Answer:
a) dA/dt = 125,42 mm/min
b) dh/dt = - 1,78 mm/min
Step-by-step explanation:
The volume of the cylinder is:
V(c) = π*r²*h ( r and h radius of the base and heigh respectively )
Then the surface area is: Area of the base : π*r²
Plus lateral area : h*2*π*r
A(c) = π*r² + 2*π*r*h
With the help of differentials we obtain:
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt (1)
In this equation and at time t we know:
r = 18 mm dr/dt = 2 mm/min h = 8 mm dh/dt = ??
dA/dt = increasing rate of the surface area ( with respect to time)
To find dh/dt we know:
V(c) is constant, then
V(c) = π*r²*h then h = V(c) / π*r²
dh/dt = - [V(c)*2*π*r*dr/dt ] / π²*r⁴
By subtitution of V(c)
dh/dt = - [ π*r²*h *2*π*r*dr/dt ] / π²*r⁴
dh/dt = - [2*π²h*r³*dr/dt ] /π²*r⁴
dh/dt = - [2*h* dr/dt ] / r
dh/dt = - 2*8*2 / 18 mm/min
dh/dt = - 1,78 mm/min
By subtitution in equation (1)
dA/dt = 2*π*r*dr/dt + 2*π*h*dr/dt + 2*π*r*dh/dt
dA/dt = 2*π*18*2 + 2*π*8*2 + (- 2*π*18*1,78 )
dA/dt = 226,20 + 100,53 - 201,31
dA/dt = 125,42 mm/min
Following are solutions to the given points:
Formula:
Cylinder volume [tex]v = \pi r^2 h...............(i)[/tex]
[tex]\to \frac{dr}{dt} = 2 \frac{mm}{min}\\\\ \to \frac{dh}{dt} = -2 \frac{mm}{min}\\\\ \to h=8\\\\ \to r=18 \\\\[/tex]
Part A:
Calculating the circular area of the surface:
[tex]\to A=\pi r^2\\\\[/tex]
So, [tex]\frac{dA}{dt}=2 \pi r \frac{dr}{dt}.........(ii)[/tex]
Therefore
[tex]\to \frac{dA}{dt}= 2\pi \times 18 \times 2= 72 \pi \ \frac{mm^2}{min}\\\\[/tex]
Part B:
[tex]\to \frac{dh}{dt}= - 2 \frac{mm}{min}[/tex]
Learn more:
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PLEASE HELP!! Algebra 2
Answer:
No
Edit:
Yes, based on original equation. (Credit to greenpumpkin for correction)
Step-by-step explanation:
For this problem, we simply need to find the values of x that can make the equation true. So, let's begin by isolating the "x" variable.
sqrt(2x + 13) = x + 5
[sqrt(2x + 13)]^2 = (x + 5)^2
2x + 13 = x^2 + 10x + 25
0 = x^2 + 8x + 12
Note, we can remove the sqrt method by squaring both sides of the equation. Doing this, we see we have a quadratic equation meaning we can apply the quadratic formula to find solutions for x.
[-b +/- sqrt( b^2 - 4(a)(c) ) ] / 2a
Let a = 1, b = 8, and c = 12
[-8 +/- sqrt( (8)^2 - 4(1)(12) ) ] / 2(1)
= [-8 +/- sqrt( 64 - 48 ) ] / 2
= [-8 +/- sqrt(16) ] / 2
= [ -8 +/- 4 ] / 2
So, x = [ -8 + 4 ] / 2 and x = [-8 - 4 ] / 2
x = [-4] / 2 = -2 and x = [-12] / 2 = -6
Hence, the two values of x that can solve this quadratic equation are x = -2 and x = -6.
Therefore, we know that x = -6 is not extraneous, meaning it is a solution to our equation.
Cheers.
----------------------------------------------------
Edit:
Plugging the value of -6 back into the original equation, we get the following:
sqrt(2x + 13) = x + 5
sqrt(2(-6) + 13) = (-6) + 5
sqrt (1) = -1
1 != -1
Given that 1 cannot equal negative 1, we can say that x = -6 is an extraneous solution. (Credit to greenpumpkin for correction)
Round to the nearest whole number and cluster to give an estimate for 15.23 + 12.8 + 4.93 + 7.21.
Answer:
the answer is 40
Step-by-step explanation:
15.23+12.8+4.93+7.21=40.17 then you round 40.17 to 40
Answer:
40
Step-by-step explanation:
15.23 + 12.8 + 4.93 + 7.21
27.31 + 12.34
39.65
round the number to a whole number
40
Please give me the correct answer
Answer:
i dont think so.
Step-by-step explanation:
Q#2 Pleaseeee answer my guy it’s literally the biggest grade I got and I’m tiredddd
Answer:
Add 3 to both sides.
2x=9+3
simplify 9+3 to 12
2x=12
Divide both sides by 12
x= 12
2
simplify
x=12
please answerrrrr!!! im soo confused!!!
Answer:
97%
Step-by-step explanation:
If you get 100% on a test, you got all the answers correct.
It doesn't matter how many questions there are. If you got all of them correct, you get 100%.
What if you have 100 questions on a test?
If you got 85 questions correct, on a 100 question test, your grade would be 85%.
If you got 35 questions correct, on a 100 question test, your grade would be 35%.
If you got 98 questions correct, on a 100 question test, your grade would be 98%.
If you count 100 trees, and 97 of them were evergreen, the percentage of trees that are evergreen would be 97%.
BRainliest and 5stars question below
9514 1404 393
Answer:
∆KAF, by rule LA
Step-by-step explanation:
The angle bisector divides angle FAP into two equal angles KAF and KAP. The two right triangles share side KA, so we have a leg KA and an angle KAF, KAP that are the same in the two triangles. That is enough to invoke rule LA (leg, angle) to claim congruence.
∆KAP ≅ ∆KAF by rule LA
Is the following relation a function?
Yes
No
Answer:
.....yes
Step-by-step explanation:
kevin has a ratio of 2 wrong answers to 7 correct answers on his math test. If he got 6 questions ewrong then how many did he answr correctly
Answer:
21 questions
Step-by-step explanation:
Given
[tex]Wrong : Right = 2:7[/tex]
Required
Determine the number of correct answers if he answered 6 wrongly
The required ratio can be represented as:
[tex]Wrong : Right = 6 : X[/tex]
Where X represents number of right answers for 6 wrong answers.
Next, we equate both ratios:
[tex]6:X = 2:7[/tex]
Convert to fraction
[tex]\frac{6}{X} = \frac{2}{7}[/tex]
Cross Multiply
[tex]X * 2 = 6 * 7[/tex]
[tex]2X = 42[/tex]
Divide through by 2
[tex]X = 21[/tex]
Hence, he answered 21 correctly
What is 1/4(8+x+4) simplified using the distributive property
Answer:
1/4x+3
Step-by-step explanation:
1/4(8+x+4)
1/4 *8 + 1/4*x+1/4*4
2+1/4x+ 1
1/4x+3
Hope this helps you!
Happy holidays!
Have a merry christmas and new year!
Answer:
2+1/4x+1
3+1/4x
Step-by-step explanation:
There you go final answe is
3+1/4x
Rick’s scores in his last 15 rounds of golf are 72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, and 72. If he scores an 80 on each of the next three rounds, which measure of center would increase more, the mean or median?
Answer:
The median increased more
Step-by-step explanation:
Given that:
Scores on last 15 :
72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, 72
Obtaining the range, mean, median and mode from the data above :
Rearranged data:
68, 70, 72, 72, 72, 74, 75, 75, 77, 78, 79, 80, 81, 83, 84
Range = 84 - 64 = 16
Mode = 72 - frequency of 3)
Mean = ΣX / n where n = sample size
Mean = 1140 / 15 = 76
Median = 0.5(n+1)th term = 0.5(16)th term =
8th term = 75
A score of 80 on each of next 3 rounds :
72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, 72, 80, 80, 80
Rearranged data:
68, 70, 72, 72, 72, 74, 75, 75, 77, 78, 79, 80, 80, 80, 80, 81, 83, 84
Range = 84 - 68 = 16
Mean = ΣX / n where n = sample size
Mean = 1380 / 18 = 76.67
Median =0.5(n+1)th term = 0.5(19)th term =
9.5 = (9th term +. 10th term) / 2 = (77 +78) / 2 = 77.5
which equation is equivalent to y= Ax + By = C
Answer:
slope intercept form
Step-by-step explanation:
that's what ax + by = c is
xoxo, your highness...The amount of money in Mark's bank account after x months is given by the function
f(x) = 1000 - 200x. Select all the true statements.
Pick up to 2 answers.
