Answer:
The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.
Step-by-step explanation:
From Geometry, the volume of the cone ([tex]V[/tex]), measured in cubic centimeters, is defined by:
[tex]V = \frac{\pi\cdot r^{2}\cdot h}{3}[/tex] (1)
Where:
[tex]r[/tex] - Radius, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
Then, we find a formula for the rate of change of the volume of the birth bath ([tex]\dot V[/tex]), measured in cubic centimeters per minute, by means of differentiation:
[tex]\dot V = \frac{\pi}{3}\cdot \left(2\cdot r\cdot h\cdot \dot r + r^{2}\cdot \dot h \right)[/tex] (2)
Where:
[tex]\dot r[/tex] - Rate of change of radius, measured in centimeters per minute.
[tex]\dot h[/tex] - Rate of change of height, measured in centimeters per minute.
In addition, we have the following relationship:
[tex]r = 2\cdot h[/tex] (3)
And by Differential Calculus:
[tex]\dot r = 2\cdot \dot h[/tex] (4)
By applying (3) and (4) in (2), we find the following expanded formula:
[tex]\dot V = \frac{\pi}{3}\cdot \left[2\cdot (2\cdot h)\cdot (2\cdot \dot h)+4\cdot h^{2}\cdot \dot h\right][/tex]
[tex]\dot V = \frac{\pi}{3}\cdot (8\cdot h+4\cdot h^{2})\cdot \dot h[/tex] (5)
If [tex]\dot V = -8\,\frac{cm^{3}}{min}[/tex] and [tex]h = 10\,cm[/tex], then the rate of change of the water level is:
[tex]\dot h = \frac{\dot V}{\frac{\pi}{3}\cdot (8\cdot h + 4\cdot h^{2}) }[/tex]
[tex]\dot h = \frac{-8\,\frac{cm^{3}}{min} }{\frac{\pi}{3}\cdot [8\cdot (10\,cm)+4\cdot (10\,cm)^{2}] }[/tex]
[tex]\dot h \approx -0.016\,\frac{cm}{min}[/tex]
The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.
Pls help me this is due today I’ll brainlest for the right answer
Answer:
decrease, 25%
Step-by-step explanation:
20/80 × 100 = 25%
Test the series for convergence or divergence (using ratio test)
Answer:
[tex]\lim_{n \to \infty} U_n =0[/tex]
Given series is convergence by using Leibnitz's rule
Step-by-step explanation:
Step(i):-
Given series is an alternating series
∑[tex](-1)^{n} \frac{n^{2} }{n^{3}+3 }[/tex]
Let [tex]U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }[/tex]
By using Leibnitz's rule
[tex]U_{n} - U_{n-1} = \frac{n^{2} }{n^{3} +3} - \frac{(n-1)^{2} }{(n-1)^{3}+3 }[/tex]
[tex]U_{n} - U_{n-1} = \frac{n^{2}(n-1)^{3} +3)-(n-1)^{2} (n^{3} +3) }{(n^{3} +3)(n-1)^{3} +3)}[/tex]
Uₙ-Uₙ₋₁ <0
Step(ii):-
[tex]\lim_{n \to \infty} U_n = \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }[/tex]
[tex]= \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }[/tex]
= [tex]= \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }[/tex]
[tex]=\frac{1}{infinite }[/tex]
=0
[tex]\lim_{n \to \infty} U_n =0[/tex]
∴ Given series is converges
find the length of side a
Answer:
12
Step-by-step explanation:
Hope this helps
equation below scatter plot (66,69)(76,71)
Pls help I’m failing math
Answer:
y = 3/7+0
Step-by-step explanation:
This is what I got, hope this helps.
2x+3= -15 what is x step by step
Answer: x = -9
Step-by-step explanation: To solve for x, we first isolate
the term containing x which in this case is 2x.
Since 3 is being added to 2x,
we subtract 3 from both sides of the equation.
On the left, the +3 and -3 cancel out
and on the right, -15 - 3 is -18.
So we have 2x = -18.
Now we can finish things off by dividing
both sides of the equation by 2.
On the left, the 2's cancel and on
the right, -18 divided by 2 is -9.
So we have x = -9 which is the solution to this equation.
