QUESTION 1
A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm/sec. How fast (in cm/sec) is the water level dropping
when the height of the water is 3 cm?(Round your answer two (2) decimal places)
Answers
The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]
We are give a cone with dimensions as seen in the diagram in the attached image.
The volume changes at the rate
[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]
the negative sign is used because the volume of water is reducing.
what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate
[tex]\frac{dh}{dt}|_{h=3cm}[/tex]
The relationship between the volume and the height is given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this
[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]
substitute into the volume formula to eliminate [tex]r[/tex]
[tex]V=\frac{\pi h^3}{27}[/tex]
differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly
[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]
to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]
[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]
So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]
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Related Questions
Find three consecutive even integers such that the
sum of the smallest and the largest is 36.
Answers
n= smallest integer
n+2= middle integer
n+4= largest integer
n + n + 4 = 36
2n+ 4 = 36
2n=32
n= 16 which means that the smallest integer is 16
then you substitute it into the equation for the largest integer
n+4=20
16, 18, 20 is the answer
Find the equation of the line passing
through the points (4, 2) and (6,10).
y = [ ? ]x + [ ]
Answers
Answer:
y = 4x -14
Step-by-step explanation:
The required answer form is slope-intercept form, so we need the slope and the y-intercept of the line.
The slope equation is ...
m = (y2 -y1)/(x2 -x1)
m = (10 -2)/(6 -4) = 8/2 = 4
The y-intercept equation is ...
b = y - mx
b = 2 -4(4) = -14
The equation of the line is y = 4x -14.
Name each polynomial by degree and number of terms .
1) -10x
2) -10r4- 8r2
3) 7
4)9a6 + 3a5 - 4a4 - 3a2 + 9
5)-3n3 + n2 - 10n + 9
6) 7x2 - 9x - 10
7) -4b
8) -9 + 7n3 - n2
Answers
Answer:
Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, a polynomial with 1 term is a monomial. A polynomial with two terms is a binomial, and a polynomial with three terms is a trinomial.
i need help 4 my brother
Answers
Answer:
$1.50
Step-by-step explanation:
pool: 46.50/6=7.75
beach: 46.25/5=9.25
9.25-7.75=1.5
Which relation is also a function? {(2,0), (3,2), (2,3)} {(0,0), (3,0), (5,0)} {(3,1), (3,2), (3,3)} {(5,2), (5,4), (2,6)}
Answers
Answer:
only{(0,0), (3,0), (5,0)} (the x axis)
Step-by-step explanation:
as all the others have more than one possible output y for a unique input x
Wayne Company is considering a long-term investment project called ZIP. ZIP will require an investment of $136,017. It will have a useful life of 4 years and no salvage value. Annual cash inflows would increase by $80,000, and annual cash outflows would increase by $41,900. Compute the cash payback period
Answers
Answer:
3
Step-by-step explanation:
dont ask me
i'm doing this for points, don't question it
The diagonals of a rectangle are always
Answers
Answer:
The diagonals of a rectangle are always congruent
Answer:
Step-by-step explanation:
Diagonals of a rectangle are always congruent.
Suppose that 100,000 men were screened for prostate cancer for the first time. Of these, 4,000 men had a positive result on the screening blood test; of those who tested positive, 800 had a biopsy indicating a diagnosis of prostate cancer. Among the remaining 96,000 men who screened negative, 100 developed prostate cancer within the following year and were assumed to be false negatives to the screen. a) set-up the two-by-two table for this data. (please provide an actual table) b) what is the prevalence of prostate cancer in this population? c) calculate and interpret the sensitivity of this screening test d) calculate and interpret the specificity of this screening test. e) Calculate and interpret the positive predictive value of this screening test.
Answers
An actual two-by-two table is a tabular representation containing two rows and two columns.
The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancerThe rows consist of the predicted positive screening and predicted negative values a)Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
b)The prevalence rate of prostate cancer in this population is:
[tex]\mathbf{ =\dfrac{900}{100000}}[/tex]
[tex]\mathbf{ =\dfrac{9}{1000}}[/tex]
= 9 per thousand.
c)
The calculation of the sensitivity of this screening is as follows:
[tex]\mathbf{=\dfrac{TP}{TP+PN_1}}[/tex]
where;
TP = True positive for cancerPN₁ = Predicted Negative for true positive cancer∴
[tex]\mathbf{=\dfrac{800}{800+100}}[/tex]
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
d)The calculation of the specificity of this screening is as follows:
[tex]\mathbf{=\dfrac{PN_2}{PN_2+TN}}[/tex]
where;
TN = True positive for cancerPN₂ = Predicted Negative for true negative cancer∴
[tex]\mathbf{=\dfrac{95900}{95900+3200}}[/tex]
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
e)
The positive predicted value of the screening test is computed as:
[tex]\mathbf{= \dfrac{TP}{TP + TN}}[/tex]
[tex]\mathbf{= \dfrac{800}{800 + 3200}}[/tex]
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
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Write the slope intercept equation of the line that passes through (2,5) and (-1,3)
Answers
Answer:
y=2/3x+11/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-5)/(-1-2)
m=-2/-3
m=2/3
y-y1=m(x-x1)
y-5=2/3(x-2)
y=2/3x-4/3+5
y=2/3x-4/3+15/3
y=2/3x+11/3
1. The side of a square is 5 units long. What is the area of the square?
20 units?
