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Luden [163]
3 years ago
11

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
1 answer:
True [87]3 years ago
5 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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In order to solve this, you have to plug in all of the costs of the gifts and add them, which in all equals $36. since jim only has 1/4 of the money he needs to buy the gifts, you need to divide 36 by 4. this gives you 9, so now you know he has 9 dollars.
and to find out how much more money he needs, you can subtract 9 from 36 which represents a fourth of the required money. the answer is 27, that's how much jim needs in order to buy his gifts.
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The answer to your question is 1/4
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Determine whether the slope line is positive or negative and then find the slope of each line?
goldenfox [79]
I he slope line is negative
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3 years ago
A small resort is situated on an island that lies exactly 3 miles from P, the nearest point to the island along a perfectly stra
Artemon [7]

Answer:

The distance from the  shoreline from P the pipe from the island will reach land in order to minimize the total construction cost is 0 m, or the pipe should be routed to the point P

Step-by-step explanation:

We note that, cost to lay pipe in water = 2.3 × cost to lay pipe on land

Distance of the small resort on the island from point p on the shoreline = 3 miles

Location of the closest source of fresh water is 10 miles along the shoreline from p

∴ The small resort, the point p and the closest source of the fresh water on the shoreline together form a right triangle with sides

Height = 3 miles

Base = 10 miles and

Hypotenuse = \sqrt{3^2 + 10 ^2} = \sqrt{109} =  10.44 \, m

To find the cost of laying the pipeline by the various route, we multiply the water routes by 2.3 and the land routes by 1 and we get

Costs:

Height =  Water route = 2.3 × 3 miles = 6.9

Base = Land route = 1 × 10 miles = 10

Hypotenuse = Water route = 2.3 × 10.44 miles = 24.012

Therefore, the two routes are either

10 miles to point p and 3 miles across the water to the resort with a cost = 10 + 6.9 = 16.9 or

Directly to the small resort through 10.44 miles across the water with cost = 24.012

Therefore, to minimize cost, the pipe should come from the resort to P from there to the fresh water source.

That is the distance from the  shoreline from P the pipe from the island will reach land in order to minimize the total construction cost = 0 m.

7 0
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Answer:

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#teamtrees #WAP (Water And Plant)

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