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vodka [1.7K]
3 years ago
11

You have two circular flower beds, as shown. The sum of the areas of two flower beds is 136 pi square feet. Find the radius of e

ach bed.
Mathematics
1 answer:
finlep [7]3 years ago
8 0

Answer:

Radius of larger flower bed = 10 feet

Radius of smaller flower bed = 6 feet

Step-by-step explanation:

<u>Complete question:</u>

"You have two circular flower beds, as shown. The sum of the areas of two flower beds is 136 pi square feet. Find the radius of each bed.<em>"</em>

<em>Radius of larger flower bed = r</em>

<em>Radius of smaller flower bed = r - 4</em>

<em />

Now,

Area of circle is  \pi r^2

Since, total area is 136\pi, we can write:

\pi r^2 + \pi (r-4)^2=136\pi

Expanding and solving for r:

\pi r^2 + \pi (r-4)^2=136\pi\\r^2+(r-4)^2=136\\r^2 + r^2 - 8r + 16 = 136\\2r^2-8r-120=0\\2(r+6)(r-10)=0\\r=-6,10

Radius cannot be negative, so r = 10  &  r-4 = 10 -4 = 6

Radius of larger flower bed = 10 feet

Radius of smaller flower bed = 6 feet

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Answer: [0, 396]

Step-by-step explanation:

The domain is the acceptable values of x in the function.  In this case, x = t, the number of tiles.  If you think about it, the minimum number of tiles is 0 (you can't have a negative number of tiles), and the maximum number of tiles is 44 (you only have 44 tiles).  So, the domain for this function is from 0 to 44.

0 to 44 written in interval notation is [0,44].

The range is the acceptable values of y in the function.  In this case, y = A, the area given.  A(t) = 9t, so you can use the acceptable values of t to get the range.  Again, the minimum area is 0 because you can't have negative area. To find the maximum area, plug in the maximum number of tiles: 9.

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