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PSYCHO15rus [73]

3 years ago

13

The wholesale price for a of shoes is $7.50. A certain department store marks up the wholesale price by 50%. Find the price of t

he pair of shoes th department store . Round your answer to the nearest cent , as necessary
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1 answer:

morpeh [17]3 years ago

4 0

Answer:

$11.25

Step-by-step explanation:

1.5×7.5=11.25

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Digiron [165]

Find ab….using your calculator

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2 years ago

I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur

Butoxors [25]

$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

Setting $x=5\sin\theta$ , you have $\mathrm dx=5\cos\theta\,\mathrm d\theta$ . Then the integral becomes

$\displaystyle\int\frac{\sqrt{25-(5\sin\theta)^2}}{5\sin\theta}5\cos\theta\,\mathrm d\theta$
$\displaystyle\int\sqrt{25-25\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{1-\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

to

$\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\dfrac{\cos^2\theta}{\sin\theta}\,\mathrm d\theta$

Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

$\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta$

Then integrate term-by-term to get

$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
$=-5\ln|\csc\theta+\cot\theta|+\cos\theta+C$

Now undo the substitution to get the antiderivative back in terms of $x$ .

$=-5\ln\left|\csc\left(\sin^{-1}\dfrac x5\right)+\cot\left(\sin^{-1}\dfrac x5\right)\right|+\cos\left(\sin^{-1}\dfrac x5\right)+C$

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

$=-5\ln\left|\dfrac{5+\sqrt{25-x^2}}x\right|+\sqrt{25-x^2}+C$

4 0

3 years ago

Read 2 more answers

Given the data, as shown in the image below, determine if the distribution is uniformly distributed, symmetrically distributed,

Sedbober [7]

Answer:

The distribution is symmetric.

Step-by-step explanation:

<em>The distribution will be skew left, if the data is more distributed on left side of graph.</em>

<em>The distribution will be right left, if the data is more distributed on right side of graph.</em>

<em>The distribution is symmetric if from the center, the data is distributed symmetrically, equal increase or decrease on either side.</em>

<em>The distribution is uniform if the value of data remains constant throughout the graph.</em>

Above here, the from the center, the data decreases symmetrically on both the sides, same values of data for Cat-Rabbit pair and Dog-Mice pair.

Thus, distribution is symmetric.

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3 years ago

PLEASE!! I REALLY NEED HELP WITH THIS!!!

ioda

Do you have an example of what the "Constant of proportionality" would be for a different question?

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3 years ago

Joe’s favorite basketball team is the Tigers. Joe’s favorite basketball team is in first place right now. What can you conclude?

Arturiano [62]

Answer:

The Tigers are in first place and Joe has a good taste in basketball teams. I'm not sure if you can conclude anything else from that.

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3 years ago