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3 years ago

There is three fourths of a box of cereal remind you eat 2/5 of the remaining cereal what fraction of the box do you eat

Mathematics

1 answer:

Alinara [238K]3 years ago

8 0

First you convert them to 15/20 then 8/20 after that subract them, so 7/20

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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 y chosen from the interval [2, 4], a height of x = 2/y, and thickness ∆y. For infinitely many shells, we have ∆y converging to 0, and each super-thin shell contributes an infinitesimal volume of

2π (radius)² (height) = 4πy

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 - x (this is the distance between a given x value in the orange shaded region to the axis of revolution) and a height of 8 - x ³ (and this is the distance between the line y = 8 and the curve y = x ³). Then each shell has a volume of

2π (9 - x)² (8 - x ³) = 2π (648 - 144x + 8x ² - 81x ³ + 18x ⁴ - x 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

Find the midpoint of the segment with the following endpoints. (5,5) and (10,8)

Solnce55 [7]

Answer: G

Step-by-step explanation:

8 0

3 years ago

A microscope can magnify the object it is looking at 10×4 times. How many times is that? (MCC.8.EE.3) A. 40,000 times B. 40 time

damaskus [11]

Answer:

10×4 = 40

10^4 = 10,000

Step-by-step explanation:

10^4 is another way to write 10⁴ = 10·10·10·10 = 10,000.

Essentially, the exponent tells you how many places to the right of the leading digit the decimal point lies (here, the number of zeros in the number).

_____

Comment on the answer choice

The appropriate answer depends on what you mean by your problem statement. Some microscopes magnify 40 times; others magnify 10,000 times, so we cannot tell the appropriate answer using our knowledge of microscopes.

3 0

3 years ago

Complete the steps to solve 1.02 ÷0.06

ki77a [65]

Answer:

your answer is 17 hope I helped

7 0

3 years ago

Read 2 more answers

the sides of a triangle are in the ratio 3: 4: 5 what is the lenghth of each side if the perimeter of the triangle is 90cm

ehidna [41]

3x+4x+5x=90

combine like terms

12x = 90

divide by 12

x = 7.5

sides: 3(7.5) ,4(7.5) ,5(7.5)

22.5, 30, 37.5

6 0

4 years ago