What ratios are equivalent to 5/9
1 answer:
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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
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
Let's assume
x represent the number of trips that the larger truck makes
so, we are given
If the smaller truck makes 18 more trips than the larger
so,
number of trips for larger truck =x
number of trips for smaller truck =x+18
The capacities of two trucks are 3 tons and 4 tons respectively
so, capacity of smaller truck per trip =3 tons / trip
total ton carried by smaller truck = (number of trips for smaller truck)*(capacity of smaller truck per trip)
now, we can plug values
total ton carried by smaller truck =3*(x+18)
total ton carried by larger truck = (number of trips for larger truck)*(capacity of larger truck per trip)
total ton carried by larger truck =4x
it can deliver 12 more tons of freight than the larger
so, we get
we can move 4x on left side
we get
...............Answer