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Scrat [10]
3 years ago
7

Oil is leaking from a tanker at the rate of R(t) = 2000e^(-0.2t) gallons per hour where t is measured in hours. How much oil lea

ks out of the tanker from the time t = 0 to t = 10
...?
Mathematics
1 answer:
Kipish [7]3 years ago
6 0
The calculation of the integral will give us the answer.

Amount = Int (2000e^(-0,2t))dt

With t = 0 to t = 10

A = 2000.In(e^(-0,2t))dt


Making U = -0,2t

U = -0,2t

dU/dt = d(-0,2t)/dt

dU/dt = -0,2

dU = -0,2dt

dt = dU/-0,2
_______________


Then,

A = 2000.Int (e^U).dU/-0,2

A = -10.000.Int(e^U)dU

A = -10.000.e^U

A = -10.000.e^(-0,2t) | (0,10)

A = -10.000.(e^(-2)) - [ -10.000.e^(0)]

A = -10.000.e^(-2) + 10.000

A ~ 8,646 Gallons


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It is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).

<h3>What are the domain and range of a function?</h3>
  • The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x).
  • A function's range is the set of values that the function can take.
  • This is the set of values that the function returns after we enter an x value.

To find the domain and range:

  • The given function in the problem is: g(x)=\sqrt{x+4}
  • Because the square root function does not exist for negative numbers, the domain is denoted by: x+4 ≥ 0 → x ≥ -4
  • Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).
  • The range of the square root function is x ≥ 0, which remains the same as there are no vertical translations.

Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).

Know more about the range here:

brainly.com/question/26098895

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The complete question is given below:

What are the domain and range of g of x equals the square root of the quantity x plus 4?

(A) D: [4, ∞) and R: [0, ∞)

(B) D: (–4, ∞) and R: (–∞, 0)

(C) D: [–4, ∞) and R: [0, ∞)

(D) D: (4, ∞) and R: (–∞, 0)

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