A conical water tank with vertex down has a radius of 10 feet at the top and is 20 feet high. If water flows into the tank at a rate of 10 ft3/minft3/min, how fast is the depth of the water increasing when the water is 15 feet deep?
Answers
V=(ph^3)/12
V(15)=281.25p and since V=10t, t=28.125p
V=(ph^3)/12
dV/dh=(3ph^2)/12=(ph^2)/4 and since V=10t, dV/dt=10
(dh/dV)(dV/dt)=dh/dt=12/(3ph^2)*10
dh/dt=120/(3ph^2) and we want the rate when h=15 so
dh/dt(15)=120/(675p)
dh/dt=0.05658 ft/min
Final answer:
The rate at which the water's depth is increasing when it is 15 feet deep is approximately 0.028 feet per minute.
Explanation:
The subject of the student's question is related to the concept of volumes of revolution and rates of change in calculus. This is a practical application of those principles.
If we use the formula for the volume of a cone, we get: V = 1/3(pi*r²*h). Looking at our provided situation, we see that r = h/2, so we can replace r with h/2, giving us V = 1/3(pi*(h/2)²*h). This simplifies down to V = 1/12*pi*h³.
Next, differentiate the volume with respect to time (t), giving us dV/dt = 1/4*pi*h²*dh/dt. We know that dV/dt = 10 ft³/min (the rate at which water is flowing into the tank), and we want to find dh/dt when h = 15 ft.
Substitute these values into the differentiated equation to solve for dh/dt: 10 = 1/4*pi*(15)²*dh/dt therefore dh/dt = 10 / (1/4*pi*15²) which gives us approximately 0.028 ft/min.
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Answers
Hi there!
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I believe your answer is:
m = (7/4)
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Here’s why:
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The line passes through the points (3,4) and (-1, -3).
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Hope this helps you. I apologize if it’s incorrect.
Answers
Answer:
I think it is greater than
Answers
Answer:
B. $213.30
Step-by-step explanation:
Mean amount spent on Christmas gifts = Σx / n
Where,
Σ= sum of
x= cost of each Christmas gifts
n= number of Christmas gift
Mean amount spent on Christmas gifts = Σx / n
= ( $178.622 + $247.583 + $228.454 + $176.645 + $180.226 + $268.45 ) / 6
= $1,279.98 / 6
= $213.33
Round to the nearest cent
= $213.30
Option b is the correct answer
Final answer:
The mean amount spent by six college buddies on Christmas gifts, They spent: approximately $213.33 when rounded to the nearest cent.
Explanation:
The process is quite straightforward and involves the principles of statistics, particularly the calculation of the arithmetic mean. Here are the steps we can follow to solve this problem:
- First, we need to find the total amount spent. We do this by adding the amounts together: $178.62 + $247.58 + $228.45 + $176.64 + $180.22 + $268.45. When we add these values, we get a total of $1,279.96.
- Next, we need to calculate the mean, which in statistics is also commonly referred to as the average. Since there were six buddies, we divide the total amount ($1,279.96) by 6. When we do this, we find that the mean or average amount spent is approximately $213.33 (when rounded to the nearest cent).
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Answers
Answer:
64
Step-by-step explanation:
If the mean is 15, the sum of 5 numbers is:
- 5*15 = 75
Minimum value for the first four numbers would be:
- 1, 2, 3, 4
Then the fifth number is:
- 75 - (1+2+3+4) = 75 - 10 = 65
So the maximum difference is:
- 65 - 1 = 64
Answers
Answer:
(7, 3)
Step-by-step explanation:
Given segment AB, where:
- A = (-1, -1)
Mid point
- M = (3, 1)
- Point B = (x, y)
As per mid point formula:
- (-1+x)/2 = 3 ⇒ -1 + x = 6 ⇒ x = 6+ 1 = 7
- (-1 + y)/2 = 1 ⇒ -1 + y = 2 ⇒ y = 2 + 1 = 3
So, the point B is:
- B = (7, 3)
B. y = 6x + 1
C. y = -6x - 1
D. y = 6x - 1
Answers
Answer:
C
Step-by-step explanation:
I’m rusty with my math, so I’m not 100% sure this is correct. My best attempt.
(1,-5) & (3,-17)
1=1x, -5=1y, 3=2x, -17=2y
Formula is y2-y1/x2-x1
-17 - -5 = -12
3 - 1 =2
So -12/2 = -6
Formula for the line is
y-y1 = m (x-x1)
In this equation m=-6
Y - -5 = -6 ( x - 1 )
Answer:C
Step-by-step explanation: