Water is leaking out of an inverted conical tank at a rate of 10700 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 26 centimeters per minute when the height of the water is 2.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Answers
Solution :
The diameter of the tank = 3 m = 300 cm
Radius of the tank = 1.5 m = 150 cm
Height of the tank = 8 m = 800 cm
The rate of increase of height of water level = 26 cm/min
∴ [tex]$\frac{dh}{dt} = 20 \ cm/min$[/tex]
The water is leaking at a rate of = 10700 cubic centimeters per min
∴ rate out = 10,700 [tex]$cm^3 / cm $[/tex]
At time 't', the height of water level is 'h' with radius 'r' and volume 'V'.
By the property of similarity of triangles we can write
[tex]$\frac{h}{r} = \frac{800}{150} $[/tex]
[tex]$\frac{h}{r} = \frac{16}{3} $[/tex]
[tex]$r = \frac{3}{16}h$[/tex]
Volume of water at time 't' is given as
[tex]$V= \frac{1}{3} \pi r^2 h $[/tex]
[tex]$V= \frac{1}{3} \pi \left(\frac{3}{16}h\right)^2 h $[/tex]
[tex]$V =\frac{3}{256} \pi h^3$[/tex]
Now differentiating w.r.t 't'
[tex]$\frac{dv}{dt} = \frac{9}{256} \pi h^2 \frac{dh}{dt}$[/tex]
The rate of increase in tank = rate of inward flow - rate of outward flow
[tex]$\frac{dv}{dt} $[/tex] = rate of inward flow - 10,700
rate of inflow = 10,700 + [tex]$ \frac{9}{256} \pi h^2 \frac{dh}{dt}$[/tex]
Substituting the values we get
rate of inflow = 10,700 + [tex]$ \frac{9}{256} \times 3.14 \times (250)^2 \times 26$[/tex]
∴ rate of inward flow = [tex]$1.9 \times 10^5 \ cm^3/min$[/tex]
Related Questions
0.095-20/5=
Write it as a decimal
Answers
Answer:
-3.905
Step-by-step explanation:
0.095 - 20/5
0.095 - 4
-|4-0.095|
-|3.905|
-3.905
The coolor below holds 10 gallons. How many quarts will the jug hold?
40 quarts
20 quarts
160 quarts
20 quarts
Answers
Write an expression for 2 times the difference of 8 and d
Answers
Answer:
2(8-d)
Step-by-step explanation:
16 - 2d
Answer:
2 x (8 - d)
Step-by-step explanation:
2 times means multiply by 2
difference of 8 and d means 8 minus d → 8 - d
Which of the following expressions is a correct interpretation of the expression 2-(-7)
PLEASE ANSWER NOW!!! DURNING A QUIZ
Answers
Answer:
B
Step-by-step explanation:
Because you are subtracting a negative number from a positive number, the two negatives will cancel each other out and it will move to the right.
200 people purchase a lottery ticket. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $5, how many ways can the prizes be awarded?
Answers
EEEEEEEEeeEeeEeEeeEeEeE
5/6=1/3+d
Thank you for the help and have a good day :)
Answers
Answer:
d = 1/2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
5/6 = 1/3 + d
Step 2: Solve for d
Subtract 1/3 on both sides: 5/6 - 1/3 = dRewrite fraction: 5/6 - 2/6 = dSubtract: 3/6 = dSimplify: 1/2 = dRewrite: d = 1/2A cookie costs $1.95. How much would 15 cookies cost at the same price per cookie?
Answers
Answer:
cost of cookie = $1.95
cost of 15 cookies = $1.95 *15
cost of 15 cookies = $29.25
Step-by-step explanation:
3. Lunch
Steven owns a restaurant that specializes in steak burgers! 4 burgers and 3 fries cost $24.50. If a burger costs $5, how much is each order of fries?
LET X =
EQUATION:
5. Dinner
The restaurant is full! There are some four-person tables and 8 tables with couples. If there are 56 people here, how many four-person tables are there?
LET X =
EQUATION
7. Dessert
Stuart’s bought a cake and 6 servings of ice cream. The cake was $12 and the total bill was $33. How much was each order of ice cream?
LET X =
EQUATION
Answers
Step-by-step explanation:
3)
4(5)+3x=24.50
20+3x=24.50
-20 -20
3x=4.50
/3 /3
x=$1.50
5)
4x+2(8)=56
4x+16=56
-16 -16
4x=40
/4 /4
x=10 tables
7)
1(12)+6x=33
12+6x=33
-12 -12
6x=21
/6 /6
x=$3.5
The answer for part (3) is $1.5 each fry, answer for part (5) is 10 four-person table, and answer for part (7) is $3.5 each order of ice cream.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
3)
Let x be the cost of each fry.
4×5 + 3x = 24.50
20 + 3x = 24.50
3x = 4.5
x = $1.5 each fry
5)
Let x be the number of tables for a four-person.
Couple means two persons.
56 - 2×8 = 4x
4x = 40
x = 10 four-person tables
7)
Let x be the cost of each order of ice cream:
12 + 6x = 33
x = $3.5 each order of ice cream.
