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Bezzdna [24]
2 years ago
12

At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates proportional?

Mathematics
2 answers:
frutty [35]2 years ago
6 0
Michael:
3 books = $6
1 book = $6 ÷ 3 = $2

Darnell:
5 books = $10
1 book = $10 ÷ 5 = $2

Both Michael and Darnell bought their book at $2/book. The rates are proportional.

Answer Yes, the rate of proportional.
Doss [256]2 years ago
5 0
3 for $6 = 6/3 = $2/book
-------------↑-----------------
             Michael
_____________________________________________________________

5 for $10 = 10/5 = $2/book
---------------↑-------------------
              Darnell
_____________________________________________________________

Yes,they can form a proportion because they are equal

Hope this helps :)
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A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
creativ13 [48]

Answer:

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

2r+s=18

s=r \theta

2r+r \theta=18

solve for r

r=\frac{18}{2+\theta}

step 2

Find the value of s

s=r \theta

substitute the value of r

s=\frac{18}{2+\theta}\theta

step 3

we know that

The area of complete circle is equal to

A=\pi r^{2}

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}

substitute the value of r

A=\frac{(\frac{18}{2+\theta})^2\theta}{2}

A=\frac{162 \theta}{(\theta+2)^2}

Convert to function notation

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

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Answer:

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