The circumference of an NBA-approved basketball is 29.6 in. Given that the radius of Earth is about 6400 km, how many basketball
1 answer:
Answer:
167,886,383 basketballs
Step-by-step explanation:
We are asked to find how many basketballs would take to circle around the equator. We have given the earth's radius. So, we need the formula to obtain it's perimeter. Thus:
Earth's diameter is simply radius*2. It means:
On the other hand, we have a basketball crcumference; however, we need to obtain its diameter so that we can later calculate how many basketballs fit on earth's equator by simply dividing earth's circumference by a basketball's diameter.
Diameter of a basketball:
We need to change units to fit in the international system.
29.6 in to cm =
Then:
We have to convert earth's perimeter in km to cm:
Finally, dividing total earth's circumference by a basketball diameter:
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Answer:
5/4
Step-by-step explanation:
I think this makes sense, if this is what ur asking for.
We need to set up a system, rather than a single equation, because there are two variables involved.
The first equation represents the fact that the two numbers are in a 3:2 ratio:
The second equation represents the fact that their sum is 35:
So, we have the following system:
Using the expression for x in the first equation, the second one becomes
which implies
<h3>Answer: A) 35</h3>
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Short Explanation:
Subtract the arcs and divide by 2 like so
angle 1 = (longerArc - shorterArc)/2
angle 1 = (100 - 30)/2
angle 1 = 70/2
angle 1 = 35 degrees
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Longer explanation:
Refer to the diagram below. I have replaced the 100 and 30 degree arcs with A and B respectively. I've also added in the arc measures of y and z.
Note how the smaller circle arc pieces A, B, y and z all form a complete full circle. So those values add to 360. We get A+B+y+z = 360. We'll use this later.
In the diagram, I've also drawn a blue segment to form a triangle. The angle x we want to find has replaced angle 1. The angles (y+B)/2 and (z+B)/2 are found through the inscribed angle theorem.
Focus on the triangle. The three angles of any triangle always add to 180, so,
(z+B)/2 + (y+B)/2 + x = 180
we can multiply both sides by 2 and we end up with
z+B + y+B + 2x = 360
z+y+2B + 2x = 360
Since we have 360 on the right hand side of this equation, and the equation A+B+y+z = 360, this means that the left sides of each equation are the same.
We can then say the following
z+y+2B + 2x = A+B+y+z
2B+2x = A+B
2x = A+B-2B
2x = A-B
x = (A-B)/2
This is the formula used in the "short explanation" section above. In this case, A = 100 and B = 30, so
x = (A-B)/2
x = (100-30)/2
x = 70/2
x = 35
The measure of angle 1 is 35 degrees.
Side note: With that formula above, we always have A > B.