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scoutrussel4life
19.09.2019 •
Mathematics
Can someone answer these as well worth lots of points. only appropriate answers pls : ).
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Ответ:
- For triangle RTS:
S (2,1), T (1,3) and R (5,5). Using a graphic tool or the distance formula
Now we can use Heron's formula:
We can conclude that the area of triangle RTS is 4.9 square units.
- For triangle MNL:
M (2,-4), N (-2,-3), and L (0,-1). Once again, using a graphic tool or the distance formula we get that MN=4.1, ML=3.6, and NL=2.8.
Lets find the semi-perimeter of our triangle to use Heron's formula:
We can conclude that the area of triangle MNL is 4.9 square units.
2. To find the volume of our pyramid, we are going to use the formula for the volume of a rectangular pyramid:
where
From our picture we can infer that
To find the volume of the cone, we are going to use the formula:
where
From our picture we can infer that the diameter of the cone is 9; since radius is half the diameter,
We can conclude that the volume of the pyramid is 600 cubic units and the volume of the cone is 254.5 cubic units
3. To find
and to the nearest whole number:
We can conclude that
4. To solve this, we are going to find the volume of the cube first; to do it we are going to use the formula for the volume of a cube:
where
Since the sphere fits exactly in the cube, the edge of the cube is equal to the diameter of the sphere; therefore,
Next, we are going to use the formula for the volume of a sphere:
where
We know form our problem that the diameter of the sphere is 12 units, since radius is half the diameter,
Now, to find the volume of the empty space in the cube, we just need to subtract the volume of the sphere form the volume of the cube:
We can conclude that the volume of the empty space in the cube is 823.2 cubic units
4. To solve this, we are going to use the arc length formula:
where
Lets, find
Since BE is the diameter of the circle, AB is its radius; therefore
We can conclude that
Ответ:
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