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Molodets [167]
3 years ago
12

Mr. and Mrs. Delgado each own an equal number of shares of stock. Mr. Delgado sells 1/3 of his shares for $2700. What was the to

tal value of Mr. and Mrs. Delgado's stock before the sale
Mathematics
1 answer:
lesya [120]3 years ago
8 0
The total value before stock sold would be $16,200 
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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
Perform the indicated operation. (-7) • (-5)<br> -12 <br> 35<br> 12<br> -35
Flauer [41]
Hi,


Equation:

- 7 \times  (- 5)

Multiplying two negatives equals a positive.

( - ) \times ( - ) = ( + )

Now equation looks like:

7 \times 5 = 35

Hope this helps.
r3t40
6 0
3 years ago
Read 2 more answers
PLEASE HELP MEEEE!!!!
Vlad [161]

Answer:

  A.  P(n) = 12·2^n

Step-by-step explanation:

From one generation to the next, the population grows by a factor of ...

  24/12 = 2

Only one offered expression is an exponential function with a base of 2:

  P(n) = 12·2^n

7 0
2 years ago
In AQRS OR=7, RS=11 M&lt;=42 IN AUVT VT=26, TU= 44 M
N76 [4]
I think the answer to In AQRS OR=7, RS=11 M<=42 IN AUVT VT=26, TU= 44 M is THE TRIANGLES ARE NOT SIMILAR.
6 0
3 years ago
0.09 is one tenth of
liq [111]
<u>0.09</u> = <u>1 </u>
0.9      10

I hope this helps.

4 0
3 years ago
Read 2 more answers
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