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9966 [12]
3 years ago
11

The Rodriguez family went to dinner at at Pasta Palace. Mr. Rodriguez ordered a meal for $6.25; Mrs. R ordered a meal for $7.50;

the 2 children ordered individual pizzas for $4.99 each. The sales tax rate was 7.25% and they left a 15% tip. How much was the total bill.
Mathematics
1 answer:
lidiya [134]3 years ago
4 0
Cost of the meal ordered by Mr. Rodriguez = $6.25
Cost of the meal ordered by Mrs. Rodriguez = $7.50
Cost of each pizza ordered by the two children = $4.99
Then
The cost of the 2 pizzas ordered by the 2 children = (2 * 4.99) dollars
                                                                                 = 9.98 dollars
So
The total cost of the orders = (6.25 + 7.50 + 9.98) dollars
                                             = 23.73 dollars
Percentage of tip on the bill = 15%
Then
Amount of tip paid = (15/100) * 23.73 dollars
                              = 355.95/100 dollars
                              = 3.56 dollars
Percentage of tax paid on the bill = 7.25%
Amount of sales tax that was paid = (7.25/100) * 23.73 dollars
                                                       = 172.04/100 dollars
                                                       = 1.72 dollars
So
The total bill that was paid = (23.73 + 3.56 + 1.72) dollars
                                           = 29.01 dollars
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WINSTONCH [101]

Answer:

a) y(t) = y_{0}e^{4t} + 2. It does not have a steady state

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Step-by-step explanation:

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We have to find the eigenvalues of this differential equation, which are the roots of this equation:

r - 4 = 0

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So:

y_{n}(t) = y_{0}e^{4t}

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

y_{p}(t) = C

So

(y_{p})' -4(y_{p}) = -8

(C)' - 4C = -8

C is a constant, so (C)' = 0.

-4C = -8

4C = 8

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The solution in the form is

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y(t) = y_{0}e^{4t} + 2

b) y' +4y = 8

The first step is finding y_{n}(t). So:

y' + 4y = 0

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

r + 4 =

r = -4

So:

y_{n}(t) = y_{0}e^{-4t}

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

y_{p}(t) = C

So

(y_{p})' +4(y_{p}) = 8

(C)' + 4C = 8

C is a constant, so (C)' = 0.

4C = 8

C = 2

The solution in the form is

y(t) = y_{n}(t) + y_{p}(t)

y(t) = y_{0}e^{-4t} + 2

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x² - 100

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