Answer:
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Step-by-step explanation:
Given
Represent radius with r and height with h
[tex]h = 12ft[/tex]
[tex]r = 10ft[/tex]
[tex]Rate = \frac{8ft^3}{min}[/tex] when [tex]h = 10ft[/tex]
Express radius in terms of height
[tex]\frac{r}{h} = \frac{10}{12}[/tex]
[tex]\frac{r}{h} = \frac{5}{6}[/tex]
[tex]r = \frac{5}{6}h[/tex]
First, we need to determine the volume of the cone in terms of height.
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Substitute [tex]r = \frac{5}{6}h[/tex]
[tex]V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^3[/tex]
[tex]V = \frac{25}{108} \pi h^3[/tex]
Differentiate both sides w.r.t time (t)
[tex]\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}[/tex]
Solve for [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}[/tex]
At this point, [tex]h = 10[/tex] and [tex]\frac{dv}{dt} = \frac{8ft^3}{min}[/tex]
So, we have:
[tex]\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{864}{7500\pi}[/tex]
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Hence:
The rate is [tex]\frac{216}{1875\pi} ft/min[/tex]
Using implicit differentiation, it is found that the depth of water changes at a rate of -0.0764 feet per minute.
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
Applying implicit differentiation, we can find it's rate of change, thus:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
In this problem:
Height of 12 ft and radius of 10 ft, thus [tex]h = 12, r = 10[/tex].Radius does not change, thus [tex]\frac{dr}{dt} = 0[/tex].Water leaks at a rate of 8 cubic feet per minute, thus [tex]\frac{dV}{dt} = -8[/tex]Then:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
[tex]-8 = \frac{\pi (10)^2}{3}\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = -\frac{24}{100\pi}[/tex]
[tex]\frac{dh}{dt} = -0.0764[/tex]
The depth of water changes at a rate of -0.0764 feet per minute.
A similar problem is given at https://brainly.com/question/9543179
slove the equation
7h-5(3h-8)=-72
Answer:
Step-by-step explanation:
You can break it down into steps if you'd like.
-5 ( 3h - 8) = -15h + 40
So,
7h - 5 ( 3h -8 ) = -72
7h - 15h + 40 = -72
Now you can combine the like terms
-8h + 40 = -72
Add 8h to both sides
40 = -72 + 8h
Add 72 to both sides
40 + 72 = 8h
112 = 8h
Divide both sides by 8 to find h.
h = 112/8 = 14
What is the answer to m<4
Answer:
124°
Step-by-step explanation:
Supplementary angles are when two angles add up to 180°
If angle 3 is 56° then you subtract
180 - 56 = 124
Is this a function or not
Answer:
no its a not funtion
Step-by-step explanation:
bc 1 n 3 is reapeat
please answer for brainlesit
Answer:
(-3, -2) that is the answer please give me brainiest
Step-by-step explanation:
Please help me be right! Ordered pairs
Answer:
the answer is C
Step-by-step explanation:
both the ordered pair satisfy the equation
g(f(x)) easy hw question
Answer:
b
Step-by-step explanation:
-2x⁴-x³+2x²-6
hope this helps
10 pol
Mariska draws a red card and then a black card. The sum is positive. The
number on the black card must be greater than the number on the red
card. *
True
False
False, The sum is positive, no subtraction is being done and no negatives are present.
A positive plus a positive is another positive.
A ring-shaped region shown below. Its inner diameter is20 yd. The Width of the ring is 3 yd. Find the area. Of the shaded region.
9514 1404 393
Answer:
216.66 yd²
Step-by-step explanation:
One way to find the area of a ring like this is to multiply its centerline length by the width of the ring.
Here, the diameter of the circle that is the centerline of the ring is 23 yd. The circumference of that circle is ...
C = πd = 3.14(23 yd) = 72.22 yd
Then the ring area is ...
