brine flows into a conical tank at a constant rate of 3 cubic feet per minute. the radius of the cone is 5 feet and its height is 12 feet. how fast is the radius increasing when the radius is 2 feet?
Answers
Applying derivative on the formula of volume of cone and using the provided values, The answer is 0.059 feet per minute.
What do you mean by derivative?The rate at which a function changes in relation to a variable in mathematics.
What is a cone and it's formula for volume?A cone is a three-dimensional geometric structure with a smooth transition from a flat base often but not always circular to the point at the top, also known as the apex or vertex.
Formula for volume of cone is:
\(V= \pi r^{2}\frac{h}{3}\)
derivate the formula for volume of cone , we get,
\(\frac{dV}{dt} = 2\pi r * \frac h3 * \frac {dr}{dt}\)
dV / dt = 3
r=2
h=12
dr/dt = 0.059 feet per minute.
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Related Questions
PLEASE HELP< ILL GIVE 45 POINTS AFTER YOU ANSWER!!!
△XYZ is translated up 3 units to form the image ∆X′Y′Z′.
What are the coordinates of the vertices of ∆X′Y′Z′ ?
Enter your answer by filling in the boxes.
X′ =
Y′ =
Z′ =
Picture:
A right triangle on a grid with a range from negative eight to eight on the x and y axis whose coordinates are negative four comma six for point X, six comma one for point Y, and one comma one for point Z on a grid
Answers
Given:
Vertices of △XYZ are X(-4,6), Y(6,1) and Z(1,1).
To find:
The vertices of ∆X′Y′Z′.
Solution:
According to the question, △XYZ is translated 3 units up to form the image ∆X′Y′Z′, so rule of translation is defined as
\((x,y)\to (x,y+3)\)
Now,
\(X(-4,6)\to X'(-4,6+3)\)
\(X(-4,6)\to X'(-4,9)\)
Similarly,
\(Y(6,1)\to Y'(6,1+3)\)
\(Y(6,1)\to Y'(6,4)\)
and,
\(Z(1,1)\to Z'(1,1+3)\)
\(Z(1,1)\to Z'(1,4)\)
Therefore, \(X'=(-4,9),Y'=(6,4),Z'=(1,4)\).
Tell me the solution
\(4 \times 100 \\ \div 7\)
Answers
Step-by-step explanation:
4×100=400
400÷7=57.14......
hope it helps!
have a great day :)
Factor
-2.8 out of -16.8m - 11.2.
-16.8m – 11.2 = -2.80
+
Answers
Answer: the answer is m=–1/2
Step-by-step explanation: To factor –2.8 out of –16.8m–11.2, you’ll need to factor and set each factor equal to zero. If you mark me brainliest please I will be happy if not I won’t be happy! :)
Muriel is considering leasing a car, and she is even thinking about buying it after the lease is up. She's trying to make sense of the terms of the lease before she makes her decision, but she's having a little trouble figuring it all out. The terms of the lease are as follows.
Terms:
Length of lease: 32 months
MSRP of the car: $26,260
Purchase value of the car after lease: $14,330
Down payment: $1270
Security deposit: $605
Acquisition fee: $765
Lease factor: 0.00073
Provide Muriel with some assistance by answering the following questions. 5 points: Part I - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point; Part V - 1 point)
What is the amount of the cash due at signing?
What would be Muriel's monthly payment? What is the total amount of money that Muriel would spend on monthly payments? What is the total cost of leasing the car, assuming that Muriel does not get the security deposit back?
What is the total price of the car if Muriel buys it after leasing, assuming that she does not get the security deposit back
Answers
The amount of cash due based on the terms of the lease that Muriel will pay is $2640.