A. The account began with $1000.
B. The account began with $200.
C. Mark withdraws $1000 each month.
D. Mark withdraws $200 each month.
E. Mark deposits $200 each month.
There are 2 answers for this
(Please use a comma to separate them)
Emma got 90% of the questions on her history test correct if she answered 27 questions correctly, how many questions did Emma get wrong?
There were (A) questions on the test so she got (B) questions wrong
Answer:
There were 30 questions on the test so she got 3 questions wrong.
Step-by-step explanation:
Given that:
Correct answers by Emma = 27
Percentage of correct answers = 90%
Let,
x be the total number of questions on test
90% of x = 27
[tex]\frac{90}{100}x=27[/tex]
[tex]0.9x=27[/tex]
Dividing both sides by 0.9
[tex]\frac{0.9x}{0.9}=\frac{27}{0.9}\\x=30[/tex]
There were 30 questions on the test.
Wrong answers = Total questions - Correct answers
Wrong answers = 30-27 = 3
Hence,
There were 30 questions on the test so she got 3 questions wrong.
The solution to the system of equations shown is (2, 0).3x − 2y = 6x + 4y = 2When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14.Which system of equations will also have a solution of (2, 0)?6x - 4y = 6x + 4y = 26x − 4y = 62x + 8y = 2x + 4y = 27x = 146x − 4y = 67x = 14
the answer is c i got it on edge 2020
Answer:
c
Step-by-step explanation:
Find the solution set of the inequality
- 4x + 35 > 2
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 33/4
Interval Notation:
(− ∞, 33/4)
4(5a + 3) = 20a + 12 represent which property of multiplication?
Answer:
Distributive property of multiplication
Step-by-step explanation:
The distributive property of multiplication is basically distributing the terms outside the bracket to all the terms inside the bracket. In this case, 4 is multiplied to 5a as well as 3.
A reading teacher brought sets of different numbers of books for her class. She paid the same price for each book
Complete the table to show the number of books she bought or the price she paid
(Put your answers in the Order of a,b,c)
Answer:
A) $15
B) 8
C) $25
Step-by-step explanation:
The day after a protest held by an employee's union, 32 out of 40 employees did not show up for work at the shoe factory, Which represents the percent of the employees who did show up for work the day after the protest?
Answer:
Step-by-step explanation:
32 out of 40 did not show
8 out of 40 did show
When you ask "What is 8 out of 40?" you want to know what percent 8 is out of 40.
Here are step-by-step instructions showing you how we calculated 8 out of 40 as a percentage:
The first step is to divide 8 by 40 to get the answer in decimal form:
8 / 40 = 0.2000
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.2000 * 100 = 20.00%
Answer:
20 %
Step-by-step explanation:
Dennis has less than 70 min. to spend on some homework questions. He spent 10 min. on the first two questions. The rest of the questions will take 52 min. each.
Which statement describes the solution to this inequality?
Drag and drop the answer into the box.
Answer:
A. Dennis can complete less than 24 questions.
Step-by-step explanation:
Let x represent the remaining number of questions to be completed. He can complete each of them in 5/2 minutes each; this gives us the expression 5/2x.
He has already spent 10 minutes; this gives us 5/2x+10.
He has less than 70 minutes to spend; this gives us the inequality
5/2x+10<70
Subtract 10 from each side:
5/2x+10-10 < 70-10
5/2x < 60
Divide both sides by 5/2:
5/2x÷5/2 < 60÷5/2
x < 60/1 ÷ 5/2
To divide fractions, flip the second one and multiply:
x < 60/1 × 2/5
x < 120/5
x < 24
Answer:
Dennis can complete fewer than 24 questions.
Step-by-step explanation:
How to find inequalities
Answer:
Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
Step 2 Simplify by combining like terms on each side of the inequality.
Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.
Hope that helped happy holidays!
What’s the quotient ? I’m helping out with my sisters homework once again and I don’t wanna explain it to her. Please help me ;-;
Answer:
quotient is the answer to division. So if 7/2=3 with a remainder of 1, then the quotient is 3
Jamie borrows $2,000 to purchase a new living room furniture set. She will pay an 8% interest rate over 18 months. How much will Jamie pay in interest?
Answer: 2800 dollars in intrest
Step-by-step explanation:
Don’t worry about the one at the bottom BUT HELP MEEEEE
Answer:
e. 79/30 f. 18.2
Step-by-step explanation:
Salvador bought 6 lbs of coffee for $18.66. What is the unit price per pound?
