Can someone pls help me out
1 answer:
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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.
Given, the rate of growth of St. Augustine grass is cm per week.
We have to find the number of weeks that the grass grow to cm.
Let's take the number of weeks be x.
In 1 week the grass grow = cm
So in x weeks the grass grow = cm
So we can write,
To solve it for x, first we will move 7 to the right side by multiplying it to both sides. We will get,
Now to get we will move 4 to the right side by dividing it to both sides. We will get,
So we have got the required answer.
After 3 weeks the grass grow .