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3 years ago

A 54-kg jogger is running at a rate of 3 m/s. What is the kinetic energy of the jogger? A. 18 J B. 81 J C. 162 J D. 243 J

Mathematics

2 answers:

Mrrafil [7]3 years ago

5 0

Answer:

The answer would be be D.243 j

Step-by-step explanation:

Wewaii [24]3 years ago

4 0

$\displaystyle\bf\\\text{\bf kinetic energy}=\frac{mv^2}{2}=\frac{54\times3^2}{2}=27\times9=\boxed{\bf243~J} \\\\\text{\bf Correct answer: D.}$

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sweet [91]

Answer: The answer is 35 minutes.

Step-by-step explanation: Given that Gavin goes for a run at a constant pace of 9 minutes per mile and after 10 minutes, Lars started running along the same route, at a constant pace of 7 minutes per mile. We need to find the number of minutes Lars will take to reach Gavin.

In 9 minutes, distance run by Gavin = 1 mile.

So, in 1 minute, distance travelled by Gavin will be

$d_G=\dfrac{1}{9}=\dfrac{7}{63}~\textup{miles}.$

Similarly,

In 7 minutes, distance run by Lars = 1 mile.

So, in 1 minute, distance travelled by Lars will be

$d_L=\dfrac{1}{7}=\dfrac{9}{63}~\textup{miles}.$

Now, since Lars started after 10 minutes, so distance run by Gavin in those 10 minutes will be

$d_{G10}=\dfrac{10}{9}=\dfrac{70}{63}~\textup{miles}.$

Now, difference between Lars and Gavin's rate of runnings is

$\dfrac{9}{63}-\dfrac{7}{63}=\dfrac{2}{63}.$

Therefore, the time taken by Lars to reach Gavin is given by

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Thus, the required time is 365 minutes.

6 0

3 years ago

Simplify cos^2 A/1+sin A

Stels [109]

Answer:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

Step-by-step explanation:

We want to simplify:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}$

Recall the Pythagorean Identity:

$\sin^2(A)+\cos^2(A)=1$

So:

$\cos^2(A)=1-\sin^2(A)$

Substitute:

$\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}$

Factor. We can use the difference of two squares pattern:

$\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}$

Cancel. Hence:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

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2 years ago

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Answer:

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Step-by-step explanation:

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