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beks73 [17]
3 years ago
15

Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 + y2 = 25 and the sphere x2 + y2

+ z2 = 49.
Mathematics
1 answer:
Inessa05 [86]3 years ago
6 0

Answer:

Step-by-step explanation:

we are asked to find the volume of solid that lies within both the cylinder

x^2 + y^2 = 25

and

the spherex^2 + y^2 + z^2 = 49.

Conversion from rectangular to cylindrical is

x=rcost\\y = rsint\\z=z

|J| =r

In cylindrical coordinates the volume is bounded by the cylinder r=5 and

r^2+z^2 =49

Hence we can write volume as

\int \int \int dxdydz\\=\\\int _0^5 \int_0^{2\pi} \int_{-\sqrt{49-r^2} } ^{\sqrt{49-r^2} rdzdtdr\\= 2\pi \int _0^5 (2\sqrt{49-r^2} rdr\\=4\pi (-(49-r^2) (2/3)\\= \frac{4\pi}{3} (343-48\sqrt{6} )

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Write the equation of the line that passes through the points (-6, -9) and
e-lub [12.9K]

Answer:

y - 7 = 16/13(x - 7)

General Formulas and Concepts:

<u>Alg I</u>

Point-Slope Form: y - y₁ = m(x - x₁)  

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  • y₁ - y coordinate
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Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (-6, -9)

Point (7, 7)

<u>Step 2: Find slope </u><u><em>m</em></u>

  1. Substitute:                   m=\frac{7+9}{7+6}
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<u>Step 3: Write equation</u>

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Imagine a recessive mutation in rabbits that causes wiry fur (whereas the dominant, normal allele causes fluffy fur). If two het
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Answer: the required probability is  0.03516

Step-by-step explanation:

Given the data in the question;

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ff = Wiry fur

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and there cross will be; Ff x Ff

now Offspring will be;

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F                                FF                    Ff

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and the probability that the offspring will have wiry fur = 1/4

The probability that the first 2 out of 4 offspring will have fluffy fur will be;

⇒ 3/4 × 3/4 × 1/4 × 1/4 =  0.03516

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Answer:

32.33 <= m

Step-by-step explanation:

Since we are dealing with below sea level our initial starting point and max level will both be negative values, while our descending rate will also be negative because we are going down. Using the values provided we can create the following inequality...

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Now we can solve the inequality to find the max number of minutes that the submarine can descend.

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