25 units
10 units?
15 units?
Answers
Answer: 25 units squared
Step-by-step explanation:
1) A square has 4 equal sides.
2) The area of a square is length x width.
3) Therefore, 5x5 = 25 units squared (area is always reported in units squared).
Determine if the ordered pair (6, 4) is a solution to the inequality y is greater than negative one half times x plus 7. Yes, because (6, 4) is above the line No, because (6, 4) is below the line Yes, because (6, 4) is on the line No, because (6, 4) is on the line
Answers
Answer:
No, because (6, 4) is on the line
Step-by-step explanation:
y>-1/2(x)+7
4>-1/2(6)+7
4>-3+7
4>4
I have 17 ones, 15 tens, and 7 thousands
Answers
Answer:
You have 7,167
Step-by-step explanation:
If this was to be converted into a whole number, it would be:
7,167
If 2 people can paint 2 fences in 5 hours, how many hours in all will it take for 8 people to paint 8 fences.
Answers
Answer:
I believe that it would take 5 hours for 8 people to paint 8 fences.
Step-by-step explanation:
If 2 people are painting 2 fences in 5 hours, then 8 people can also paint 8 fences in the same time because each person is painting one fence. It take 5 hours to paint 1 fence if 1 person is painting it. The same goes for 2 or 8 people painting the same amount of fences as there are people. Im not 100% sure if this is accurate but I hope it helps.
Cameron wants to buy a camera for $259. He has $50 and plans to save $20 each week. How many weeks will it take to save enough money to buy the camera? (not including
sales tax)
Answers
Answer:
About 11 Weeks
Step-by-step explanation:
I found out by multiplying 11 by 20 and got 220. Then, adding 50 is 270, which is just over 259. It's not ten because 200 is just underneath his goal.
Maria is riding her bike through the Red Rock Loop. Maria recorded her distance traveled at five different
points during her bike ride. The table of values below shows the results of her bike ride.
Answers
Answer:
MOoo
Step-by-step explanation:
MOoo
Plz HELP ME NOWWWWWWWW
Answers
Answer:
x=13
Step-by-step explanation:
(4x-20+x-1)/8 = (3x-9+4x-16)/12
(5x-21)/8=(7x-25)/12
(5x-21)/8 x 12/1 = (5x-21)/2 x 3/1 = (15x -63)/2
15x - 63 = 14x - 50
x=13
find the answer pleasere
Answers
Answer:
b is the answer f(e) gives us b
5/50 divided by 15/30 solve it out for me please
Answers
Answer:
1/5
Step-by-step explanation:
First and foremost, I want to simplify these fractions, just to make everything a lot easier when I actually get to dividing. 5/50 can be divided by 5/5 to get 1/10, and 15/30 can be divided by 15/15 to get 1/2. So, now we're dividing 1/10 by 1/2.
To divide fractions, we can multiply the first fraction (in this case, 1/10) by the reciprocal of the second fraction (in this case, 1/2). The reciprocal of 1/2 is 2, so we can multiply 1/10 by 2 to find our answer. 1/10 × 2 = 2/10, or 1/5, so this is our final answer.
Hopefully that's helpful! If you have any further questions, let me know. :)
The quotient of given fractions is 1/5.
Given that, 5/50 divided by 15/30.
What are fractions?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Now, 5/50 ÷ 15/30
Keep the first fraction 5/50 same change the division symbol and reciprocate the fraction 15/10
That is, 5/50 × 30/15
= 1/10 × 2/1
= 2/10
= 1/5
Therefore, the quotient of given fractions is 1/5.
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Complete the table for the equation Y=2x+3
Answers
Hope it helps.
Don't forget to click the Brainliest button and if you have any query, feel free to ask in the comment section.
Tell whether tripling the dimensions of a square pyramid would triple the
surface area.
