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]
Learn more about related rate of change here: https://brainly.com/question/15576763
Related Questions
The two legs of right triangle measures 6 and 8 inches respectively. What is the area of the circle that contains all 3 verticals of the triangle
Answers
Answer:
See image.
Step-by-step explanation:
Remember if you have a right angle inside of a circle, the hypotenuse is going to land exactly on the diameter. Also, Area of a circle = (pi)r^2 Lastly, remember pythagorean triples such as 3,4,5 or at least, the Pythagorean theorem a^2 + b^2 = c^2
What is the sum of the coefficients in the expression below?
22°y2 + 5x+ y2 - 6xy' +7
Answers
Answer:
485y to the power 2 + 5x to the power 2 - 6xy to the power 3 + 7
Step-by-step explanation:
I hope this helps. Also, there's this free app called Quick Math. If you need the steps, you should check there first, and maybe you should try that for other math problems as well.
Good luck and have a great rest of your day.
what is an equation of the line that passes through the points 0,-2and 0,-5
Answers
Answer:
Any equation with a slope of 3 will work. You can use any y-intercept. This equation will work: y = 3x+1
Step-by-step-explanation:
3x says that the slope is 3, and on a coordinate plane, 2 is 3 places above 5, and since the slope is 3, it will go 3 spots up, and run into (0,2)
What is the next step in constructing an angle (MNO ) congruent to the given angle (ABC ) with a straightedge and a compass?
Answers
The next step in constructing an angle (MNO ) congruent to the given angle (ABC ) is, using N as the center and the same radius as before, draw an arc that intersects |NO|. label the arc PQ where Q intersects |NO|.
To construct angle MNO congruent to the given angle ABC, the following conditions must be satisfied:
The two angles must be equal (∠ABC = ∠MNO).The radius of the two triangles must be equal.The radius from center N must be equal to radius BA and BC.The radius of angle MNO is NO and it must equal BA and BCThus, we can conclude that, the next step in constructing an angle (MNO ) congruent to the given angle (ABC ) is, using N as the center and the same radius as before, draw an arc that intersects |NO|. label the arc PQ where Q intersects |NO|.
Learn more about construction of congruent angles here: https://brainly.com/question/20097419
Mrs. terrance has a large bin of 236 crayons. She divides them equally among four containers.
Answers
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students were surveyed ?
Answers
Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:
375 x 2 = 750
In 2020 researchers took random samples to compare the proportion of adult females to the proportion of adult males who use 2 or more credit/debit cards. The adults were aged 21 and older and they lived in all areas of the U.S. Based on the data collected, the researchers computed a 96 percent confidence interval for the true difference between the proportions of adult females minus the proportion of adult males who use 2 or more credit/debit cards. The confidence interval is: (0.013, 0.049). Assume all checks have been verified.
Question:
Choose the best answer below concerning the confidence interval for the difference between the true proportions of adult females minus the true proportion of adult males who use 2 or more credit/debit cards.
Answers
Using the z-distribution, it is found that the correct option is:
[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
A confidence interval is given by:
[tex]p \pm zs[/tex]
In which:
p is the estimate of the proportion.z is the critical value.s is the standard error.In this problem, the proportions are:
A proportion [tex]p_1[/tex] in a sample of size [tex]n_1[/tex].[tex]p_2[/tex] in a sample of size [tex]n_2[/tex].Hence, the standard errors are:
[tex]s_1 = \sqrt{\frac{p_1(1 - p_1)}{n_1}}, s_2 = \sqrt{\frac{p_2(1 - p_2)}{n_2}}[/tex]
When two proportions are subtracted, the estimate is the subtraction of proportions, while the standard error of the subtraction is the square root of the sum of each standard error squared, hence:
[tex]p = p_1 - p_2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Thus, the interval is:
[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
A similar problem is given at https://brainly.com/question/12517818
State the postulate or theorem you would use to prove each pair of triangles congruent.
a) SSS
b) SAS
c) ASA
d) AAS
e) HL
f) Not possible
Answers
Answer:
f) Not possible
Step-by-step explanation:
The triangles can be shown to be similar by SAS, but the corresponding sides are not marked as congruent. With the given information, it is not possible to show the triangles are congruent.
Solve the inequality 2x^2-6>0
Answers
Answer:0
Step-by-step explanation:
HELP
HOW AM I MEANT TO ANSWER THIS QUESTION I WOULD ASO LIKE ANSWER.
THX
100 point on the line
Answers
Answer:
2^5, 6^2 ,3^4, 5^3
Step-by-step explanation:
6^2 = 36
3^4 = 81
2^5 = 32
5^3 = 125
Answer:
Step-by-step explanation:
Solve for the value of x
Answers
Answer:
x=9
Step-by-step explanation:
To solve for x, you can set up a proportion between the 2 triangles we see.
The small triangle can be written as [tex]\frac{16}{20}[/tex], and the large triangle can be written as [tex]\frac{16+12}{20+2x-3} = \frac{28}{2x+17}[/tex].
Set both proportions equal to each other.
[tex]\frac{16}{20}=\frac{28}{2x+17}[/tex]
Cross multiply and solve for x.
[tex]16(2x+17)=(28)(20)[/tex]
32x+272=560
32x=288
x=9
What is the value of x and y?
