Mathematics : asked on perez120
 06.06.2023

A jogger runs along a straight track. The jogger’s position is given by the function p(t), where t is measured in minutes since the start of the run. During the first minute of the run, the jogger’s acceleration is proportional to the square root of the time since the start of the run. Write a differential equation that describes this relationship, where k is a positive constant?

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Step-by-step answer

17.02.2022, solved by verified expert
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The required differential equation will be A jogger runs along a straight track. The jogger’s, №15222578, 06.06.2023 09:12 or A jogger runs along a straight track. The jogger’s, №15222578, 06.06.2023 09:12.

Given information:

A jogger runs along a straight track. The jogger’s position is given by the function p(t), where t is measured in minutes since the start of the run.

During the first minute of the run, the jogger’s acceleration is proportional to the square root of the time.

Let a be the acceleration of the jogger.

So, the expression for acceleration can be written as,

A jogger runs along a straight track. The jogger’s, №15222578, 06.06.2023 09:12

Now, the acceleration is proportional to square root of time.

So,

A jogger runs along a straight track. The jogger’s, №15222578, 06.06.2023 09:12

Therefore, the required differential equation will be A jogger runs along a straight track. The jogger’s, №15222578, 06.06.2023 09:12 or A jogger runs along a straight track. The jogger’s, №15222578, 06.06.2023 09:12.

For more details about differential equations, refer to the link:

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Faq

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

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