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trasher [3.6K]
3 years ago
13

A submarine dives to a depth of 54.6 meters below the surface of the water in 4 minutes. What integer represents the constant ra

te the submarine travels per minute? I need work with the answer to. step by step
Mathematics
1 answer:
Katen [24]3 years ago
8 0
Just divide the depth he dove by the time it took him to dive.

54.6 / 4 = 13.65

So he traveled at a constant rate of 13.65 meters a minute.
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A) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given cur
Leno4ka [110]

(a) See the attached sketch. Each shell will have a radius <em>y</em> chosen from the interval [2, 4], a height of <em>x</em> = 2/<em>y</em>, and thickness ∆<em>y</em>. For infinitely many shells, we have ∆<em>y</em> converging to 0, and each super-thin shell contributes an infinitesimal volume of

2<em>π</em> (radius)² (height) = 4<em>πy</em>

Then the volume of the solid is obtained by integrating over [2, 4]:

\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}

(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - <em>x</em> (this is the distance between a given <em>x</em> value in the orange shaded region to the axis of revolution) and a height of 8 - <em>x</em> ³ (and this is the distance between the line <em>y</em> = 8 and the curve <em>y</em> = <em>x</em> ³). Then each shell has a volume of

2<em>π</em> (9 - <em>x</em>)² (8 - <em>x</em> ³) = 2<em>π</em> (648 - 144<em>x</em> + 8<em>x</em> ² - 81<em>x</em> ³ + 18<em>x</em> ⁴ - <em>x</em> ⁵)

so that the overall volume of the solid would be

\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}

I leave the details of integrating to you.

3 0
3 years ago
Select the correct answer.
givi [52]

Answer:

B

Step-by-step explanation:

The cube of twice a number =

{2m}^{3}

Decreased by 11 =

- 11

Hence, the cube of twice a number decreased by 11 =

{2m}^{3}  - 11

7 0
3 years ago
For an acute angle θ, the equation sin (θ) = cos (7°)is true. What is the value of θ?
8_murik_8 [283]

Answer:

  θ = 83°

Step-by-step explanation:

For acute angles, the sine of an angle is the cosine of its complement, and vice versa.

__

  sin(θ) = cos(90° -θ) . . . . relation between sine and cosine

  sin(θ) = cos(7°) . . . . . . . . given

  90° -θ = 7° . . . . . . . . . matching arguments of cos( )

  θ = 83° . . . . . . . . . add θ -7° to both sides

5 0
2 years ago
Over the past year, your friend Maura has been saving up for an epic road trip to travel across the country this summer. Her goa
Misha Larkins [42]
<span>"Give an example of a sound financial decision Maura might make to support this goal. Why is it sound?"
<span>
</span>She could choose to carefully budget her trip and avoid overspending at all costs. This prevents going into debt. She should also save up extra money in the event of an emergency.

</span><span>Then give an example of a poor financial decision Maura might make considering her goal. Why is it a poor decision?</span><span>

Not having a plan would be a poor decision on her part. She could end up spending too much and not realize how much money she has left.


I hope I helped!
</span>
8 0
3 years ago
Which expression is equivalent to the square root of 120x
iren [92.7K]
(120x)^1/2 see attached photo for steps

5 0
4 years ago
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