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Vlad1618 [11]
2 years ago
11

Peter takes 7 minutes and 30 seconds to run 1 mile. How many miles can he run in 15 minutes?

Mathematics
1 answer:
Snezhnost [94]2 years ago
4 0

Answer:

2 miles

Step-by-step explanation:

Peter takes 7 minutes and 30 seconds per mile.

7 times 2 is 14 minutes.

30 seconds times 2 is 1 minute.

If you add these 2 values together you get 15 minutes.

So we need to times the miles by 2 to get 2 miles.

I hope this helps, have a lovely day.

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Find the area of the region that lies inside the first curve and outside the second curve.
marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = \dfrac{1}{2}

\theta = -\dfrac{\pi}{3}, \ \  \dfrac{\pi}{3}

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \  \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \  5^2 d \theta

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \  \theta  d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \   d \theta

A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  \dfrac{cos \ 2 \theta +1}{2}  \end {pmatrix} \ \ d \theta - \dfrac{25}{2}  \begin {bmatrix} \theta   \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}

A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  {cos \ 2 \theta +1}  \end {pmatrix} \ \    d \theta - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}}    \ \ - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{2 \pi}{3} \end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3})  \end {bmatrix} - \dfrac{25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} +   \dfrac{\pi}{3}  \end {bmatrix}- \dfrac{ 25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3}   \end {bmatrix}- \dfrac{ 25 \pi}{3}

A =    \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx
7 0
3 years ago
Benito rune 1/10 of a mile each day. Which shows how to find the number of days it will take for Benito to run 3/5 of a mile
juin [17]
It'll take him 6 days to run 3/5 of a mile.... 

6 0
3 years ago
Read 2 more answers
Please help ASAP. The picture is above
Setler [38]
Every triangle’s inner angles’ addition equals to 180°
So if we find the x:
38°+x+2°+x=180°
40°+2x=180°
2x=180°-40°=140°
x=140°/2
x=70°
Now if we find the I hope this helped :)
7 0
2 years ago
Read 2 more answers
Your famous cookie recipe calls for
damaskus [11]

Answer:

I GOT -42 SO LIKE 4 1/2

Step-by-step explanation:

3 0
3 years ago
Help&amp;EXPLAIN <br> •••••••••••••••••••
TiliK225 [7]

Answer:

68cm^2

Step-by-step explanation:

Well there's not much to explain - the problem statement does it for us.

The surface area is equal to the sum of areas of the walls. There's 2 l*w walls, 2 l*h walls and 2 h*w walls.

SA = 2*l*h + 2*l*w + 2*h*w

SA = 2*4cm*6cm + 2*4cm*1cm + 2*6cm*1cm = 48cm^2 + 8cm^2 + 12cm^2 = 68cm^2

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3 years ago
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