*σ

b) P(Y≥ μ+3*σ ) ≥ 0.90

b= μ+3*σ

Step-by-step explanation:

from Chebyshev's inequality for Y

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

where

Y = the number of fish that need be caught to obtain at least one of each type

μ = expected value of Y

σ = standard deviation of Y

P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean

k= parameter

thus for

P(| Y - μ|≤ k*σ ) ≥ 1-1/k²

P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16

then

P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90

using one-sided Chebyshev inequality (Cantelli's inequality)

P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)

P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ

then for

P(Y≥ μ+3*σ ) ≥ 0.90

5 0

2 years ago

A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of

Tanya [424]

Answer:

The probability is 0.31

Step-by-step explanation:

To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.

In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is $\binom{25}{6}$ , where $\binom{n}{k} = \frac{n!}{(n-k)!k!}$ . We have that $\binom{25}{6} = 177100$

Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in $\binom{10}{3}\cdot \binom{15}{3} = 54600$

So the probability of having 3 laser printers and 3 inkjets is given by

$\frac{54600}{177100} = \frac{78}{253} = 0.31$

4 0

2 years ago