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V125BC [204]
3 years ago
12

Suppose that y varies inversely as x and that y=8 when x=3. Calculate the value of y when x= 10.

Mathematics
1 answer:
Svetach [21]3 years ago
3 0

\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} y = 8\\ x = 3 \end{cases}\implies 8=\cfrac{k}{3}\implies 24=k~\hfill \boxed{y = \cfrac{24}{x}} \\\\\\ \textit{when x = 10, what is \underline{y}?}\qquad \qquad y = \cfrac{24}{10}\implies y = \cfrac{12}{5}

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Multiply 3/sqrt17- sqrt2 by which fraction will produce an equivalent fraction with rational denominator
zzz [600]

Answer:

B.

Step-by-step explanation:

To simplify something that looks like \frac{\text{whatever}}{\sqrt{a}-\sqrt{b}} you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:

\sqrt{a}+\sqrt{b}.

If you had  \frac{\text{whatever}}{\sqrt{a}+\sqrt{b}}, then you would multiply top and bottom the conjugate of \sqrt{a}+\sqrt{b} which is \sqrt{a}-\sqrt{b}.

The conjugate of a+b is a-b.

These have a term for it because when you multiply them something special happens.  The middle terms cancel so you only have to really multiply the first terms and the last terms.

Let's see:

(a+b)(a-b)

I'm going to use foil:

First:  a(a)=a^2

Outer: a(-b)=-ab

Inner:  b(a)=ab

Last:    b(-b)=-b^2

--------------------------Adding.

a^2-b^2

See -ab+ab canceled so all you had to do was the "first" and "last" of foil.

This would get rid of square roots if a and b had them because they are being squared.

Anyways the conjugate of \sqrt{17}-\sqrt{2} is

\sqrt{17}+\sqrt{2}.

This is the thing we are multiplying and top and bottom.

3 0
3 years ago
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The table answers for the second equation are
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8 0
3 years ago
Jenny made $315.25 for 8 hours of work. How much would Jenny make for 40 hours of work
bagirrra123 [75]
If Jenny made $315.25 for 8 hours of work:

Then it means that she made:
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If Jenny works for 40 hours, then she will make:

40 hours × $39.41 = $1,576.25


Please mark my answers as the Brainliest if you find my explanations/solution helpful :)
6 0
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pishuonlain [190]

Answer: kindly check explanation

Step-by-step explanation:

Given the data :

5 3 3 1 4 4 5 6 4 2 6 6 6 7 1 1 14 1 2 4 4 4 5 6 3 5 3 4 5 6 8 4 7 6 5 9 11 3 12 4 7 6 5 15 1 1 10 8 9 2 12

Frequency and relative frequency table can be found in the attachment below.

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Answer: 4p^2-2p

Step-by-step explanation:

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