the height of a cylinder is increasing at a constant rate of 2 centimeters per second, and the volume is increasing at a rate of 1152 cubic centimeters per second. at the instant when the height of the cylinder is 33 centimeters and the volume is 403 cubic centimeters, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v
Answers
Answer:
about 2.758 cm/s
Step-by-step explanation:
You want the rate of change of a cylinder's radius, when its height is 33 cm increasing at 2 cm/s, and its volume is 403 cm³ increasing at 1152 cm³/s.
Rate of changeThe volume of a cylinder is given by the equation ...
V = πr²h
Solving for the radius gives ...
r = √(V/(πh))
Differentiating, we have ...
[tex]r'=\dfrac{1}{\sqrt{\pi}}\left(\dfrac{1}{2}V^{-\frac{1}{2}}h^{-\frac{1}{2}}V'-\dfrac{1}{2}V^{\frac{1}{2}}h^{-\frac{3}{2}}h'\right)=\dfrac{hV'-Vh'}{2h\sqrt{\pi Vh}}[/tex]
Filling in the values V = 403, V' = 1152, h = 33, h' = 2, we have ...
r' = (33·1152 -403·2)/(2·33·√(π·403·33)) = 37210/(66√(13299π))
r' ≈ 2.758 . . . . . cm/s
The rate of change of the radius is about 2.758 cm/s.
Related Questions
Test Prep Complete the equation so that it has the solution c = 4 5(2c_ )=2(c+11)
Answers
The unknown value that has the solution as c = 4 of the given algebraic equation is; 2
How to solve algebra word problems?The given algebraic expression for which we want to input a value and solve is given as; 5(2c − ?) =2(c + 11)
Now, we want to find the unknown value that has the solution as c = 4. Thus, we will plug in 4 for c into the given equation to get;
5(2(4) − ?) =2((4) + 11)
5(8 − ?) = 30
divide both sides by 5 to get;
(8 − ?) = 6
Add -6 + ? to both sides to get;
8 − ? - 6 + ? = 6 - 6 + ?
? = 2
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Complete question is;
Complete the equation so that it has the solution c = 4.
5(2c − ?) =2(c+11)
Sir Ronald Fisher's F-distribution is used in many statistical tests. Which one of the following uses the F-distribution for their test statistic?
a. To compare several population means simultaneously
b. Comparison of samples to see if they came from populations with the same proportions.
c. Test of two samples to see if they are from populations with the same median
Answers
The one which uses Sir Ronald Fisher's F-distribution for the test statistic is to compare several population means simultaneously.
What is the F-distribution?The F-distribution was developed by Sir Ronald Fisher to study the behavior of two variances from random samples taken from two independent normal populations. The F-distribution allows us to use a F statistic to compare two populations.
The F-distribution is also known as a right-skewed distribution used commonly in another statistical test called an Analysis of Variance (ANOVA). For ANOVA tests we can use the F-distribution to check whether the variance among the means of two populations significantly differ. The F-distribution can also be used in regression analysis to compare the fit of different models.
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every week, greg spends at least three times the number of hours traveling to work as he does being at work. if greg is at work for 10 hours a week, how much time does he spend traveling to work each week? question 12 options: a) at least 30 hours b) at least 16 hours c) at least 22 hours d) at least 25 hours
Answers
If Greg is at work for 10 hours a week, he spends 30 hours traveling to work.
Explanation
No of hours he works in a week = 10
No of hours he spends on travelling = 3 * no of hours he works in a week
=10 x 3 =
30 hours
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.
The repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
In addition to addition, subtraction, and division, multiplication is a mathematical operation. The four fundamental arithmetic operations are taught to students in their primary classes.
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Select all of the expressions that are equivalent to 5% of 60.
Answers
Answer:
1, 2, and 3
Step-by-step explanation:
5% = 0.05 = 1/20
The first expression is equal, as 5% is equal to 1/20.
The second expression is equal, as 5% in decimal form is 0.05.
The third expression is equal, as 5% is 5/100 in fraction form, which can be simplified to 1/20.
The fourth expression is NOT equal, as it is 20%, not 5%. 1/5 = 0.2.
The fifth expression is NOT equal becauase 0.5 is one half (1/2), which is not equal to 0.05.
Luna Brennan's is depositing $320 in currency,
$1.55 In coins, a check for $213.40, and a check for
$400.25 What is the total deposit?
Answers
the Total deposit will be $935.2.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Luna Brennan's is depositing $320 in currency, currency, $1.55 In coins, a check for $213.40, and a check for $400.25.
So Total deposite will be $320+$1.55+ $213.40+$400.25 = $935.2
Hence the Total deposit will be $935.2
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HELP ASAP
Use the drop-down menus to correctly complete the statement. Consider the equation, y=51(1.42)^t. Since the Choose... is Choose..., this equation represents an Choose... function.
Answers
1.42 is the base of the equation and equation [tex]y = 51 (1.42)^t[/tex] represents the exponential function
What is an exponential function?An exponential function is a function which can be defined as f(x) = aˣ, Where 'x' is a variable and 'a' is a constant.