Dan buys a car for £2100.
It depreciates at a rate of 2.2% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
Answer:£472.92
Step-by-step explanation:
£2100(0.78)^6
A dolphin is at the surface of the ocean. What is the dolphin’s elevation?
Answer:
80 metors or less
Step-by-step explanation:
If I am wrong I am so sorry but I am preety sure its 80
Can someone tell me how to do this?
Answer:
6w+32
Step-by-step explanation:
Let f(x)=−42x+3. Evaluate f(−1)
Step-by-step explanation:
f(-1)=-42(-1)+3....placing -1 in x
f(-1)=42+3
f(-1)=45
Hurry please it’s a test question and I’m timed
Answer:
The collector pays %1.50 for each card.
Step-by-step explanation:
Put it together in a big problem
87 + 9 - 16 + 3 = 83c
$124.50 / 83 = 1.5
=$1.50
Answer:
B. $1.50
Step-by-step explanation:
He starts out with 87 cards.
87 + 9 = 96
96 - 16 = 80
80 + 3 = 83
Total sale = $124. 50
124.5 ÷ 83 = $1.50
Answer: $1.50
Hope this helps!!
Which statement is true about the value of the expression below?
PLEASE HELP
Answer:
The answer is It is between 0 and 1
Step-by-step explanation:
If you solve the problem step by step as (-2^3)^-2<1 then it comes out as true so it would be less than 1 but more then 0.
According to the 68-95-99.7% rule, what percentage of the data from a bell-shaped distribution will be within one standard deviation of the mean
Answer:
68% of the distribution will be within one standard deviation of the mean
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Bell-shaped = Normally distributed.
This means that 68% of the distribution will be within one standard deviation of the mean
Answer:
c 95%
Step-by-step explanation:
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 350 nails. The contractor bought a total of 9 boxes that have 2400 nails altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answer:
3 small boxes and 6 large ones
Step-by-step explanation:
3 times 100 equals 300 and 6 times 350 is 2100 and 2100 plus 300 is 2400.
What is the first quartile of the following data set?
15, 18, 20, 21, 23, 24, 26, 29, 34, 37, 40
Answer:
20.5
Step-by-step explanation:
20 + 21 = 41. Divide 41 by 2 than you get 20.5.
The first quartile of the given data set is 20.
Here,
To find the first quartile of a data set, we first need to arrange the data in ascending order.
Then, we can calculate the position of the first quartile using the formula:
Position of the first quartile (Q1) = (n + 1) / 4
where n is the number of data points in the data set.
Given data set: 15, 18, 20, 21, 23, 24, 26, 29, 34, 37, 40
Arranging the data in ascending order: 15, 18, 20, 21, 23, 24, 26, 29, 34, 37, 40
Now, let's calculate the position of the first quartile:
n = 11 (since there are 11 data points in the data set)
Position of the first quartile (Q1) = (11 + 1) / 4 = 12 / 4 = 3
The first quartile (Q1) is the value at the 3rd position in the ordered data set, which is 20.
So, the first quartile of the given data set is 20.
learn more on quartile :
https://brainly.com/question/29081024
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I have an answer but I’m not sure if it’s correct can someone pls correct me or confirm pls
Answer:
looks good to me
Step-by-step explanation:
SOLVE FOR X AND Y !! WILL GIVE BRAINLIEST
Answer:
x=21, y=17
Step-by-step explanation:
180-42= 138
2x+138=180
2x= 42
x= 21
8y+2+2x=180
8y+2 + 42=180
8y= 136
y= 17
Answer:
x=21, y=68
Step-by-step explanation:
We're given that the quadrilateral on the left is a parallelogram as indicated by the arrow markings on the sides. We're also told that the angle on the right is 42 degrees. So, we can find the bottom right angle in the parallelogram by subtracting 42 from 180, because it forms a straight angle. 180-42 is 138. By the alternate interior angles theorem, 8y+2=138, because 138 is also the angle measure of the opposite corner. we also know that the bottom left angle in the parallelogram is the same as 2x. by the alternate interior angles theorem. Notice how the sides of the parallelogram with two arrow markings are parallel, which means that the bottom left angle and the 42 degree angle are congruent, or have the same measure, because of the parallel lines. This means that 2x=42, and the bottom left angle is 42. We can solve for x and y with simple algebra now. 8y+2=138, 8y=138-2, 8y=136, y=68. 2x=42, x=42/2, x=21. So, x is 21 and y is 68.
