The volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3.
To find the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis, we can use the disk method. The disk method involves slicing the region into thin disks and adding up their volumes.
The volume of each disk is πr2h, where r is the radius of the disk and h is the thickness of the disk. In this case, the radius of each disk is x and the thickness is dx.
So, the volume of the region is:
V = ∫0ln(3)πx2dx
We can use the power rule for integration to solve this integral:
V = π∫0ln(3)x2dx = π[(x3)/3]0ln(3) = π[(ln(3)3)/3 - (03)/3] = (πln(3)3)/3
Therefore, the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3. This is the exact form of the volume.
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Answer: 570 adult tickets and 215 children tickets were sold
Step-by-step explanation:
Let x represent the number of adult tickets that were sold for the movie Saturday.
Let y represent the number of children tickets that were sold for the movie Saturday.
One Saturday the theater sold 785 tickets. This means that
x + y = 785
The movie theater charges 5 for an adult ticket and 2 for a child's ticket. The total sales on Saturday was 3280. This means that
5x + 2y = 3280 - - - - - - - - - - --- 1
Substituting x = 785 - y into equation 1, it becomes
5(785 - y) + 2y = 3280
3925 - 5y + 2y = 3280
- 5y + 2y = 3280 - 3925
- 3y = - 645
y = - 645/- 3
y = 215
x = 785 - y = 785 - 215
x = 570
Answer:
On average the children on the camp made 7 new friends in the week.
Step-by-step explanation:
Given:
Average number of new friends camp made in 6 days = 5
Number of new friends made on the last day = 2
We need to find the number of new friends on average did the children make during the one week summer camp.
Solution:
Now we can say that;
to find the number of new friends on average did the children make during the one week summer camp is equal to sum of Average number of new friends camp made in 6 days and Number of new friends made on the last day.
framing in equation form we get;
the number of new friends on average made in 1 week =
Hence On average the children on the camp made 7 new friends in the week.
On average, each child made 30 friends in the first six days of camp and another 2 on the last day, totaling an average of 32 friends made during the one week summer camp.
The children participating at the summer camp made an average of five new friends each for the first six days. This means they made a total of 5 friends/day * 6 days = 30 friends on average in the first six days. On the last day of camp, each child made two more friends. So, for the week as a whole, each child made an average of 30 friends from the first six days + 2 friends from the last day = 32 friends on average during the week-long summer camp.
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4X-(9-3X)=8X-1
In the equation, if we are to solve for x, the result would be -8.
To solve for x in the expression, the first step would be to collect like terms. Thus, we would have;
4x - (9 - 3x) = 8x - 1
4x -9 + 3x = 8x - 1
Collect similar terms
4x + 3x - 8x = -1 + 9
-x = 8
Divide both sides by -1
x = -8
So, the value of x in this equation is -8.
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7.92 g/cm³ is the density of the iron sheet.
Density is calculated by the formula:
= Mass / Volume
The mass here is 28.5 g
The Volume is:
= Volume of water after iron shot added - Volume before shot added
= 49.10 - 45.50
= 3.6 mL
The units for density is g / cm³ so you need to convert the mL to cm³.
1 cm³ = 1 mL
3.6 mL is therefore 3.6 cm³.
Density is:
= 28.5 / 3.6
= 7.92 g / cm³
In conclusion, the density of the iron shot is 7.92 g /cm³.
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30 milliliters every 4 hours
milliliters per hour
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