Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,
which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,
If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.
Answer:
See below in bold.
Step-by-step explanation:
a. |x| = 6
x = 6, -6.
b. |x − 5| = 4
x - 5 = 4
x = 9.
x - 5 = -4
x = 1.
c. 2|x + 3| = −10
No solution because |x + 3| is an absolute value so is always positive.
Correct answer:
First reflect across the y-axis, then rotate 90 degrees clockwise about point K, then shift 3 units down.
S+(2+1/2)s+20=48
2/2s+5/2s=48-20
7/2s=28
7s=28*2=2(20+8)=40+16
7s=56
s=56/7
s=8
ANSWER
EXPLANATION
Since
line s and t are both transversals.
This implies that,
are alternate angles.
Alternate angles are equal. Therefore,
Also,
because corresponding angles are equal.