How to calculate the cash due?The amount of cash due is calculated thus:
= Security deposit + Acquisition fee + Down payment
= $605 + $1270 + $765
= $2640
The monthly lease payment will be:
= Depreciation + Interest
= $133 + $28.7
= $161.70
Depreciation was calculated as:
= ($24990 - $14330) / 32 = $133
Interest was calculated as:
= Capitalized cost + Residual value × Money factor
= ($24990 + $14330) × 0.00073
= $28.70
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HELP PLEASE, LOOK AT PICTURE FOR WHOLE PROBLEM.. PLEASE ANSWER QUICK I DON'T HAVE MUCH TIME LEFT TO ANSWER
Answers
Answer:
2\(\sqrt{8}\)
Step-by-step explanation:
According to Euclidian theorem :
h^2 = 4*8
h^2 = 32 find the root for both sides
h = 2\(\sqrt{8}\)
Consider an investment of $10,000 with an interest of 5% compounded quarterly. Which
statements are correct?
A. An exponential function models the situation. B. In 5 years, the investment has a value of more than $12,762. C. This situation can be modeled by the function = 1. 05 + 10,000. D. The situation can be modeled by the function = 10,000 (1 + 0. 05)
4t
4
Answers
An investment of $10,000 with 5% interest compounded quarterly is modeled by an exponential function. The investment value after 5 years is $12,833.44. The correct function to model the situation is A = 10,000(1.05)^(4t). The correct options are A, B and D.
Statement A is correct. An exponential function is used to model compound interest situations, where the interest is added to the principal at regular intervals, such as quarterly.
Statement B is correct. To find the future value of the investment after 5 years, we need to use the formula:
A = P(1 + r/n)^(n*t)
where A is the future value, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
Substituting the given values, we get:
A = 10,000(1 + 0.05/4)^(4*5) = $12,833.44
Therefore, the investment has a value of more than $12,762 after 5 years.
Statement C is incorrect. The given function, = 1.05 + 10,000, is not an exponential function and does not model the compound interest situation correctly.
Statement D is correct. The correct formula to model the situation is:
A = P(1 + r/n)^(n*t)
Substituting the given values, we get:
A = 10,000(1 + 0.05/4)^(4t)
Simplifying the expression, we get:
A = 10,000(1.0125)^4t
which can be written as:
A = 10,000(1.05)^(4t)
Therefore, the correct function to model the situation is A = 10,000(1 + 0.05/4)^(4t) or A = 10,000(1.05)^(4t).
The correct answers are A, B and D.
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If Rosa walks 3 miles in 40 minutes, then Rosa will walk how far in 70 minutes if she walks at the same
speed the whole time? If necessary, round your answer to the nearest tenth of a mile.
miles.
Answers
Answer:
5.25 miles.
Step-by-step explanation:
1) Rosa spends 10 minutes in 3/4=0.75 miles, then
2) Rosa can spend 70 in 0.75*7=5.25 miles.
Answer:
5.3 miles
Step-by-step explanation:
3miles/40min =x miles/70min
cross multiply the fractions
3*70 = 40*x
210=40x
divide by 40 on both sides
210/40 = 5.25
x=2 and x= 9 absolute value
Answers
Answer:
if u need to write an equation for it, it would be |2x-11| =7
A nurse is caring for an infant who has gastroesophageal reflux. Which of the following findings are associated with this condition? (Select all that apply.)
a) rigid abdomen
b) wheezing
c) vomiting
d) weight loss
e) pallor
Answers
The correct answers are: c) vomiting and d) weight loss. Gastroesophageal reflux can cause frequent vomiting, which can lead to weight loss in infants.
A nurse caring for an infant with gastroesophageal reflux may observe the following findings associated with this condition:
b) wheezing
c) vomiting
d) weight loss
Infants and children diagnosed with gastroesophageal reflux should not sit or lie down immediately after a meal; patients will be advised to lie face down for at least the first hour after a meal; Sleeping in this position has been shown to reduce the frequency of gastroesophageal reflux. Expressed milk can be thickened as described, in addition to increasing the frequency of feedings; in addition, early teaching (at three (3) months) to eat rice can be attempted; small meals are also recommended; oily and spicy. foods that promote postprandial reflux by increasing gastric emptying and slowing digestion; Chocolate, mint, tomato, citrus fruits, and caffeine should be avoided, which lowers LES pressure.
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Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in
producing large tubes of toothpaste.
O 2.1.3.4
O 4.1,2,3
O 4,3,1,2
Answers
The companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2 that is option C.
Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste.
Toothpaste company
Large tubes
Small tubes
1) Sparkling
100 per hour
200 per hour
2) Bright White
100 per hour
250 per hour
3) Fresh!
200 per hour
250 per hour
4) Mint
150 per hour
150 per hour
Formula for comparative advantage is
CA=rate of producing large tubes/rate of producing small tube
For 1 Sparkling:
CA = 100/200
CA = 0.5
For 2 Bright White:
CA = 100/250
CA = 0.5
For 3 Fresh:
CA = 200/250
CA = 0.8
For 4 Mint:
CA = 150/150
CA = 1
thus, to place the companies in order of greatest comparative advantage to least comparative advantage in producing large tubes of toothpaste is 4, 3, 1, 2.
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Complete question:
Use the numbers to place the companies in order of greatest comparative advantage to least comparative advantage in
producing large tubes of toothpaste.
2.1.3.4
4.1,2,3
4,3,1,2
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john is constructing a satellite dish . The receiver is going to be located 15 inches above the vertex of the dish. The dish is going to be 84 inches wide. How deep will the dish be
Answers
The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.
How can the equations of a parabola be used to find the depth of the dish?The location of the receiver = 15 inches above the vertex
Width of the dish = 84 inches
The receiver of a satellite dish is normally located at the focus (focal point).
Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;
Coordinates of the focus = (0, a)
Where;
a = The distance of the focus above the vertex
Therefore;
a = 15 inches
The dish is horizontally spaced equally about the vertex.
The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.
At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;
X = 84 ÷ 2 = 42
Which gives;
42² = 4 × 15 × Y
Y = 42² ÷ (4 × 15) = 29.4
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I need help please Will mark brainliest
Answers
Answer:
which ones do you need answered
Step-by-step explanation:
What is $15.60 to $11.70
Answers
Answer:
25
Step-by-step explanation:
15.60 divided by 11.70 = 25
The function f(x) = g(x), where f (x) = 2x - 5 and g(x) = x? - 6.
The table below shows the process of solving using successive approximations.
Continue this process to find the positive solution to the nearest tenth.
X=?
Answers
The given function f(x) = g(x) can be rewritten as 2x - 5 = x - 6. To find the positive solution to the nearest tenth,
we can use successive approximations to narrow down the possible values of x. The table below shows the process of solving using successive approximations:
Approximation x
0 7
1 6.5
2 6.25
3 6.125
4 6.0625
5 6.03125
6 6.015625
7 6.0078125
8 6.0039062
To obtain each successive approximation, we start with an initial guess for x (in this case, 7) and substitute it into the equation 2x - 5 = x - 6.
The resulting value of x is then used as the new guess, and the process is repeated until the value of x converges to a specific value.
In this case, the successive approximations converge to 6.0039062, which is the positive solution to the nearest tenth.
This means that x = 6.0 is a close approximation to the solution, but x = 6.1 is too high.
By continuing the process of successive approximations, we can obtain a more accurate approximation of the solution to any desired degree of precision.
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Find an equation of a plane containing the line r=⟨−1,−4,−4⟩+t⟨−9,4,−2⟩ which is parallel to the plane −2x−3y+3z=−3 in which the coefficient of x is −2. =0
Answers
The equation of the plane containing the line and parallel to the given plane is: -2x - 3y + 3z - 2 = 0
To find an equation of a plane containing the given line and parallel to the plane, we need to find a vector normal to both the line and the given plane. Since the plane's coefficient of x is -2, the normal vector of the plane is ⟨-2, -3, 3⟩.
Since the line is parallel to the plane, any point on the line will also lie on the desired plane. Let's choose the point (-1, -4, -4) on the line.
Using the point (-1, -4, -4) on the plane and the normal vector ⟨-2, -3, 3⟩, we can write the equation of the plane in the form ax + by + cz + d = 0, where a, b, c are the components of the normal vector and d is the constant term:
-2x - 3y + 3z + d = 0
To determine the value of d, we substitute the coordinates of the chosen point (-1, -4, -4) into the equation:
-2(-1) - 3(-4) + 3(-4) + d = 0
2 + 12 - 12 + d = 0
2 + d = 0
d = -2
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Find the volume of a pyramid with a square base, where the area of the base is 16\text{ m}^216 m
2
and the height of the pyramid is 25.4\text{ m}25.4 m. Round your answer to the nearest tenth of a cubic meter.
