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emmasim [6.3K]
3 years ago
6

Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate

slowly. If v is the volume of such a cube with side length x, calculate the derivative when x = 4 mm.
Mathematics
1 answer:
Setler79 [48]3 years ago
6 0

Answer:

48 mm ^ 2

Step-by-step explanation:

We know we have a cube of side x, therefore the volume of that cube will be equal to:

V = x ^ 3, because it is a cube and each side is the same.

Now the derivative of the volume with respect to the length (that is, x) would be:

dV / dx = 3 * (x ^ 2)

They tell us that x takes a value of 4, replacing we have:

dV / dx = 3 * (4 ^ 2) = 48

That is, 48 mm ^ 2 would be the value of dV / dx when x is equal to 4 mm.

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Mandarinka [93]

Answer:

Volume of a cup

The shape of the cup is a cylinder. The volume of a cylinder is:

\text{Volume of a cylinder}=\pi \times (radius)^2\times heightVolume of a cylinder=π×(radius)

2

×height

The diameter fo the cup is half the diameter: 2in/2 = 1in.

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\text{Volume of the cup}=\pi \times (1in)^2\times 4in\approx 12.57in^3Volume of the cup=π×(1in)

2

×4in≈12.57in

3

2. Volume of the sink:

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This gives the number of cups that contain a volume equal to the volume of the sink:

\dfrac{1072in^3}{12.57in^3}=85.3cups\approx 85cups

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Step-by-step explanation:

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