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4 years ago

What is the answer to this question?

Mathematics

1 answer:

Serjik [45]4 years ago

5 0

Answer:

For 2 hours of dog stinting the total cost will be the same for the two services.

Step-by-step explanation:

x to represent the number of hours of dog sitting

Derrick's Dog Sitting

Fixed charged rates = $12

Sitting charges per hour = $7

⇒Charges for x hours siting = x ( Charges per hour)

= x ( $7) = 7x

⇒Total charges of Derrick's Dog Sitting for x hours = Fixed charge + Hourly Rate

= $7x + 12

 Darlene's Dog Sitting

Fixed charged rates = $16

Sitting charges per hour = $5

⇒Charges for x hours siting = x ( Charges per hour)

= x ( $5) = 5x

⇒Total charges of Darlene's Dog Sitting for x hours = Fixed charge + Hourly Rate

= $5x + 16

Now, according to the question:

for x hours sitting, both company charges are same.

⇒ $7x + 12 = $5x + 16

or, 7x - 5x = 16 - 12

or, 2x = 4

⇒ x = 2

Hence, for 2 hours of dog stinting the total cost will be the same for the two services.

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3 years ago

In each of Problems 5 through 10, verify that each given function is a solution of the differential equation.

WARRIOR [948]

Answer:

For First Solution: $y_1(t)=e^t$

$y_1(t)=e^t$ is the solution of equation y''-y=0.

For 2nd Solution: $y_2(t)=cosht$

$y_2(t)=cosht$ is the solution of equation y''-y=0.

Step-by-step explanation:

For First Solution: $y_1(t)=e^t$

In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

$y_1(t)=e^t$

First order derivative:

$y'_1(t)=e^t$

2nd order Derivative:

$y''_1(t)=e^t$

Put Them in equation y''-y=0

e^t-e^t=0

0=0

Hence $y_1(t)=e^t$ is the solution of equation y''-y=0.

For 2nd Solution:

$y_2(t)=cosht$

In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.

$y_2(t)=cosht$

First order derivative:

$y'_2(t)=sinht$

2nd order Derivative:

$y''_2(t)=cosht$

Put Them in equation y''-y=0

cosht-cosht=0

0=0

Hence $y_2(t)=cosht$ is the solution of equation y''-y=0.

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3 years ago