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3 years ago

11

Wayne and Sarah both leave Sacramento at noon exactly. Wayne is driving west at 40 mph, while Sarah is driving south at 70 mph.

Find the rate at which the distance between them is changing at 2pm. Show all your work, include units in your answer. You do not need to simplify!

1 answer:

bulgar [2K]3 years ago

4 0

Answer:

30units because we are dealing with speed

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Answer: use google calculator It’s reliable

Step-by-step explanation:

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3 years ago

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PLS HELP !!!!!!!!!!!!!!!!!!<br><br> pls show ur work

Reil [10]

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Snowboarder: 15m/s

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Step-by-step explanation:

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3 years ago

A dealer marks his goods at 35% above the cost price and allows a discount of 20% on the marked price. Find his gain or loss per

vovikov84 [41]

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Step-by-step explanation:

100(1.35(0.8)p-p)/p=8%

Since this is positive the dealer makes an 8% profit.

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3 years ago

Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x2/(x4 +

ella [17]

Answer:

Given the function: $f(x) =\frac{x^2}{x^4+16}$

A geometric series is of the form of :

$\sum_{n=0}^{\infty} ar^n$

Now, rewrite the given function in the form of $\frac{a}{1-r}$ so that we can express the representation as a geometric series.

$\frac{x^2}{x^4+16}$

Now, divide numerator and denominator by $x^4$ we get;

$\frac{\frac{1}{x^2}}{1+\frac{16}{x^4}}$ = $\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2}$

Therefore, we now depend on the geometric series which is;

$\frac{1}{1+x} =\sum_{n=0}^{\infty} (-1)^n x^n$

let $x \rightarrow x^2$ then,

$\frac{1}{1+x^2} =\sum_{n=0}^{\infty} (-1)^n x^{2n}$

to get the power series let $x \rightarrow \frac{4}{x^2}$

so,

$\frac{1}{1+(\frac{4}{x^2})^2} =\sum_{n=0}^{\infty} (-1)^n (\frac{4}{x^2})^{2n}$

Multiply both side by $\frac{1}{x^2}$ we get;

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =\frac{1}{x^2} \cdot \sum_{n=0}^{\infty} (-1)^n (\frac{4}{x^2})^{2n}$

or

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =x^{-2} \cdot \sum_{n=0}^{\infty} (-1)^n (16)^n (x^{-2})^{2n}$

or

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =\sum_{n=0}^{\infty} (-1)^n (16)^n x^{-4n} \cdot x^{-2}$

Using $x^n \cdot x^m = x^{n+m}$

we have,

$\frac{\frac{1}{x^2}}{1+(\frac{4}{x^2})^2} =\sum_{n=0}^{\infty} (-1)^n (16)^n x^{-4n-2}$

therefore, the power series representation centered at x =0 for the given function is: $\sum_{n=0}^{\infty} (-1)^n (16)^n x^{-4n-2}$

6 0

3 years ago

Three shoppers from the survey are selected at random, one at a time without replacement. What is the probability that none of t

Travka [436]

Answer:

0.395

Step-by-step explanation:

The computation of the probability that none of the three shoppers purchased electronics is shown below:

So, first we have to determine the number of shoppers without considering the purchase i.e

= Total number of shoppers - electronics

where,

Total number of shoppers = Offices supplies + electronics + clothing + beauty supplies - electronics

= 18 + 25 + 40 + 12 - 25

= 95 - 25

= 70

Now the probability is

= $\frac{70}{95}\times\frac{69}{94}\times\frac{68}{93}$

= 0.395

5 0

3 years ago