Please. Help. I. Need. Assistance.
Answer:
what do you need help with
Answer:
what do you need help with?
Step-by-step explanation:
Determine if the sequence is arithmetle or geometne, and find the common difference or ratio
(1,81), (2,72),(3,63),(4,54)
I’m desperate ✨
Domain and Range functions
Which sequence of transformations performed on triangle J could result in similar triangle J'?
Answer:
B
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
JUst got right
Find the coordinates for point R that proves figure TRAP is an isosceles trapezoid.
Answer:b
Step-by-step explanation: I got it right on my test
The coordinates for point R that proves figure TRAP is an isosceles trapezoid is (c - a, b)
From the diagram, we have the following highlights
There are two parallel sides in the trapezoidThe parallel sides of the trapezoid are horizontal linesThis means that the y-coordinate of point R is the same as the y-coordinate of point T.
Given that the y-coordinate of point T is b, the y-coordinate of point R can be represented as:
[tex]R =(x,b)[/tex]
For the shape to be an isosceles trapezoid, then the following must be true
[tex]x = c - a[/tex]
So, we have:
[tex]R =(c - a,b)[/tex]
Hence, the coordinates of R is (c - a, b)
Read more about trapezoid at:
https://brainly.com/question/2141851
At a water elevation of 6,391 ft, Mono Lake has a volume of 2,939,000 ac-ft, and a surface area of 48,100 ac. Annual inputs to the lake include 8 in of direct precipitation, runoff from gauged streams of 150,000 ac-ft per year, and ungauged runoff and groundwater inflow of 37,000 ac-ft per year. Evaporation is 45 in per year.
Required:
a. Make a water budget showing inputs, in ac-ftper year and outputs in ac-ft per year. Does the input balance the output?
b. Will the average lake level rise or fall from the 6391ft elevation over the long-term?
c. What would be the lake surface area when the inputs blance the outputs? ( Assume that the volume of gauged and ungauged runoff and ground-water inflows remain constant with a change in lake surface area).
d. What is the residence time for water in Mono Lake when the water surface is at 6391ft?
Answer:
Step-by-step explanation:
love you babe
PLZ HELP I NEED IT DONE IN 5 MINUTES PLZ HURRY Determine the approximate ordered pair for f(x)=g(x)
Answer:
the 2 lines cross at 2,18
Which expression represents three more than two times a number?
OA 5x
OB 3(2x)
OC 2x + 3
OD 2(x + 3)
The ratio of the measures of three angles in a triangle is 14:5:11. Find the measures of the angles
Answer:
84 degrees
30 degrees
66 degrees
Step-by-step explanation:
14 + 5 + 11 = 30
180/30 = 6
14 × 6 = 84 degrees
5 × 6 = 30 degrees
11 × 6 = 66 degrees
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Solve for X
Answers:
3
5
-8
11
Please Help
find the value of x.
Answer:
x=136°
Step-by-step explanation:
according to the question
44+x=180
x=180-44
x=136
How much money will Tracy repay to the bank for a loan of $1000 that she borrows for 2 years 8 months at a 12% simple interest rate?
A certain drug dosage calls for 17 mg per kg per day and is divided into two doses (1 every 12 hours). If a person weighs 255 pounds, how many milligrams of the drug should he receive every 12 hours? Round your dosage to the tenth of a milligram.
Answer:
985.15mg
Step-by-step explanation:
Calculation for how many milligrams of the drug should he receive every 12 hours
First step is to calculate the weight in kg
255 lbs = 255/2.2 = 115.9 kg
Second step is multiply mg/kg in order to get total medicine per day
Dose per day=115.9kg × 17 mg
Dose per day= 1,970.3
Third step is to calculate how many milligrams of the drug should he receive by dividing the day dose by 2
Dose milligrams=1,970.3/2
Dose milligrams=985.15mg
Therefore how many milligrams of the drug should he receive every 12 hours will be 985.15mg