Thus, the answer for part (3) is $1.5 each fry, answer for part (5) is 10 four-person table, and answer for part (7) is $3.5 each order of ice cream.
Learn more about the linear equation here:
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Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part III: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same amount in fees?
Part IV: How many checks would Cecily need to write per month for the accounts to charge the same amount in fees?
Answers
Part 3
Checking account A has a monthly fee of $16 and a per-check fee of $0.08
If she writes x checks, where x is some nonnegative whole number, then she is charged an additional 0.08x dollars on top of the 16 dollar fee.
The total cost of checking account A is 0.08x+16 dollars.
The total cost of account B is 0.12x dollars for similar reasoning. We don't have a monthly fee, but the cost per check is higher.
Set the two expressions equal to one another to get your answer.
Answer: 0.08x+16 = 0.12x
==============================================
Part 4
Let's solve the equation we set up in part 3
0.08x+16 = 0.12x
16 = 0.12x-0.08x
16 = 0.04x
0.04x = 16
x = 16/0.04
x = 400
If Cecily wrote 400 checks per month, then the cost of each account would be the same.
For account A, it would cost her 0.08*x+16 = 0.08*400+16 = 48 dollars
For account B, it would cost her 0.12*x = 0.12*400 = 48 dollars.
Answer: 400 checks per month
The ratio of the number of silver watches to the number of gold watches in a shop is 2:3. Which of the following best describes the number of silver and gold watches in the shop?
Answers
Answer:
let it snow
Step-by-step explanation:
merry christmas
What is the value of x 39 (2x+1)
Answers
Answer:
2xx_{39}+x_{39}
Step-by-step explanation:
x 39 ( 2 x + 1 )
Use the distributive property to multiply x_{39} by 2x+1.
2x_{39}x+x_{39}
2xx_{39}+x_{39}
Which of the following is equal to 4 2/3 divided by 3 1/2 ? (2 points)
a.
4 2/3 times 3 1/2
b.
14/3 times 2/7
c.
14/3 times 7/2
d.
42/3 times 2/31
Answers
Answer:
c I'm to 100 percent sure but if not it's b it's around 14 for sure
Find the area round to the nearest 10th if necessary
Answers
Answer:
5th
Step-by-step explanation: because its the half and the closest area of the figure
What is the equation relating x and
y together?
X
10
15
20
25
30
y=[?]x +
Answers
when you subtract numbers what are some things you should remember
Answers
Free fall reaches 216km per hour. What is rate in meters per second.? How many meters fall during 20 seconds free fall?
Answers
Given,
Rate of free fall = 216 km/h
Solution,
km/h to m/s is converted as follows :
[tex]216\ \dfrac{km}{h}=216\times \dfrac{1000\ m}{3600\ s}\\\\=60\ m/s[/tex]
So, the rate of fall is 60 m/s.
If t = 20 s
Assume, initial velocity = 0
It will move under the action of gravity.
Using equation of motion,
[tex]h=ut+\dfrac{1}{2}gt^2\\\\h=0+\dfrac{1}{2}\times 10\times 20^2\\\\h=2000\ m[/tex]
Hence, this is all for the solution.
Which equation represents A, the area in square centimeters of the
rectangle below?
23 cm
16
cm
O A. A= 23+ 16
O B. A = (2x 23) + (2 x 16)
O C. A = 23 x 16
O D. A= (23x 16) x 2
Answers
Answer:
C - formula of area of rectangle is l×w
so 23×16
Is k=4 a solution of 4 K + 7=7 k-1
Answers
Answer:
k=8/3
Step-by-step explanation:
Let's solve your equation step-by-step.
4k+7=7k−1
Step 1: Subtract 7k from both sides.
4k+7−7k=7k−1−7k
−3k+7=−1
Step 2: Subtract 7 from both sides.
−3k+7−7=−1−7
−3k=−8
Step 3: Divide both sides by -3.
−3k
−3
=
−8
−3
k=
8
3
The value of k is equal to 8/3 for the given expression.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
The given expression is 4 K + 7=7 k-1, the value of k is calculated as,
4K + 7=7k-1
Separate the like terms in the above equation and solve for the value of k,
4K + 7=7k-1
7k - 4k = 7 + 1
3k = 8
k = 8/3
Therefore, the value of k will be 8/3 in the given equation. The value of k = 4 is wrong.
To know more about an expression follow
https://brainly.com/question/4365680
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What is the slope of the following equation? y =- 1/2×+1
Answers
Answer:
-1/2
Step-by-step explanation:
Answer: -1/2
Reason: In the equation of y = mx + b. The m is the slope, and the b is the y intercept, so that is how I figured out the Slope of the equation. I hope this helps, and Happy Holidays! :)
According to a report in USA Today, more and more parents are helping their young adult children buy homes. You would like to construct a 90% confidence interval of the proportion of all young adults in Louisville, Kentucky, who received help from their parents in buying a home. How large a sample should you take so that the margin of error is no more than 0.06?