(72.22 yd)(3 yd) = 216.66 yd² . . . area of shaded region
Find value of x, first gets brain
Answer:
53
Step-by-step explanation:
Solve two-step equations
2 = 4s + –10 i need it ASAP
Answer:
s=3
Step-by-step explanation:
Answer:
s=3
Step-by-step explanation:
simplify the equation to the form, which is simple to understand
and then move all terms containing s to the left and all other terms to the right!
Ken and Vincent each want to run for president of their school's student body council. In
order to do so, they must collect a certain number of signatures and get a nomination. So far,
Ken has 10 signatures, and Vincent has 30. Ken is collecting signatures at an average rate of
3 per day, whereas Vincent is averaging 2 signatures every day. Assuming that their rate of
collection stays the same, eventually the two will have collected the same number of
signatures. How long will that take?
00
Write a system of equations, graph them, and type the solution.
Sn
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Daniel and Paul went exploring in the woods. On the first day Daniel saw 3 rabbits and Paul saw 8 deer. On the second day Daniel saw 4 rabbits and Paul saw 7 deer. On which day of hunting did Daniel and Paul catch a higher ratio of rabbits to deer?
Answer:
first day when they say 3 rabbits and 8 deers 3:8
True or False? Complementary Angle’s are two angles that add up to 90 degrees
Answer:
True
Step-by-step explanation:
Definition of Complementary Angle’s
HDHSJSJSDVSV HELP ME
Answer:
let me see the drop box options !! it helps alot!
NEED HELP FAST I WILL MARK BRAINLYEST
Answer:
13/48
Step-by-step explanation:
13/6 / 8 = 13/6 x 1/8
13 x 1 = 13
6 x 8 = 48
13/48
Answer:
13/48
Step-by-step explanation
Select the best answer for the question.
5. Solve the equation: 7x = 42.
O A.X=-7
O B.x=7
O C.x=-6
O D. x = 6
write an equation to solve for x what is the value of x will mark brainious this is very confusing for me
Answer:
equation: 3x - 2 + 4x - 9 + 3x - 9 = 180x = 20Step-by-step explanation:
add all internal angles
∠H + ∠I + ∠J = 180
where:
∠H = 3x - 2
∠I = 4x - 9
∠J = 3x - 9
plugin the values into the ∠H + ∠I + ∠J = 180 formula:
equation: 3x - 2 + 4x - 9 + 3x - 9 = 180
combine similar terms: 3x + 3x + 4x = 180 + 2 + 9 + 9
simplify: 10x = 200
divide 10 both sides: x = 20
what is the meaning of this symbol^
Answer:
[tex]superscript, \:used\: to\: raise\: objects\: to\: power[/tex]
least common multiple
3/6 , 2/12
Answer:
6
Step-by-step explanation:
3,6,9.12
2,4,6,8,10,12
What is the average speed of a baseball that is thrown 90 feet in 2 seconds?
A. 180 feet/second
B. 45 feet/second
C. 92 feet/second
D. A variable most often found on the y-axis
3. A store manager reports that the mean grocery bill at her store on a Saturday is between
$28.25 and $36.75. To do this, she considered a random sample of customers that Saturday.
What was the sample mean? (Remember that the sample mean is the center of the confidence
interval). What was the margin of error?
Answer:
Hope you understand, and never stop striving to learn!
Step-by-step explanation:
The sample mean is both values added together then divided by 2.
$46.63
The margin of error is the low value divided by the high value * 100% =76.8% (then you have to minus this from 100% so the margin of error is 23.2%)
Which of these numbers are perfect squares or perfect cubes? Select all that apply
A. 8
B. 16
C. 32
D. 64
E. 128
3. Which size package of pasta shown in the
table has the lowest unit price?
A. 3 oz
C. 16 oz
B. 8 oz
D. 32 oz
Size (oz) Cost ($)
3
0.99
8
2.59
16
5.69
32
11.89
Answer:D
Step-by-step explanation:
I divided all of them and d was the lowest unit rate
Joey has 25 candy bars and is addin 2 candy bars to his collection each day. How many days will it take him to reach 51 candy bars?
