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Monica [59]
3 years ago
15

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $27 monthly fee

and charges an additional $0.12 for each minute of calls. The second plan has no monthly fee but charges $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Mathematics
1 answer:
NikAS [45]3 years ago
4 0
The first plan : y = 27 + 0.12x
Second plan : y = 0.16x

27 + 0.12x= 0.16x
27 = 0.04x

x = 67.5 minutes
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Shalnov [3]

Answer:

Step-by-step explanation:

Volume of tank is 3000L.

Mass of salt is 15kg

Input rate of water is 30L/min

dV/dt=30L/min

Let y(t) be the amount of salt at any time

Then,

dy/dt = input rate - output rate.

The input rate is zero since only water is added and not salt solution

Now, output rate.

Concentrate on of the salt in the tank at any time (t) is given as

Since it holds initially holds 3000L of brine then the mass to volume rate is y(t)/3000

dy/dt= dV/dt × dM/dV

dy/dt=30×y/3000

dy/dt=y/100

Applying variable separation to solve the ODE

1/y dy=0.01dt

Integrate both side

∫ 1/y dy = ∫ 0.01dt

In(y)= 0.01t + A, .A is constant

Take exponential of both side

y=exp(0.01t+A)

y=exp(0.01t)exp(A)

exp(A) is another constant let say C

y(t)=Cexp(0.01t)

The initial condition given

At t=0 y=15kg

15=Cexp(0)

Therefore, C=15

Then, the solution becomes

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5 0
3 years ago
Write 0.00605 in scientific notation.
vichka [17]
How many jumps is it from the decimal point to the position to the right of the 6

The answer to that is 3 jumps.  Since the move of the decimal made the number larger than it really is, it will take a negative value to put it back where it belongs.

So A) is the correct answer.  It is in scientific notation and if you move the decimal back 3 place you get the number you stared with.
5 0
3 years ago
I don't have any idea. ​
kaheart [24]

Answer:

Domain = ( -∞,∞), {x|x ∈  R}

Range (-∞,2], {y|y ≤ 2}

Vertex (h,k) = (6,2)

Step-by-step explanation:

(Domain / Range) The absolute value expression has a V shape. The range of a negative absolute value expression starts at its vertex and extends to negative infinity.

(Vertex) To find the x coordinate of the vertex, set the inside of the absolute value

x − 6 equal to 0 . In this case, x − 6 = 0 .

x−6=0

Add 6 to both sides of the equation.

x=6

Replace the variable x with 6 in the expression.

y=−1/3⋅|(6)−6|+2

Simplify−1/3⋅|(6)−6|+2.

y=2

The absolute value vertex is ( 6 , 2 ) .

(6,2)

Hope this helps

6 0
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Tony's taking cookies to a bake sale. He already made 70 cookies on Monday, and wants to make more on Tuesday. His plan allows h
kotegsom [21]
70+14 x 7 =168 :-]  :-]  :-]

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Jeff is 15 years from retiring. He opens an account at the First American Bank. He plans to deposit $1,406.14 each month into th
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Ok 1,506.14 x (12x15) divide by 5.27 I think..

6 0
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