Answers
Answer:
The value is [tex]n = 188 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.06[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally will assume that the sample proportion young adults in Louisville, Kentucky, who received help from their parents in buying a home is [tex]\^ p = 0.5[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.645}{0.06 } ]^2 * 0.5 (1 - 0.5 ) [/tex]
=> [tex]n = 188 [/tex]
Which set of numbers represents the RANGE for the following table
x -3 4 6 -12
y 5 -6 2 0
A
{−6,0,2,5}
B
{4, 5, 6, 12}
C
{−3,4,6,12}
D
{0, 5, 6, 2}
Answers
Answer:
The range of the table is:
Range R = {-6, 0, 2, 5}
Hence, option A is true.
Step-by-step explanation:
Given the table
x -3 4 6 -12
y 5 -6 2 0
Determining the range:
We know that the range of a table consists of all the y-values of the given points.
From the given table, it is clear that the y-values are:
y = 5, -6, 2, 0
Thus, the range of the relation in ascending order is:
Range R = {-6, 0, 2, 5}
Please note that the duplicated elements in the range, if any, are written only once.
Therefore, the range of the table is:
Range R = {-6, 0, 2, 5}
Hence, option A is true.
WILL GIVE BRAINLIEST
Answers
Answer: x = 28
Step-by-step explanation:
Trust me :)
Ask any question. i gottu
Answers
Answer:
why?
Step-by-step explanation:
Answer:
..is cereal a soup?
Step-by-step explanation:
is it tho?
The answer to my question.
Answers
Answer:
145°
Step-by-step explanation:
As per the given information: quadrilateral ABCD is a parallelogram.
[tex] m\angle B + m\angle DCB =180\degree \\[/tex]
(adjacent angles of a parallelogram)
[tex] 110\degree + m\angle DCB =180\degree \\
m\angle DCB =180\degree - 110\degree \\
m\angle DCB =70\degree\\
m\angle DCG=\frac{1}{2} m\angle DCB \\(\because GC \: bisects \: \angle DCB) \\
m\angle DCF=\frac{1}{2}\times 70\degree... (\because C-G-F) \\
m\angle DCF=35\degree\\
m\angle BFC = m\angle DCF = 35\degree\\ (Alternate \: \angle s) \\\\
m\angle BFC + m\angle CFA = 180\degree\\ (straight \: line \: \angle s) \\\\
35\degree + m\angle CFA= 180\degree\\
m\angle CFA = 180\degree-35\degree \\\\
m\angle CFA= 145\degree \\\\
\huge\purple {\therefore m\angle GFA = 145\degree} \\(\because C-G-F) \\[/tex]
Which quadrant are the following points located:
(3, –2)
A.
4
B.
2
C.
3
D.
1
Answers
Answer:
A
Step-by-step explanation:
x is positive and y is negative
please help needed today
Answers
Answer:
-9
Step-by-step explanation:it is 2.5 diffrence for each place on the graph so 2.5 times 30 (cause 60 and 90 have a 30 point diffrence) would give you 75 and seince the numbers are decresing to the right side i subtracted 75 from 66 and the awnser is -9. hope this helps and sorry my spelling is bad
The distance from Greg's house to Tanya's house is 7/10 of a mile. Which number correctly shows the number of miles a decimal?* Greg's house C Tanya's house Homile mile 07.10 7.0 0.7 0.07
Answers
Answer:
7 divide by 10=0.7 so 0.7 is the correct answerIn 20 free throw attempts, Raul made 8. Based on this data, what is a reasonable estimate of the probability that Raul will make his next free throw?
Answers
Answer:
40%.
Step-by-step explanation:
Given that Raul made 8 of his 20 free throw attempts, it could be argued that he was 40% efficient on those free throws. This then 8/20 is equal to 0.40. Therefore, following this reasoning, it would be logical to say that Raul has a 40% chance of making his next shot, since that is his hitting percentage so far.
You currently make $18.32 an hour, get time and a half for anything over 40 hours, and a 10% commission on
all sales for the month. Determine your gross monthly salary given that your sales on average are $7,891 per
month and you work 5 hours of overtime a week.
a. $4,011.78
b. $4,132.95
C. $4,269.90
d. $4,320.12
Answers
Answer: b
Step-by-step explanation:
The correct answer is:
C) $4269.90.
Explanation:
40 hours per week at 18.32:
40*18.32 = 732.80.
Over time is time and a half; this means:
18.32*1.5=27.48 per hour overtime.
5 hours of overtime per week would be:
27.48*5=137.40.
Together this makes:
732.80+137.40=870.20 per week.
There are 4 weeks in a month;
4*870.20=3480.80.
You make 10% commission on the sales; 10% = 0.1.
0.1*7891=789.10.
Add this to the monthly income:
3480.80+789.10=4269.90.
A rectangle is drawn so the width is 4 inches longer than the height. If the rectangle's diagonal measurement is 46 inches, find the height.
Give your answer rounded to 1 decimal place.
Inches.
Answers
Answer:
30.5 iches
Step-by-step explanation: