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AlladinOne [14]
3 years ago
13

Find the range of allowable values based on the given information. Round to the nearest tenth.

Mathematics
1 answer:
Firdavs [7]3 years ago
4 0

Answer:

24×3.5%=0.84 so round to nearest tenth is 0.9.

Step-by-step explanation:

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Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
0.27=_ hundredths<br><br>please help me​
Alexeev081 [22]

Answer:

27 hundredths

Step-by-step explanation:

.2 is in the tenths place,

.07 is in the hundredth place,

.27 is 27 hundredths

4 0
3 years ago
Read 2 more answers
What is 1/4x24 I need help
ZanzabumX [31]

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{6}}}}}

Step-by-step explanation:

\sf{ \frac{1}{4}  \times 24}

Multiply the numerators for the numerator , and multiply the denominators for its denominator and reduce the fraction obtained after Multiplication into lowest term

\dashrightarrow{ \sf{ \frac{1 \times 24}{4 \times 1}}}

\dashrightarrow{ \sf{ \frac{24}{4}}}

\dashrightarrow{ \sf{6}}

Hope I helped!

Best regards! :D

7 0
3 years ago
The volume of each cone round the answer to decimal places
snow_tiger [21]

Answer:

1. 322.01

Step-by-step explanation:

Formula: v=pi X r^2(h/3)

4 0
3 years ago
Is y = 0.860x + 3.302 a linear function?
gulaghasi [49]

Answer:

yes

Step-by-step explanation:

Yes.  The given function has the form y = mx + b, which is that of a linear function.  Here the slope, m, is 0.860, and the y-intercept is 3.302.

8 0
3 years ago
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