Answer:
$3.11
Step-by-step explanation:
It is given that,
Salvador bought 6 lbs of coffee for $18.66.
We need to find the unit price per pound.
The unit price per pound is calculated by dividing total cost by 6 as follows :
[tex]C=\dfrac{18.66}{6}\\\\=\$3.11[/tex]
Hence, the unit price per pound is $3.11
The probability that a vehicle will change lanes while making a turn is 45%. Suppose a random sample of 7 vehicles are observed making turns at a busy intersection. Find the probability that a least 5 vehicles will change lanes while making the turn.
Answer:
0.1529
Step-by-step explanation:
Given that:
Probability of changing lane ; p = 45% = 0.45
Sample size (number of trials) = n = 7
Probability that atleast 5 vehicles will change lane :
Using the binomial probability formula :
P(x = x) = nCx * p^x * (1 - p)^(n-x)
(1 - p) = 1 - 0.45 = 0.55
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x = 5) = 7C5 * 0.45^5 * 0.55^2
P(x = 5) = 21 * 0.45^5 * 0.55^2 = 0.117221
P(x = 6) = 7C6 * 0.45^6 * 0.55^1
P(x = 6) = 7 * 0.45^6 * 0.55^1 = 0.031969
P(x = 7) = 7C7 * 0.45^7 * 0.55^0
P(x = 7) = 1 * 0.45^7 * 0.55^0 = 0.003736
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x ≥ 5) = 0.117221 + 0.031969 + 0.003736
P(x ≥ 5) = 0.152926
P(x ≥ 5) = 0.1529
Using the binomial distribution, it is found that there is a 0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.
For each vehicle, there are only two possible outcomes, either they change lanes while making a turn, or they do not. The probability of a vehicle changing lanes while making a turn is independent of any other vehicle, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The probability that a vehicle will change lanes while making a turn is 45%, hence [tex]p = 0.45[/tex].A sample of 7 vehicles is taken, hence [tex]n = 7[/tex].The probability that at least 5 vehicles will change lanes while making the turn is:
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.45)^{5}.(0.55)^{2} = 0.1172[/tex]
[tex]P(X = 6) = C_{7,6}.(0.45)^{6}.(0.55)^{1} = 0.0320[/tex]
[tex]P(X = 7) = C_{7,7}.(0.45)^{7}.(0.55)^{0} = 0.0037[/tex]
Then
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1172 + 0.0320 + 0.0037 = 0.1529[/tex]
0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
help me pleaseeeeeeeee
Answer:
C is because it doesn't have any repeating x-values or y-values
Step-by-step explanation:
I need help with this I’ll mark you
Answer:
The answer is C
The temperature in Minsk was recorded over a period of four hours. The
equation
y = -5x + 54
describes the temperature over this time, where y is the temperature in
degrees Fahrenheit (°F) and x is the number of hours since measurements
started. Which of the following statements correctly describes the
temperature?
A. It was -5°F after four hours, and it is rising by 54 degrees per
hour.
B. It was 54°F when the temperature was first measured, and it is
dropping by 5 degrees per hour.
c. It was -5°F when the temperature was first measured, and it is
rising by 54 degrees per hour.
O D. It was 54°F after four hours, and it is dropping by 5 degrees per
hour
Answer:
D.) it was 54 degrees Fahrenheit when the temperature was first measured, and it is dropping by 5 degrees per hour
Step-by-step explanation:
I took the quiz
Answer:
D
Step-by-step explanation:
I took the test
Can someone solve this for me please?
1/3h = -2/3
Answer:
h = -2
Step-by-step explanation:
Just plug it into a calculator
Answer:
h=-2
Step-by-step explanation:
1/3h = -2/3
To find the h divide both sides by 1/3.
1/3h÷1/3 = -2/3÷1/3
h=-2
i need help with this asap! i will give brainliest!!
Answer:
97
Step-by-step explanation:
Angle on a straight line = 180
106 + ∠st = 180
∠st = 180 - 106 = 74
x = ∠st + 23
= 74 + 23
= 97
Answer:
51 degrees
Step-by-step explanation:
This is a scalene triangle. Which means it sums up to 180 degrees. Therefore, you have to add up all the degrees to 180. 106+23 is 129, and 180 - 129 is 51.