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almond37 [142]
3 years ago
15

Jim needs to reach the gutters on his house which are 12 feet off the ground. If his ladder is 10 feet long, what is the maximum

distance away from the house he can rest the base of the ladder?
Mathematics
1 answer:
Setler [38]3 years ago
4 0
2 because he need  2 more feet    to reach
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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
2 years ago
When given the equation y = 3/4x − 6 , Find the x intercept and y intercept.
STALIN [3.7K]

Answer:

the y-intercept is (0,-6)

the x-intercept is (8,0)

Step-by-step explanation:

<em>Solving for the y-intercept:</em>

Since the equation 'y=3/4x - 6' is in the 'y=mx + c' form (where m is the slope and c is the y-intercept):

3/4 is m (which is the slope)

-6 is c (which is the y-intercept)

<em>Solving for the x-intercept:</em>

When the line intersects with the x-axis, the y-value is 0. Hence, the coordinate is (x,0). Substituting this into 'y=3/4x - 6':

0 = 3/4x - 6

3/4x - 6 + 6 = 6

3/4x = 6

x = 4/3 * 6

= 8

Hence,

the y-intercept is (0,-6)

the x-intercept is (8,0)

<em>Hope this helps and be sure to have a wonderful time ahead at Brainly! :D</em>

7 0
2 years ago
westfalls is 7 miles south of edenville and concord is 13 miles west of westfalls. what is the distance from edenville to concor
jok3333 [9.3K]

Answer:

The distance from Endnville to Concord = 14.8 miles

Step-by-step explanation:

∵ Westfalls is 7 miles South of Endnville

∵ Concord is 13 miles West of Westfalls

∵ South and West are ⊥

∴ The distance from Endnville to Concord = √(7)² + (13)²

                                                                      = 14.8 miles

7 0
3 years ago
I need help please help me pu
Luba_88 [7]

Answer:

D: x=12

Step-by-step explanation:

7 0
2 years ago
Which mountain range separates Georgia from Russia?<br>​
agasfer [191]

Answer:

Step-by-step explanation:

The Caucasus Mountains

6 0
3 years ago
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