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3 years ago

If p is inversely proportional to the square of q, and p is 22 when q is 8, determine p when q is equal to 2. 9 w

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

7 0

Answer:

167.42

Step-by-step explanation:

p = 1/q²

22 = k* 1/8² .........k is the constant which we re finding now

k = 1408

p = 1408/2.9²

= 167.42

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lina2011 [118]

There you go. I assumed you know how to derrivate!

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3 years ago

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OlgaM077 [116]

so, let's keep in mind that

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}$

so let's make a quick table of those solutions, say A, B, C solutions with x,y,z liters of acid, with an acidity of 0.25, 0.40 and 0.60 respectively.

$\bf \begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ A&x&0.25&0.25x\\ B&y&0.40&0.4y\\ C&z&0.60&0.6z\\ \cline{2-4}&\\ mixture&78&0.45&35.1 \end{array} \\\\\\ \begin{cases} x+y+z=78\\ 0.25x+0.4y+0.6z=35.1 \end{cases}$

we know she's using "z" liters and those are 3 times as much as "y" liters, so z = 3y.

$\bf \begin{cases} x+y+3y=78\\ x+4y=78\\[-0.5em] \hrulefill\\ 0.25x+0.4y+0.6(3y)=35.1\\ 0.25x+0.4y=1.8y=35.1\\ 0.25x+2.2y=35.1 \end{cases}\implies \begin{cases} x+4y=78\\\\ 0.25x+2.2y=35.1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x+4y=78\implies \boxed{x}=78-4y \\\\\\ \stackrel{\textit{using substitution on the 2nd equation}}{0.25\left( \boxed{78-4y} \right)+2.2y=35.1}\implies 19.5-y+2.2y=35.1$

$\bf 1.2y=15.6\implies y=\cfrac{15.6}{1.2}\implies \blacktriangleright y=13 \blacktriangleleft \\\\\\ x=78-4y\implies x=78-4(13)\implies \blacktriangleright x=26 \blacktriangleleft \\\\\\ z=3y\implies z=3(13)\implies \blacktriangleright z=39 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{25\%}{26}\qquad \stackrel{40\%}{13}\qquad \stackrel{60\%}{39}~\hfill$

5 0

3 years ago

Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that perchlorate

ser-zykov [4K]

Answer:

$H_1 : \mu > 24.5$

Step-by-step explanation:

From the given information:

The sample size is 28

The population mean is 24.5 (ppb)

The sample mean is 225.3 (ppb)

Thus, the null and the alternative hypothesis can be computed as:

Null hypothesis:

$H_o : \mu \le 24.5$

Alternative hypothesis:

$H_1 : \mu > 24.5$

8 0

3 years ago

Can you answer this for me plssss 0.5(r+2.75)=3

lora16 [44]

Step-by-step explanation:

0.5 ( r + 2.75 ) = 3

r + 2.75 = 3 / 0.5

r + 2.75 = 6

r = 6 - 2.75

r = 3.25

4 0

4 years ago

Read 2 more answers

You are considering two cars that you plan on keeping for 5 years. One has an EPA combined city and highway rating of 33 mpg. Th

amid [387]

Answer:

a) $86.11

b) $467.33

Step-by-step explanation:

no. of gallons saved 'n' per year

n = (10000/33) - (10000/36)

n = 2500/99

Amount saved = 3.41×n = 3.41×2500/99

= $86.11

b) over 5 years:

86.11( 1 + (1.041) + (1.041)² + (1.041)³ + (1.041)⁴ )

= 86.11(5.427157431)

= $467.33

6 0

3 years ago

If p is inversely proportional to the square of q, and p is 22 when q is 8, determine p when q is equal to 2. 9 w​

If p is inversely proportional to the square of q, and p is 22 when q is 8, determine p when q is equal to 2. 9 w