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matrenka [14]
3 years ago
14

Find the volume of the portion of the solid sphere rholess than or equals5 that lies between the cones variant phiequalsStartFra

ction pi Over 6 EndFraction and variant phiequalsStartFraction 5 pi Over 6 EndFraction .

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
5 0

Answer:

Volume = (250π√3)/3 unit³

Step-by-step explanation:

The shape is a solid sphere

Where rho = ρ

ρ ≤ 5

Where Phi = φ

φ = π/6 (lower limit)

φ = 5π/6 (upper limit)

Note 1π rad = 180°

We would apply triple integrals and spherical coordinates to solve for the volume of a solid sphere.

See attachment for details

From calculations,

The volume of the portion of solid sphere = Volume = (250π√3)/3 unit³

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Pls help in a middle of an exam
KIM [24]

Answer:

\frac{2x^2+4x-9}{(2x-3)(2x+3)(x-1)}

Step-by-step explanation:

\frac{2x}{4x^2-9} + \frac{3}{2x^2+x-3} can be simplified to:
\frac{2x}{(2x-3)(2x+3)}+\frac{3}{(2x+3)(x-1)}

Make them have common denominators so:
\frac{(2x)(x-1) +3(2x-3)}{(2x-3)(2x+3)(x-1)}

Simplify:
\frac{2x^2-2x+6x-9}{(2x-3)(2x+3)(x-1)} = \frac{2x^2+4x-9}{(2x-3)(2x+3)(x-1)}

I don't think you can simplify that fraction further so that's the answer.

3 0
2 years ago
If the length of each side of a cuboid decreases by 20%, find the percentage decrease in its volume.
just olya [345]

Answer:

Step-by-step explanation:

(1+25 /100) (1-20/100) (1-50/100)  <1

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(1+25 /100) (1-20/100) (1-50/100)  x 100

=48.8%

6 0
2 years ago
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OlgaM077 [116]
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4 0
3 years ago
Read 2 more answers
Which figure has the same area as the parallelogram shown below? A. A triangle with a base of 4 mm and a height of 20 mm B. A tr
Arisa [49]
<h2>Answer:  A trapezoid with bases of 6 mm and 14 mm and a height of 8 mm </h2>

The parallelogram in the figure has an area of 80mm^{2}, according to the following formula, which works for all rectangles and parallelograms:

A_{parallelogram}=(b)(h)   (1)

Where b is the base and h is the height

The<u> area of a triangle</u> is given by the following formula:

A_{triangle}=\frac{1}{2}(b)(h)   (2)

So, for option A:

A_{triangle}=\frac{1}{2}(4mm)(20mm)=40mm^{2} \neq 80mm^{2}    

Now, the <u>area of a trapezoid </u>is:

A_{trapezoid}=\frac{1}{2}(b_{1}+ b_{2})(h)   (3)

For option B:

A_{trapezoid}=\frac{1}{2}(15mm+25mm)(2 mm)=40mm^{2} \neq 80mm^{2}    

For option C:

A_{trapezoid}=\frac{1}{2}(6mm+14mm)(8 mm)=80mm^{2}>>>>This is the correct option!

For option D:

A_{rectangle}=(30mm)(8mm)=240mm^{2} \neq 80mm^{2}    

<h2>Therefore the correct option is C</h2>
5 0
3 years ago
2 tables. Table 1 is titled Population data with entries 2, 4, 8, 5, 1, 1, 10, 5, 4, 2, 3, 3. Table 2 is titled Sample data with
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Step-by-step explanation: EGDEUNITY

7 0
3 years ago
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