Answers
The volume of the pyramid with a square base is 135.5 cubic m if the base area is 16 cubic m and the height is 25.4 m.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the centre of the square.
We know the volume of the square pyramid V;
V = Bh/2
B is the base area, B = 16 square m
h is the height of the pyramid, h = 25.4 m
V = (16×25.4)/3
V = 135.46 ≈ 135.5 cubic m
Thus, the volume of the pyramid with a square base is 135.5 cubic m if the base area is 16 cubic m and the height is 25.4 m.
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a Right circular cylinder has the dimensions shown below
R= 17.2 m
H = 15.3
what is the volume of the cylinder
Answers
The volume of the right circular cylinder is approximately 14,864.77 cubic meters.
What is the right circular cylinder?
A right circular cylinder is a three-dimensional solid shape that consists of a circular base and a curved side that is perpendicular to the base. The term "right" refers to the fact that the axis of the cylinder is perpendicular to the base, and the term "circular" refers to the shape of the base, which is a circle.
The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder. The formula for the surface area of a right circular cylinder is A = 2πrh + 2πr^2, where r is the radius of the base and h is the height of the cylinder.
Right circular cylinders are commonly used in engineering, architecture, and everyday objects such as cans, pipes, and containers.
The formula for the volume of a right circular cylinder is \(V = \pi r^2h\), where r is the radius of the base and h is the height of the cylinder.
In this case, the radius is 17.2 meters and the height is 15.3 meters.
Plugging in these values, we get:
\(V = \pi (17.2)^2(15.3)\)
V ≈ 14,864.77 cubic meters
Therefore, the volume of the right circular cylinder is approximately 14,864.77 cubic meters.
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Which fraction is equivalent to 16.6%
Answers
Answer:
16.6%=83500 , this is roughly equal to 16
Una caja contiene 3 bolas verdes, 5 bolas rojas y 2 bolas azules. Si se extraen al azar dos bolas sin reposición, ¿cuál es la probabilidad de que la primera sea azul y la segunda sea verde?
Answers
Responder:
1/15
Explicación paso a paso:
Dado que :
Número bolas verdes = 3
Número de bolas rojas = 5
Número de bolas azules = 2
Dibujo sin reemplazo; probabilidad de que el primero sea azul, el segundo sea verde
Probabilidad = resultado requerido / Total de resultados posibles
Resultados posibles totales = 3 + 5 + 2 = 10
P (1er azul) = número de azules / 10
P (1er azul) = 2/10 = 1/5
Sin reemplazo :
Total restante = 10 - 1 = 9
P (segundo verde) = número de verdes / 9 = 3/9
Probabilidad del primer azul y del segundo verde:
1/5 * 3/9 = 3/45 = 1/15
The probability that the first is blue and the second is green is 1/15
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcomeIf a box contains 3 green balls, 5 red balls and 2 blue balls, the total number of balls is 10balls
Total outcome = 10 ballsIf blue is selected at first, the probability of selecting blue is 2/10 = 1/5If green is selected without replacement, the probability of selecting green will be 3/9Pr(selecting red and then green) = 1/5 * 1/3 = 1/15Learn more on probability here: https://brainly.com/question/24756209
If M=1,000,P=2.25, and Y=2,000, what is velocity? a. 2.25 b. 4.5 c. 2 d. None of the above is true
Answers
Answer:d
Step-by-step explanation:
The answer is d. None of the above is true.
To calculate velocity, we need to use the equation:
Velocity = M * P / Y
Given:
M = 1,000
P = 2.25
Y = 2,000
Plugging in the values:
Velocity = 1,000 * 2.25 / 2,000
Simplifying:
Velocity = 2.25 / 2
The result is:
Velocity = 1.125
Therefore, the correct answer is: d. None of the above is true.
