1. Convert 30 ft per s to mi per min.

1 answer:

4 0

In converting measurements, we use conversion factors to multiply to the given value. For the first item, the conversion factor would be 5280 ft = 1 mi and 1 min = 60 s. We calculate as follows:

30 ft / s ( 1 mi / 5280 ft ) ( 60 s / 1 min ) = 0.34 mi / min

For the second item, we calculate as follows:

Turtle's speed: 12 mi / hr ( 5280 ft / 1 mi ) ( 1 yd / 3 ft ) (1 hr / 60 min) = 352 yd / min

Boy's speed: 4.4 ft / s ( 1 yd / 3 ft ) ( 60 s / 1 min ) = 88 yd / min

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Find the area of the shaded region. round answers to the nearest tenth. assume all inscribed polygons are regular. 29.3 units2

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The picture in the attached figure

we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]

step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²

step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²

step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²

therefore

the answer is
the area of the shaded region is 44.22 units²