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andriy [413]
3 years ago
7

A food manufacturer uses an extruder (a machine that makes bite size cookies)that yields revenue for the firm at a rate of $200

per hour when in operation. However, the extruder breaks down an average of two times every day it operates. If Y denotes the number of breakdowns per day, the daily revenue generated by the machine is
R=1600−50Y².
Find the expected daily revenue for the extruder.
Mathematics
1 answer:
julsineya [31]3 years ago
3 0

Answer:

$1300

Step-by-step explanation:

The extruder yields a revenue of $200per hour

Y denotes the number of breakdown per day.

The daily revenue generated is given as

R = 1600 - 50Y^2

We have an average of 2 breakdown per day

Lamda = 2

Represent lamda as β

E(Y) = β

E(Y(Y-1)) = β^2

E(Y^2) = E[Y(Y-1)] + E(Y)

= β^2 + β

E(R) = E(1600 - 50Y^2)

= 1600 - 50E(Y^2)

= 1600 - 50(β^2 +β)

Recall that β = lamda = 2

= 1600 - 50(2^2 + 2)

= 1600 - 50(4+2)

= 1600 - 50(6)

= 1600 - 300

= 1300

$1300

The expected daily revenue of the extruder is $1300

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Answer:

D = L/k

Step-by-step explanation:

Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is

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Since litter falls at a constant rate of L  grams per square meter per year, in flow = L

Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow

So,

dA/dt = in flow - out flow

dA/dt = L - Ak

Separating the variables, we have

dA/(L - Ak) = dt

Integrating, we have

∫-kdA/-k(L - Ak) = ∫dt

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1/k㏑(L - Ak) = t + C

㏑(L - Ak) = kt + kC

㏑(L - Ak) = kt + C'      (C' = kC)

taking exponents of both sides, we have

L - Ak = e^{kt + C'} \\L - Ak = e^{kt}e^{C'}\\L - Ak = C"e^{kt}      (C" = e^{C'} )\\Ak = L - C"e^{kt}\\A = \frac{L}{k}  - \frac{C"}{k} e^{kt}

When t = 0, A(0) = 0 (since the forest floor is initially clear)

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So, D = R - A =

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when t = 0(at initial time), the initial value of D =

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3 years ago
Which expression is equivilent to 6(3x-4)+2x
motikmotik

Answer:

44x,

Step-by-step explanation:

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4 0
2 years ago
I'm having a hard time with this question so someone help please
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Answer:

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Step-by-step explanation:

This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.

<h3>Law of Sines</h3>

The Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...

  t/sin(T) = p/sin(P) = j/sin(J)

We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.

<h3>Setup</h3>

We know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:

  7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j

<h3>Solution</h3>

This can be solved in two steps. First, we find angle P, then we use that to find length j.

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Now, we can find j:

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The distance from the tower to the plane is about 7.7 km.

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<em>Additional comment</em>

We have used T, P, and J to refer to the vertices at the tower, plane, and jet.

The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.

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