Answers
No. Tripling the dimensions (the side of the square base and the height) would increase the surface area of the pyramid by a factor of [tex]3^2[/tex] or [tex]9[/tex]
Let
[tex]h=\text{the height of the pyramid}\\s=\text{length of one side of the square base}\\t=\text{total surface area of the pyramid}[/tex]
The total surface area of the square-based pyramid is given by
[tex]t=b(b+\sqrt{4h^2+b^2})[/tex]
Let the tripled dimensions be given by [tex]B=3b[/tex] and [tex]H=3h[/tex], then the new surface area will be
[tex]T=B(B+\sqrt{4H^2+B^2})\\=3b(3b+\sqrt{4(3h)^2+(3b)^2})\\=3b(3b+\sqrt{9(4h^2+b^2)})\\=3b(3b+3 \sqrt{4h^2+b^2})\\=9b(b+\sqrt{4h^2+b^2})\\=9t[/tex]
The new surface area will be greater than the original by a factor of [tex]9[/tex]
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Answer: It will be more than triple the area because you square the side to find the area of the base.
Step-by-step explanation:
It will be more than triple the area because you triple the side to find the area of the base. To calculate the surface area of a square pyramid, you need to first calculate the area of the base. To do this, you will need to multiply the length of one side of the square by itself (or square it). Since you are tripling the dimensions of the square pyramid, you will need to triple the side of the base, which will result in an area that is more than three times larger.
help i made it worth a lot of points
Answers
Answer:
36x^6/y^10
Step-by-step explanation:
First evaluate the parentheses, 6x^3 x 6x^3 = 36x^6
y^5 x y^5 = y^10 ; remember m^k x m^r = m^k+r
final answer should be 36x^6/y^10
hope this helps :')
Answer:
[tex] \dfrac{36x^6}{y^{10}} [/tex]
Step-by-step explanation:
First, deal with the exponent 2 outside the parentheses.
Raise each factor to the second power.
[tex] (\dfrac{6x^3}{y^5})^2 = [/tex]
[tex] = \dfrac{6^2(x^3)^2}{(y^5)^2} [/tex]
To raise a power to a power, multiply the powers.
[tex] = \dfrac{36x^6}{y^{10}} [/tex]
Answer fast plzz... i will give brainly
Answers
Answer:
1.15 inches
Step-by-step explanation:
Line k passes through the point (6, -7) and has a slope m= -1/2.
Which is the equation of a line that is perpendicular to line k and passes through the
point (-4, 9)?
Answers
Answer:
y = 2x + 17
Step-by-step explanation:
lmk if you want an explanation
Ella takes 1 3/5 hours to complete a
painting. Holly takes 3/4 of the time that
Ella takes. How long will Holly take to complete 5 paintings?
Answers
Answer:
6 hours
Step-by-step explanation:
FInding Holly's time of Ella's
Ella = [tex]1 \frac{3}{5}[/tex]
Holly = [tex]\frac{3}{4} \:\mathrm{of}\:1 \frac{3}{5}[/tex]
Solve:
[tex]\frac{3}{4} \:\mathrm{of}\:1 \frac{3}{5}[/tex]
[tex]= \frac{3}{4} \times1 \frac{3}{5}[/tex]
[tex]1\frac{3}{5} =\frac{8}{5}[/tex]
[tex]\frac{3}{4}\times \frac{8}{5}=\frac{24}{20}[/tex]
[tex]\frac{24}{20} =\frac{6}{5}[/tex]
Now, we can find how many hours it takes holly to complete 5 paintings:
[tex]\frac{6}{5}\times5[/tex]
[tex]=6[/tex]
Therefore, it will take Holly 6 hours to complete 5 paintings.
What is the inverse of y=5x-5
Answers
Answer:the answer is in the picture below
Step-by-step explanation:plz give brainlist
The total cost for a piece of land is 600000. If the land is 100 meter shorter and each meter costs 1000 more the total cost would remain unchanged. Use a quadratic equation to determine the length of the land.
Answers
Answer:
5,00000000
Step-by-step explanation:
6000000000
The graph show how many minutes it takes Ziah to run a certain distance in the city What is the constant of proportionality? Write your answer as a decimal
need answer in 5 minutes will give brainliest
Answers
Explanation:
The constant of proportionality is the same as the slope for equations of the form y = kx.
To find the value of k, we divide the y over x values.
k = y/x = 12/8 = 1.5
or
k = y/x = 6/4 = 1.5
Either way the answer is 1.5
This means Ziah ran at a rate of 1.5 city blocks per minute.
Find the slope of the line.
Answers
The diameter of a circle fits around the circle ______ times.
Answers
Answer:
it fits around [tex]\pi[/tex] times which is approximately 3 times
Step-by-step explanation:
[tex]\pi[/tex]
in hillary's garden, she has 5 variety of snake plants and 15 variety of orchids. what is the ratio of snake plants to orchids?
Answers
Answer:
1:3
Step-by-step explanation:
She has 1 snake plant for every 3 orchids.