The given equation is,
[tex]y = 51 (1.42)^t[/tex]
The given function is in exponential power of t.
Since, the 1.42 is the base of the given function
And equation [tex]y = 51 (1.42)^t[/tex] represents the exponential function.
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David pays a flat rate per day to rent his bike. The cost of David's bike rental plan, B(t), can be represented by which of the following functions?
A. B(t) = 5(0,6)^t
B. B(t) = 5(1 + 0.6)^t
C. B(t) = 0.6t + 5
D. B(t) = -0.6t + 5
Answers
The function that represents the cost of David's bike rental plan, B(t) is C. B(t) = 0.6t + 5
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, David pays a flat rate of $5 and and extra $0.6 per day to rent his bike. The cost of David's bike rental plan, B(t). Let the extra day be illustrated by t.
This will be:
B(t) = 5 + (0.6 × t)
B(t) = 5 + 0.6t
The correct option is C.
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Complete question
David pays a flat rate of $5 and and extra $0.6 per day to rent his bike. The cost of David's bike rental plan, B(t), can be represented by which of the following functions?
A. B(t) = 5(0,6)^t
B. B(t) = 5(1 + 0.6)^t
C. B(t) = 0.6t + 5
D. B(t) = -0.6t + 5
Dominic solves the equation 3(x - 5) + 2x = 0 for x using the steps below. drag and drop the correct values to make his work and answer correct
Answers
Answer:
x = 3
Step-by-step explanation:
First, distribute the 3.
3(x - 5) + 2x = 0
3x - 15 + 2x = 0
Next, combine the x's.
(3x + 2x) - 15 = 0
5x - 15 = 0
Then, add 15 to both sides.
5x = 15
Finally, divide by 5 on both sides.
x = 3
The cost of 6 sandwiches and 4 drinks is $36. The cost of 4 sandwiches and 6 drinks is $34. how much does one sandwich cost?
Answers
Answer: $4/sandwich
do not consider the effect of shear stress. find the results in terms of p, e and iz. the beam is thin which means the u and v will be functions of x and y only
Answers
The shear and moment throughout the beam as functions of x are V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft and V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft
What is meant by shear and moment?The ability to construct shear force diagrams (SFD) and bending moment diagrams (BMD) is essential for any student studying statics, mechanics of materials, or structural engineering. Both a long and a short route can be used to complete them. The extended method is more thorough and yields formulas for the internal shear and internal bending moments in beams in terms of x: V(x) and M(x), respectively. In introductory statics classes, this is typically the approach required to demonstrate understanding of the situation. The rapid method eliminates the need for calculations in terms of x and instead employs a more visual method that you may use to highlight the crucial areas on the diagrams before simply connecting the dots.
How to solve?
For 0 ≤ x ≤ 6 ft,
∑ Fy = 0
30 - 2 x - V = 0
V = ( 30 - 2x ) kip
∑M = 0
M + 216 + 2 x ( x / 2 ) - 30 x = 0
M = ( - x² + 30 x - 216 ) kip ft
For 6 ≤ x ≤ 10 ft,
∑ Fy = 0
V - 8 = 0
V = 8 kip
∑ M = 0- M - 8 ( 10 - x ) - 40 = 0
M = ( 8 x - 120 ) kip ft
the shear and moment throughout the beam as functions of x are :
V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft
V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft
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Boris has 22 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating N to F. Then use this equation to find the number of shirts he would have left to fold after folding 15 of them.
Answers
The number of shirts to be left for folding is 7 and the equation is F+N=22.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Boris has 22 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating N to F.
The equation will be written as,
N + F = 22
N + 15 = 22
N = 22 - 15
N = 7
Therefore, the number of shirts to be left for folding is 7 and the equation is F+N=22.
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Point A in the graph below is reflected through the line Y-X.
What are the coordinates
of Point A', the image of Point A?
Answers
Answer:
[tex](6,1)[/tex]
Step-by-step explanation:
When reflecting over [tex]y=x[/tex], [tex](x,y) \longrightarrow (y, x)[/tex].
To test the effect of a new exercise routine on muscle growth, a researcher sets up the following experiment: 60 volunteers subjects (40 men and 20 women) of average build are selected to participate in the study. Their body mass and muscle sizes (biceps, thighs, etc.) are measured. The researcher gives all the men a DVD with the new exercise routine, and the women a DVD with a standard routine, but only the researcher knows this.
The results of the experiment are likely to be invalid mostly because .
The treatment group and control group were not the same size.
The subjects were volunteers.
The subjects did not know if they were getting the real treatment.
The gender of the subject is a confounding variable in this situation.
Answers
The results most probably be invalid because the subjects were voluntary sample.
What is sample in statistics?
Any quantity from a population sample is referred to as a sample statistic. A sample is a collection of components chosen at random from the population. The parameters are the characteristics of the population, and statistics are the characteristics of the sample data. Both the population and the sample are crucial components of statistics.By utilising sample statistics, inferential statistics provides strategies for generalising population features. Consider the following statistic: "50% of kindergarten students in India watch TV for more than 20 hours a week." Not all kindergarten students in India were polled regarding their TV viewing habits in order to reach this conclusion. Instead, by using sample space to estimate the population parameters, this conclusion would have been reached.To know more about statistics check the below link:
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In a math class with 28 students, a test was given the same day that an assignment
was due. There were 20 students who passed the test and 19 students who completed
the assignment. There were 16 students who passed the test and also completed the
assignment. What is the probability that a student passed the test given that they
completed the homework?
