Answer:
Step-by-step explanation:
We have been given that a series of 3 separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers.
Each of the three tunnels is shaped like a half-cylinder with a radius of 5 meters.
Since we know that volume of a semicircular or a half cylinder is half the volume of a circular cylinder.
, where,
r = Radius of cylinder,
h = height of the cylinder.
Upon substituting our given values in volume formula we will get,
Therefore, the volume of earth removed to build the three tunnels is .
Answer:
Step-by-step explanation:
As you can observe in the image attached, the line that best fits passes through point B and C. That means we can use those point to find the slope of such line.
Where 
and 
So, the slope of the line that best fits is -11, approximately.
Now, we use the point-slope formula to find the equation.
Therefore, the line that best fits is approximately.
Remember, when we estimate a line for some data on a scatterplot, we are calculating an approximation, that's why we also said "approximately", because the line is an approximation where the majority of point meet.
Answer:
25
Step-by-step explanation:
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Answer:
SteLet a = short leg of the right triangle, b = the longer leg, and c = the hypotenuse.
The longer leg of a right triangle is 4inches longer than the shorter leg: b = a + 4
The hypotenuse is 8inches longer than the shorter leg: c = a + 8
Use the Pythagorean Theorem:
a2 + b2 = c2
a2 + (a+4)2 = (a+8)2
a2 + a2 + 8a + 16 = a2 + 16a + 64
a2 - 8a - 48 = 0
Factors to:
(a-12)(a+4) = 0
a = 12, -4
Since we can't have a side of -4, a = 12
Shorter Leg = 12 inches
Longer Leg = 12 + 4 = 16 inches
Hypotenuse = 12 + 8 = 20 inches
