Answer:
E. 6
Step-by-step explanation:
Answer:
The volume of the prism is equal to the volume of the cylinder
Step-by-step explanation:
For each solid figure, the volume formula is ...
V = Bh
where B is the cross-sectional area and h is the height. The problem statement tells us B and h have the same values for both figures. Hence their volumes are the same.
Answer:
B) 3
Step-by-step explanation:
This is because they are both circles and they each have the same equation for circumference. C=2πr
So that if pi stays x 2 then the perimeter will still be 3 x as big as the smaller circle. Which means it takes 3 full turns as to turn around the perimeter.
Answer:
401.92
Step-by-step explanation:
The formula used the calculate the volume of a cylinder is
πr^2h
π= 3.14
H= 8
r= 4
Volume= 3.14 × 4^2 × 8
= 3.14 × 16×8
= 401.92
Hence the volume is 401.92
The intersection line of two planes is the cross product of the normal vectors of the two planes.
p1: z=4x-y-13 => 4x-y-z=13
p2: z=6x+5y-13 => 6x+5y-z=13
The corresponding normal vectors are:
n1=<4,-1,-1>
n2=<6,5,-1>
The direction vector of the intersection line is the cross product of the two normals,
vl=
i j k
4 -1 -1
6 5 -1
=<1+5, -6+4, 20+6>
=<6,-2,26>
We simplify the vector by reducing its length by half, i.e.
vl=<3,-1,13>
To find the equation of the line, we need to find a point on the intersection line.
Equate z: 4x-y-13=6x+5y-13 => 2x+6y=0 => x+3y=0.
If x=0, then y=0, z=-13 => line passes through (0,0,-13)
Proceed to find the equation of the line:
L: (0,0,-13)+t(3,-1,13)
Convert to symmetric form:

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