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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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12. The geographic grid apportions the globe into hemispheres of 180 lines of longitude. Based on your knowledge of basic geomet
ANEK [815]

Answer:

For the first question, 180 degrees equals to a half of the sphere. For the second question, you need 24 central meridians for a complete sphere, which are exactly the hours in a day.

Step-by-step explanation:

A sphere is basically a 3D circle. As a circle has 360 degrees, 180 degrees would be half of a circle. Imagine you are on a satellite over the north pole or the south pole and you have a way to cut the earth by the middle. You will get two halves of sphere.

About the second question, you may need to have in mind that a day is the time spent for the earth to rotate all 360 degrees over its own axis. British fellow, on XIX century, decided they were the center of the world. As previously, back in the days, some other people decided a day had 24 hours, they decided to draw this lines and divide the earth in 24 pieces, so they could knew which time was on every point their extense kingdom had.  As I said, a circle has 360 degrees, (360 degrees)/(24 hours) equals to 15 degrees.

5 0
3 years ago
The school want to purchase enough tarp material to cover their field during bad weather. They want to get exactly eleven percen
KonstantinChe [14]

Answer:

6660 yards^2

Step-by-step explanation:

Assumption: the field is 120 yards long and 50 yards wide.

First calculate the area of the field: 120*50 = 6000 yards^2

Then, calculate the 11% of that area:  6000 yards^2*11/100 = 660 yards^2

Finally, the area of the tarp material should be 6000 yards^2 + 660 yards^2 = 6660 yards^2

5 0
3 years ago
Manuel hizo un viaje en el coche, en el cual consumió 20 litros de gasolina. El trayecto lo hizo en dos partes: en la primera, c
Alona [7]

Responder:

24 litros; 16 litros; 4 litros

Explicación paso a paso:

Dado que:

Gasolina consumida = 20 litros

Sea la cantidad de gasolina en el tanque = x

Primera parte del viaje = 2/3 de x

Segunda parte del viaje = 1/2 de (x - 2x / 3)

Cantidad de gasolina en el tanque:

2x / 3 + 1/2 (x - 2x / 3) = 20

Solución para x

2x / 3 + x / 2 - x / 3 = 20

(4x + 3x - 2x) / 6 = 20

5 veces / 6 = 20

5 veces = 20 * 6

5 veces = 120

x = 120/5

x = 24

Cantidad de gasolina en el tanque = 24 litros

Litros consumidos en cada etapa:

Primera parte = 2/3 de 24 = 48/3 = 16 litros

2a parte = 0.5 de (24 - 16) = 0.5 * 8 = 4 litros

3 0
3 years ago
Jonathan is signing a lease for an apartment that rents for $1240/month.
Leokris [45]
The answer would be $3472

8 0
3 years ago
Given f"(x) = 2, f'(1)=4, and f(2)=-2,<br> find f(x).
Anna [14]

Answer:

Step-by-step explanation:

f"(x)=2

integrating

f'(x)=2x+c

f'(1)=2+c=4

c=4-2=2

f'(x)=2x+2

integrating

f(x)=2x^2/2+2x+a

f(x)=x^2+2x+a

f(2)=-2

(2)^2+2(2)+a=-2

4+4+a=-2

a=-2-8=-10

f(x)=x^2+2x-10

6 0
2 years ago
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