Parametrization of the first segment:
x=t+1, y=4t, z=1 wherein t is on the segment [0,1].
Second segment:
x=2, y=2t+4, z=2t+1 and again t is in [0,1].
Compute the derivatives like this:
First segment: dx=1dt, dy=4dt, dz=0
Second segment:dx=0, dy=2dt, dz=2dt.
Using the above variables, the given integral becomes like this:
The above integral is classical, and simple computation we obtain:
If point R(6, 2) is rotated 180 degrees clockwise about the origin, the new point would be R'(-6, -2)
<h3>What is a transformation?</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformations are r<em>eflection, translation, rotation and dilation.</em>
Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.
If point R(6, 2) is rotated 180 degrees clockwise about the origin, the new point would be R'(-6, -2)
Find out more on transformation at: brainly.com/question/4289712
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Y = 3x2 + -27
Reorder the terms:
y = -27 + 3x2
Solving
y = -27 + 3x2
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = -27 + 3x2
Figure B i imagine is correct
Answer: Pyramid A: Base is rectangle with length of 10 meters and width of 20 meters.
Pyramid B: Base is square with 10 meter sides.
Heights are the same.
Step-by-step explanation: The volume of pyramid A is TWICE the volume of pyramid B.
If the height of pyramid B increases to twice the of pyramid A, (from 10m to 20m),
V of square pyramid = (10m)² * (10*2)/3 = 100m² * 20m/3 = 100m² * 6.67m = 666.67 m³
The new volume of pyramid B is EQUAL to the volume of pyramid A.