Answers
Answer:
x = 90y = 43Step-by-step explanation:
The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.
x° = 90°
__
The acute angles in a right triangle are complementary.
y° = 90° -47°
y° = 43°
Which ordered pair is in the solution set of 3x − 2y ≥ -1?
F.(-2, -2.5)
G.(-1, 1)
H.(2, 4)
J.(1, 2.5)
Answers
Answer:
G
Step-by-step explanation:
Therefore, the option [tex]G(-1,1)[/tex] is correct.
What is the inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Here given inequality equation
[tex]3x- 2y \geq -1[/tex]
When the points [tex](-1,1)[/tex] so it would be
[tex]3(-1)-2(1)\geq -1\\\\-3-2\geq -1\\\\-5\geq -1[/tex]
Hence, the option [tex]G(-1,1)[/tex] is correct.
To know more about the inequality
https://brainly.com/question/12679763
#SPJ6
The polygons are similar. Find the value of each variable.
Answers
Answer:
z = 2Step-by-step explanation:
Similar figures have equal ratios of corresponding sides:
z / (z + 4) = 3/ 99z = 3(z + 4)9z = 3z + 129z - 3z = 126z = 12z = 2help me please I'm stuck on this question!!!!
Answers
Answer:
1: 2.8
Step-by-step explanation:
15:42
Divide each side by 15
15/15 : 42/15
1: 2.8
What is the x-value of the vertex of f(x) = -x2 + 9x - 11 ?
Answers
Answer:
7
Step-by-step explanation:
7
You use substitution to solve a system of equations and, after simplifying, end with a statement that says 7 7. Describe what this statement means about the number of solutions and about the graph of the system.
Answers
Answer:
Sample Response: Since the statement is true, there are an infinite number of solutions to the system. This statement also indicates that the lines are equivalent.
Find the monthly house payments necessary to amortize a 10.8% loan of $125,800 over 20 years.
.
The payment size is $
Answers
Answer:
13,586400000000001 per time
Step-by-step explanation:
Which pair of fractions in not equivalent fractions? Please answer it’s a test
Answers
Answer:
7/8 , 5/6
Explanation:
7/8 , 5/6 are the only fractions that are not equivalent fractions as when they are simplified they don't share the same fraction. Hope this helps.
please help! ASAP I need help fast!!
Answers
Answer: 4.8
Explanation: divide total needed of blue paint (3) by 1/2 to find the ratio, which is 6. then multiply that by 4/5 to get the total of yellow paint, which is 4.8
Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles by SSS or SAS, write "not enough information". Explain your answer.
Write a congruence statement and give a reason why the triangles are congruent. Select the correct choice below and, if necessary, write the vertices of the second triangle in the correct order.
Answers
Answer:
option B is correct answer. ∆SVZ~=∆YVX, SSS
Step-by-step explanation:
reasons,
VY=VS, S
YX=SZ, S
VX=VZ, S
therefore, ∆SVZ~=∆YVX.
hope this helps you.
The two triangles are congruent by side angle side property. The correct option is A.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
Given that there are three triangles and these three triangles are connected to each other at the centres' A, B, and C.
The diameter of the three circles is HF, DF, and DH. The three diameters are similar in shape and are also equal to each other.
To know more about congruency follow
brainly.com/question/2938476
#SPJ2
write an equation in slope-intercept form for the line with y-intercept −8 and slope 1/3.
Answers
Answer:
y = x/3 - 6
Step-by-step explanation:
yeah-ya......... right?
How do I find the degree measure?
Answers
Answer:
The Degree Measure of the Angle = Radian x (180/)
Six movie tickets cost $96 what is the cost per ticket
Answers
Cost of 6 tickets = $ 96
Cost of 1 ticket = ?
Cost of 1 ticket = 96/6
Cost per ticket = $ 16
______
Hope it helps ⚜
Step-by-step explanation:
6 tickets=$96
1 ticket =96/6
=16
1/3(6-9j)
PLEASE HELP!!!
Answers
Answer:
2-3j
Step-by-step explanation:
Distribute 1/3 to the rest of the equation and you'll get 2-3j
I hope this helps!
1/3x6/1 = 6/3
1/3x-9j=-9j/3
6/3-9j/3
Luke portrays this time in Jesus’ ministry as very successful, but he starts giving hints of things to come. For instance, after the healing of the boy, Jesus seems to randomly say that he is going to be betrayed. Why would Jesus have picked that time to say such a thing? I think Jesus picked this time to warn the disciples about what was going to happen.
Answers
What is 5/8 divided by 1/4
Answers
Answer:
the answer should be 2.5
Step-by-step explanation:
when divided 5/8 u get 0.625 and when u divided 1/4 u get 0.25 and u divided both answer u get 2.5
somebody please help me:(
Answers
ABC has vertices A(-3,2). B(3,2), and C(0, – 3). Is ABC scalene, isosceles, or equilateral?
Is ABC scalene, isosceles, or equilateral?
Answers
Answer:
isoselses!
Step-by-step explanation:
i hope that helps
if lateral surface area of cube is double then the ratio of volume of new cube to original cube
Answers
Answer:
2√2
Step-by-step explanation:
The area ratio is the square of the side length ratio, so the ratio of side lengths is √2.
The volume ratio is the cube of the side length ratio, so the new cube has a volume that is (√2)³ times that of the original.
The volume ratio is 2√2.