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2 years ago

WORTH 20 POINTS !!! use mathematical terminology in your answer

Mathematics

2 answers:

Kazeer [188]2 years ago

6 0

The equation is y=-1/3x+4, so Chris is wrong.

leonid [27]2 years ago

3 0

The line goes 3 right for every 1 down, so the gradient is -1/3
The y-intercept is +4, so the equation is actually y=-1/3x+4, so Chris is wrong.

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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

Please help! And please explain how you did it!

Sunny_sXe [5.5K]

Answer:

Explanation:

turn 5/11 into a decimal: 0.45 which is LESS than 0.50 (0.5).

5 0

2 years ago

Read 2 more answers

There is 12/15 of a pizza left. How many 3/10 pieces can be made from the leftover pizza? Show work please!

Katyanochek1 [597]

How many 1/3 pieces can be made from 2 pizzas, we know it is 6 and it is arrived by dividing 2 by 1/3 or multiplying by its reciprocal 3/1.

Hence to find how many 3/10 pieces can be made from 12/15 pizza, we have to divide 12/15 by 3/10 or multiplying by its reciprocal 10/3, i.e.

12/15 times 10/3= 8/3 or 2 2/3

What does that mean? This means that while 2 three-tenths pieces can be made, 2/3of 3/10 i.e. <span>2/3×3/10=2/10=1/5</span> or one-fifth of pizza will be left out.

So the answer is 2 three-tenths pieces can be made, and one-fifth pizza will be left out.

5 0

3 years ago

HELPPPPP FAST PLEASEEEEEEEEEEEE

Drupady [299]

Answer:

45?

Step-by-step explanation:

7 0

2 years ago

Find the volume of the figure

mina [271]

Answer:

It is C. 233 because if you multiply 5x5x5 thats 125

If you multiply 12x3x3, its 108. So add 108+125 and that will be your final answer. Hope this helps and if so then please mark as brainliest. Remember that volume= length x width x height.

7 0

2 years ago

Read 2 more answers