(yes I'm really dumb and yes I have one minute to turn this in as a major grade :))
Answer:
13 days
Step-by-step explanation:
51-25=26
26/2=13
What is the m
R
(x + 2)°
(3x – 6°
S
Q
P
m
If a ray QT bisects ZPQR, what will be the measure of one of the resulting angles?
The value of measure ∠RQS would be,
⇒ ∠RQS = 48°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
A ray QT bisects ∠PQR.
Now, We get;
⇒ ∠PQR + ∠RQS = 180°
⇒ (3x - 6) + (x + 2) = 180
⇒ 4x - 4 = 180
⇒ 4x = 184
⇒ x = 46
Thus, The value of measure ∠RQS would be,
⇒ ∠RQS = x + 2 = 46 + 2 = 48°
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ7
I need the answer plzz help me
Answer: A) a translation 3 units down
Step-by-step explanation: Notice how your y-values are decreasing by 3.
y-values only increase or decrease, so if they’re decreasing, they are going down.
Hope this helps!
Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
Complete Question
The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 9-year period. Assume each year is independent.
Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
Answer:
The probability is [tex]P(X > 2) = 0.0007 [/tex]
Step-by-step explanation:
From the question we are told that
The probability of an IRS audit for a tax return with over $25,000 in income is p= 0.02
The sample size n = 9
Generally the distribution of IRS audit for a tax return follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that a person is not audited at all is mathematically
[tex]P(X = 0) = ^{9}C_0 * (0.02)^0 * (1- 0.02 )^{9-0}[/tex]
[tex]P(X = 0) = ^{9}C_0 * (0.02)^0 * (0.98 )^{9-0}[/tex]
[tex]P(X = 0) = 0.8337[/tex]
Generally the probability that a person is audited once is mathematically
[tex]P(X = 1) = ^{9}C_1 * (0.02)^1 * (1- 0.02 )^{9-1}[/tex]
[tex]P(X = 1) = 9* (0.02)^1 * (0.98 )^{8}[/tex]
[tex]P(X = 1) = 0.1531[/tex]
Generally the probability that a person is audited twice is mathematically represented
[tex]P(X = 2) = ^{9}C_2 * (0.02)^2 * (1- 0.02 )^{9-2}[/tex]
[tex]P(X = 2) = 36 * (0.02)^2 * (0.98 )^{7}[/tex]
[tex]P(X = 2) = 0.0125 [/tex]
Generally the probability that a person is audited more than twice is mathematically represented
[tex]P(X > 2) = 1 - [P(X = 0 ) + P(X = 1 )+ P(X =2)] [/tex]
=> [tex]P(X > 2) = 1 - [0.8337 + 0.1531+0.0125 ] [/tex]
=> [tex]P(X > 2) = 0.0007 [/tex]
the figure below consists of a rectangle and an equilateral triangle. What is the perimeter of the figure?
Answer: 28 in.
Step-by-step explanation:
The perimeter is the total distance around the entire figure. Because all the lengths of the sides are already given, you just have to add them all up.
P = 4 in. + 8 in. + 8 in. + 4 in. + 4 in. = 28 in.
Answer:
B
Step-by-step explanation:
edge 2021
Find the value of 0.4 ´ 0.023
Answer:
45-0.023=44.977
Step-by-step explanation:
What is the average of these two values?
2 x 105 and 6 x 103
Answer:
the answer should be 414
Answer:
414
or
103.5
Step-by-step explanation:
If these are singular values and for example 2 x 105 does not mean two datasets of 105 and 6 x 103 doesnt mean six datasets of 103, then your average would be as follows
((2 x 105) + (6*103)) ÷ 2
The two being how many sets of values you have
This would be solved as follows
((210) + (618)) ÷ 2 =
(828) ÷ 2 = 414
So in this case it would be 414
However, if the two in 2 x 105 means two data sets of 105;
it would be the same steps of solving but with the ÷ 2 being replaced with ÷ 8 (2 + 6)
((2 x 105) + (6*103)) ÷ 8 =
((210) + (618)) ÷ 8 =
(828) ÷ 8 = 103.5
Hope this helps.