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3 years ago

A sphere shaped orange has a diameter of 7 centimeters. Find the volume of the orange to the nearest tenth.

Mathematics

1 answer:

krok68 [10]3 years ago

3 0

22cm^3

Step-by-step explanation:

My education system is different so I dont know what nearest tenth would mean in this .

But going mathematically:

Its diameter is 7 centimetres.

So to find its volume we can use the formula pi/d or pi/r^2

Now, 22/7÷7 would be 22cm³.

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What is the exponential function that best models the number of gnats the scientists have gathered after the number of hours lis

Serjik [45]

Answer:

Option A

f(x) = 12.5(1.6)^x

Step-by-step explanation:

The number of gnats the scientists have gathered

At 0 hours, they gathered 12 gnats.

Checking all the options, applying x = 0 makes the index part become 1 (Anything raised to the power zero is 1).

So, we have the following functions

f(x) = 12.5

f(x) = 12.6

f(x) = 6.2

f(x) = 1.6

This has reduced our work, as we can screen out options C and D, they are too far from 12. This leaves us with option A and B.

At 1 hour, they gathered 20 gnats.

Checking options A and B

A. f(x) = 12.5(1.6)

= 20

B. f(x) = 12.6(6.2)

By inspection, 12 × 6 is already 72,

12.6 × 6.2 will be more.

By these, we can conclude that f(x) = 12.5(1.6)^x has the best models the number of gnats the scientists have gathered after the number of hours listed in the given table.

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3 years ago

What elements of a rectangular prism are needed to find its volume?

Dmitry_Shevchenko [17]

Answer:

Height Length And Width

Step-by-step explanation:

The formula for the volume of a retangular prisim is Volume=Length x Width x Height

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2 years ago

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Step-by-step explanation:

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3 years ago

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

A sphere shaped orange has a diameter of 7 centimeters. Find the volume of the orange to the nearest tenth.​

A sphere shaped orange has a diameter of 7 centimeters. Find the volume of the orange to the nearest tenth.