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PLEASSSSEEEE I NEED HELP WITH THIS ITS MIDDLE SCHOOL HELLLLLLLP
Sandy plays a matching game in order to advance to the next
level, she must score at least 10 points. She scores 15 points for
correct matches and -6 points for incorrect matches.
A. Write an addition expression to represent the amount of
points Sandy earned.
B. Did Sandra make it to the next level? Explain.
Answers
Answer:
A. -16
B. Yes he did as he went for a big play
What is the length of the unknown leg in the right triangle?
Answers
Answer:
15m
Step-by-step explanation:
a^2 + b^2 = c^2
a=?
b = 20m
c = 25m
a^2 + (20m)^2 = (25m)^2
a^2 + 400m^2 = 625m^2
a^2 = 625m^2 - 400m^2 = 225m^2
a = 15m
Answer:
The answer is 15
Step-by-step explanation:
I need help with math
Answers
Answer:
E) |g-540|
Step-by-step explanation:
E) |g-540|
If it weighed a bit over, say 545, you would get |545-540|=|5|=5
If it weight a little under, say 535, you would get |535-540|=|-5|=5
Either way, it tells you how far away from 540 the package is in grams from the desired weight.
a+b+c=d solve for b
Answers
Answer:a/b = c/d |cross multiply
ad = bc |divide both sides by a
d = bc/a
Step-by-step explanation:
Answer:
b = d - a - c
Step-by-step explanation:
Given
a + b + c = d ( subtract a + c from both sides )
b = d - a - c
What is the quotient and the remainder of 212 divided bye 8
Answers
Answer:
26 r 4
Step-by-step explanation:
8/212
a measurement of how well a child can do certain tasks at a certain time in comparison to other children is a(n) test.
Answers
A(n) IQ test evaluates a child's performance in relation to other kids in terms of how well they can perform specific activities at a specific time.
Each individual IQ exam is made up of a number of smaller questions, and no reading nor writing are required. Some verbal subtests consist of spoken questions with no set time restriction. Other subtests are frequently timed and typically have a visual or spatial focus. It takes one to two hours to give the exam.
115 to 129: Superior or intelligent. 130 through 144: Fairly talented. From 145 through 159: Very talented. Exceptionally talented from 160 to 179.
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What is 0.000056023 written in scientific notation?
Answers
Answer:
5.6023 × 10^-5
Step-by-step explanation:
Let me know if you need an explanation.
Answer:
0.00005602
Step-by-step explanation:
0.00005602
(hope this helps can i plz have brainlist :D hehe)
-3=k+3 please help me
Answers
Answer:
k=-6
Step-by-step explanation:
Answer:
k = -6
-3=k+3
-3 -3
-6=k
The set of ordered pairs below represents a linear function
((-2,-3), (0,-2), (2, -1), (x, y)}
What is another pair of coordinates that could be the missing ordered pair, (x,y),
in this set?
Answers
Another pair of coordinates that could be the missing ordered pair, (x,y) in this set is (1, 0)
Linear functionsLinear functions are functions that have a leading degree of one,
Given the coordinate points ((-2,-3), (0,-2), (2, -1), (x, y)}, we need to determine the missing coordinate points
Since the x-coordinates has a difference of 2, hence the missing x-coordinate is given as:
x = -1 + 2
x = 1
For the y-coordinate
y = -1 + 1
y = 0
Hence another pair of coordinates that could be the missing ordered pair, (x,y) in this set is (1, 0)
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4 ^ x - 4 ^ 0 - 255 = 0
Answers
Answer:
x = 4
Step-by-step explanation:
Given the equation:
\(\displaystyle{4^x - 4^0 - 255=0}\)
We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,
\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)
Add both sides by 256, so we have:
\(\displaystyle{4^x=256}\)
Factor 256 out:
256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸
Therefore, 256 = 2⁸.
\(\displaystyle{4^x=2^8}\)
Convert to the same base:
\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)
When two sides have same base, solve the equation through exponents:
\(\displaystyle{2x=8}\)
Divide both sides by 2, so we have:
\(\displaystyle{x=4}\)