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3 years ago

Chris is trimming trees. He can trim 2/3 of a tree in 1/2 hour. At what rate can Chris trim trees

Mathematics

1 answer:

Sedbober [7]3 years ago

7 0

For every hour he can trim 1 1/3 tree.

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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.

6 0

2 years ago

Andrew has a Frisbee™ with a radius of 5 cm. What is the approximate circumference of the Frisbee™?

Natasha2012 [34]

Answer:

the circumference of the dics is 62.8cm

Step-by-step explanation:

8 0

3 years ago

Makato and his friends rolled two fair number cubes 500 times and recorded the sum of the numbers shown on the cubes each time.

denpristay [2]

Answer:

2:12

Step-by-step explanation:

6 and 4 = 10

5 and 5 = 10

8 0

3 years ago

How would I divide this?

Lorico [155]

56/1 x 11/8 here is the equations now just multiply them

4 0

3 years ago

Read 2 more answers

Help with 12!! ASAP will gove brainliest!! How to find the surface area!!

Shkiper50 [21]

Answer: 659 13/18 yd^2 or 659.7yd^2 ^ =squared

Step-by-step explanation:

This is the answer because you have 6 sides of this prism. That means 3 sides are parallel to the sides across from them. So, 12 1/2 yd by 8 1/3 yd is 104 1/6, then multiply by 2. That equals 208 1/3. Then, 10 5/6 yd by 8 1/3 yd is 90 5/18. then times by 2. That equals 180 5/9. Next, 10 5/6yd by 12 1/2 is 135 and 5/12. then times by 2 and that is 270 5/6yd.

add 208 1/3 + 180 5/9 + 270 5/6

659 13/18 yd^2

3 0

3 years ago