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fomenos
2 years ago
5

Solve the proportion: 1/4 = x/20

Mathematics
2 answers:
tangare [24]2 years ago
8 0

Answer:

= 5

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators

1/4 = x/20

20 ⋅ 1/4 = 20 ⋅ /20

Simplify

= 5

matrenka [14]2 years ago
5 0

Answer:

5x?

Step-by-step explanation:

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The volume of sphere is increaseing
Artemon [7]

Volume of a sphere:

<em>V</em> = 4/3 <em>π</em> <em>r</em> ³

Differentiate <em>V</em> with respect to time <em>t</em> :

d<em>V</em>/d<em>t</em> = 4<em>π</em> <em>r</em> ² d<em>r</em>/d<em>t</em>

Surface area of a sphere:

<em>A</em> = 4<em>π</em> <em>r</em> ²

Differentiate <em>A</em> with respect to <em>t</em> :

d<em>A</em>/d<em>t</em> = 8<em>π</em> <em>r</em> d<em>r</em>/d<em>t</em>

<em />

You're given that the volume is increasing at a constant rate, d<em>V</em>/d<em>t</em> = 10 cm³/s, so

10 cm³/s = 4<em>π</em> <em>r</em> ² d<em>r</em>/d<em>t</em>

Solve for d<em>r</em>/d<em>t</em> (the rate of change of the sphere's radius):

d<em>r</em>/d<em>t</em> = 5/(2<em>π</em> <em>r</em> ²) cm³/s

Substitute this into the equation for d<em>A</em>/d<em>t</em> :

d<em>A</em>/d<em>t</em> = 8<em>π</em> <em>r</em> (5/(2<em>π</em> <em>r</em> ²) cm³/s)

d<em>A</em>/d<em>t</em> = 20/<em>r</em> cm³/s

At the moment the radius is <em>r</em> = 5 cm, the surface area is increasing at a rate of

d<em>A</em>/d<em>t</em> = 20/(5 cm) cm³/s = 4 cm²/s

When the surface area is increasing at a rate of d<em>A</em>/d<em>t</em> = 2 cm²/s, the radius <em>r</em> is such that

2 cm²/s = 20/<em>r</em> cm³/s

which happens when the radius is

<em>r</em> = 20/2 (cm³/s) / (cm²/s) = 10 cm

4 0
3 years ago
Which graph represents the solution set of the system of inequalities?<br><br> x+y&lt;1, 2y≥x−4
Sophie [7]

The graph to the top left

7 0
3 years ago
Similar triangles what the answer
anzhelika [568]

Answer:

x=8

Step-by-step explanation:


4 0
3 years ago
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Find the area of the figure.
mel-nik [20]

Answer:

192+128+112+36=468 not really sure if this is the answer

4 0
3 years ago
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One minute after it is released, a hot-air balloon rises 120 feet. In each succeeding minute, the balloon rises only 60% as far
MArishka [77]

Answer:

25.92 feet

Step-by-step explanation:

In the first minute, the hot air balloon rises 120 feet.

And it is given that, the balloon rises in a minute only 60% of the height it rose in the previous minute.  

Therefore, in the second minute, the balloon rises by (120×0.6) =72 feet

And in the third minute, the balloon rises by (72×0.6) =43.2 feet

Hence, in the fourth minute, the balloon rises by (43.2 ×0.6) =25.92 feet (Answer)

7 0
3 years ago
Read 2 more answers
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