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IceJOKER [234]
2 years ago
5

At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases

at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?
A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
Mathematics
2 answers:
algol [13]2 years ago
8 0

Answer:

  A)  dV/dt=-1.2x^2

Step-by-step explanation:

The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...

  dV/dt = -1.2x^2

VARVARA [1.3K]2 years ago
6 0

Answer:

C

Step-by-step explanation:

V(t) = [x(t)]³

A(t) = 6[x(t)]²

dV/dt = k × 6[x(t)]²

Where k < 0

From the options,

taking k = -0.2

dV/dt = -1.2[x(t)]²

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I can't figure out the second answer please help!!!
Mekhanik [1.2K]

Choice A is one of the answers. Nice work. This is because x+x+x turns into 3x.

Choice D is the other answer because 2(x+1) + x = 2x+2+x = 3x+2. You can find this through trial and error. Or you could graph y = x+x+x+2 and y = 2(x+1)+2 to find that they are the same exact identical diagonal line. A non-graph approach would be to set up a table of values to see that the two tables are identical.

3 0
2 years ago
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Nat2105 [25]

Answer:

m∠1 = 67

Step-by-step explanation:

8 0
2 years ago
What is the distance between the points (2, 4) and (-1,8)?
Sergeu [11.5K]

Answer:

use the distance formula

Step-by-step explanation:

d=_/(x1-x2)^2+(y1-y2)^2

plug the existing values into the formula for your answer. i don’t have a calculator atm so sorry

4 0
3 years ago
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When building a house, the number of days required to build varies inversely with with the number of workers. One house was buil
Helga [31]

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation y=\frac{k}{x} represents the relation where y is inversely proportional to x and k is the constant of proportionality.  

So our required equation would be d=\frac{k}{n}

Upon substituting our given values, we will get:

19=\frac{k}{35}

k=19\cdot 35

k=665

Since constant of proportionality is 665, so our equation would be d=\frac{665}{n}.

To find the number of days it will take to build a similar house with 5 workers, we will substitute n=5 in our equation as:

d=\frac{665}{5}

d=133

Therefore, it will take 133 days for 5 workers to build a similar house.

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2 years ago
Go through my questions there a surprise:)
gtnhenbr [62]

Answer:

I will do that buddy. I'll have fun

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2 years ago
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