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3 years ago

Emilie is training for her next track meet. She is running on

Mathematics

1 answer:

Shkiper50 [21]3 years ago

4 0

Answer:

32 laps

Step-by-step explanation:

If each mile is 1600 meters, she will need to run 4 laps per mile. To run 8 miles, multiple the laps for one mile (4) by the total number of miles (8) to get the total laps necessary (32).

Hope this helps!

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What is the equation in point-slope form of the line that passes through the point (−1, −4) and has a slope of –3 ?

sp2606 [1]

Answer:

y + 4 = -3(x + 1)

Step-by-step explanation:

point-slope form : y - y2 = m (x - x2)

In this case m = -3 and x2 = -1, y2 = -4

The equation in point-slope form

y + 4 = -3(x + 1)

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3 years ago

Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

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3 years ago

A restaurant customer left $1.80 as a tip. The tax was 5% and the tip was 20% of the after tax cost. Which information is not ne

zhenek [66]

Answer:

it's b

Step-by-step explanation:

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3 years ago

Zeb wants to make the world's longest shoelace. He has a shoelace that is 22 cm long and another shoelace that is 7 cm longer th

yawa3891 [41]

The correct answer would be 51 cm.

Hope this helps.

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3 years ago

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Solve the inequality. 5 - 4x > 3x - 9

Olegator [25]

Answer:

2 >x

Step-by-step explanation:

5 - 4x > 3x - 9

Add 4x to each side

5 - 4x+4x > 3x+4x - 9

5 > 7x-9

Add 9 to each side

5+9> 7x-9+9

14>7x

Divide each side by 7

14/7 >7x/7

2 >x

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3 years ago

Read 2 more answers