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1 year ago

Please see attached photo for problem from my homework set. Thanks in advance!

Mathematics

1 answer:

stealth61 [152]1 year ago

4 0

We have to find the equation of the line that represents the demand function.

The first step is to find the slope of the line, using the given pair of values.

$m=\frac{8.45-9.95}{95-80}=-0.1$

Now, use the point slope formula to find the equation of the line:

$\begin{gathered} p-8.45=-0.1(q-95) \\ p=-0.1q+9.5+8.45 \\ p=-0.1q+17.95 \end{gathered}$

It means that the answer is p=-0.1q+17.95.

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Use the graph to answer the question.

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3 years ago

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Write the equation of the circle with the center (3,2) and (-6,-4)

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3 years ago

Find all values of x for which the series converges. (enter your answer using interval notation. ) [infinity] (4x)n n = 1

andreyandreev [35.5K]

The series converges to 1/(1-9x) for -1/9<x<1/9

Given the series is ∑ $9x^{n} x^{n}$

We have to find the values of x for which the series converges.

We know,

∑ $ar^{n-1}$ converges to (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ $(9x)^{n}$ is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to 1/1-9x for -1/9<x<1/9

For more information about convergence of series, visit

brainly.com/question/15415793

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2 years ago

How do you simplify this expression with an answer in positive exponential notation? Please provide the process. Thank you!

Otrada [13]

$\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ 8^{-2}\cdot \cfrac{3^0-8^{-3}}{4^{-5}}\implies 8^{-2}\cdot \cfrac{1-\frac{1}{8^3}}{\frac{1}{4^5}}\implies 8^{-2}\cdot \cfrac{1-\frac{1}{(2^3)^3}}{\frac{1}{(2^2)^5}}$

$\bf 8^{-2}\cdot \cfrac{\quad \frac{512-1}{2^9}\quad }{\frac{1}{2^{10}}}\implies (2^3)^{-2}\cdot \cfrac{\quad \frac{511}{2^9}\quad }{\frac{1}{2^{10}}}\implies 2^{-6}\cdot \cfrac{511}{2^9}\cdot \cfrac{2^{10}}{1} \\\\\\ 2^{-6}\cdot \cfrac{511\cdot 2^{10}}{2^9}\implies 2^{-6}\cdot 511\cdot 2^{10}\cdot 2^{-9}\implies 2^{-6}\cdot 511\cdot 2^{10-9} \\\\\\ 2^{-6}\cdot 511\cdot 2\implies 511\cdot 2^{-6}\cdot 2\implies 511\cdot 2^{-6+1}\implies 511\cdot 2^{-5} \\\\\\ 511\cdot \cfrac{1}{2^5}\implies \cfrac{511}{32}$

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4 years ago

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trasher [3.6K]

Answer:

$volume = \pi {r}^{2} h \\ = \pi( {5}^{2} ) \times 6 \\ 150\pi \: cubic \: units$

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3 years ago

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