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3 years ago

6

Drag and drop the constant of proportionality into the box to match the table. If the table is not proportional, drag and drop "

not proportional" into the box.

2 answers:

Nonamiya [84]3 years ago

4 0

3

To find the constant of proportionality, you divide x from y.

6/2= 3

9/3= 3

12/4= 3

15/5= 3

So, the constant of proportionality is 3.

lisov135 [29]3 years ago

3 0

Answer:

3 is your answer

Step-by-step explanation:

y divided by x gives the proportionality

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It is impossible to get 6 jacks when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a proba

Vinil7 [7]

Answer:

Probability = 0

Step-by-step explanation:

If something happening is impossible, it's probability of occurring is also 0.

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Since we are not replacing the cards once we pick them, this event is impossible to occur.

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4 years ago

4-1/x divided by 16-1/xsquared

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4 - 1/x (16)-1/x 2
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3 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

Simplify the expression 1+2*[(3+1)*5+3]

Lady bird [3.3K]

1 + 2 *[(3+1)*5+3]

= 1 + 2*[(4)*5+3]

= 1 + 2*[20+3]

= 1 + 2 * 23

= 1 + 46

= 47

Answer

c. 47

7 0

3 years ago

Read 2 more answers

Explain how to use 8×5=40 to find 8×6.

Zina [86]

Answer:

Well there are many different ways to find 8x5=40 to 8x6=__

You could add 8 to 40 and get 48.

or you could draw pictures to represent the 48.

8x6=48

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3 years ago