Answers
The phrase "given that they completed the homework" indicates that we're only looking at the students who completed the homework. We're ignoring those students who didn't complete the homework.
Of the 19 students who completed the homework, 16 of those passed the test.
This gives us the fraction 16/19 which is about 0.842105263157895 or about 84.2%.
That's your probability that a student passed the test given that they completed the homework.
Solve the system of linear equations by elimination.
4x + 3y = -5
-x+3y=-10
solution:
Answers
Answer:
x=1, y=-3
Step-by-step explanation:
We first see there is a 3y in both equations. We can completely eliminate the y term by subtracting the equations.[tex](4x+3y=-5)-(-x+3y=-10)[/tex]. This gives us (4x--x)=(-5--10), which is 5x = 5. So, x = 1.
Now we can plug this value in to solve for y. Let's plug it in to [tex]-x+3y=-10[/tex]. We get [tex]-1 + 3y=-10[/tex], so 3y = -9 and y = -3. Hope this helps!
the average of a list of 4 numbers is 92.0 . a new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40 , and the fourth number in the new list is 48 . what is the average of this new list of numbers?
Answers
The average of the new list of 4 numbers is 94.
If the average of the original list of 4 numbers is 90, then the sum of these 4 numbers is:
4 x 90 = 360
If the 4th number in the original list is 80, then the sum of the first 3 numbers in the original list is:
360 - 80 = 280
If the first 3 numbers in the new list are the same as in the original list then the sum of these new first 3 numbers is also:
280
If the 4th number in the new list is 96 then the sum of the 4 numbers in the new list is:
280 + 96 = 376
Therefore, the average of the new list of 4 numbers is:
376 / 4 = 94
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7/10 - ____ + 3/2 =6/5?
What's the answer in the blank?
Answers
Answer:1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
7/10-x+3/2=6/5
7/10-x=6/5-3/2
7/10-x=-3/10
-x=-10/10
x=1
[tex]\cfrac{7}{10}-x+\cfrac{3}{2}=\cfrac{6}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{7}{10}-x+\cfrac{3}{2} \right)=10\left( \cfrac{6}{5} \right)}\implies 7-10x+15=12 \\\\\\ 22-10x=12\implies 22=10x+12\implies 10=10x\implies \cfrac{10}{10}=x\implies 1=x[/tex]
What is mZPTR?
(x+28)°
P
R
S
(2x + 16)⁰
Answers
Answer:
140 degrees
Step-by-step explanation:
first we have to find x by setting these 2 angles equal to each other
x+28=2x+16
-x. -x
28=x+16
-16. -16
12=x
Now we need to find the x+28 angle
12+28
40
And since PTR is next to it we subtract 180 from this
180-40
140 degrees
Hopes this helps
Five less than half a number is epaulets to one.
Answers
Answer:
Step-by-step explanation:
this is not a test so stop taking it down
someone pls answer this
Answers
Answer:
Below
Step-by-step explanation:
Expand the parentheses to get
1/5 b - 2a + 1/2 b + 4a gather like terms to get
2a + 7/10 b
b = 10 and m = − 2 in slope intercept form
Answers
Answer:
y=-2x+10
Step-by-step explanation:
Just use the formula y=mx+b and replace the letters with the numbers.
Answer: y = -2x + 10
Step-by-step explanation:
y = mx + b
m = -2
b = 10
x = unknown number
y = m(-2)x + b( 10)
if the angle bisector of each angle of a triangle lies on the same line as the perpendicular bisector of the opposite side, what kind of triangle is it?
Answers
The triangle is an Equilateral triangle.
What is an equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In an equilateral triangle, all three angles are 60 degrees.
Angle bisector means a bisector which divides an angle into two equal parts. A perpendicular bisector is a line which makes 90 degrees with the base and divides it into two equal parts.
In the case of an equilateral triangle, the angle bisector of each angle of a triangle and the perpendicular bisector of the opposite side is the same.
Hence the answer is an equilateral triangle.
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Plsss help!!
Geometry A
Brainliest
Answers
Answer
Step-by-step explanation:
one hundred units of part a are to be processed on a work center. the setup time is 2 hours and the run time per piece is 10 minutes. the total standard time will be
Answers
The total standard time required to processed for one hundred units as per given setup and run time is equal to 1120minutes.
As given in the question,
Number of units to be processed = One hundred units
Conversion used:
1 hour = 60 minutes
Time required for setup = 2 hours
= 2 ( 60) minutes)
= 120 minutes
Run time per piece = 10 minutes
⇒ Run time required for 100 units = 100 × 10
= 1000 minutes
Total standard time for 100 units is equal to
= Run time for 100 units + set time
= 1000 + 120
= 1120 minutes
Therefore, the total standard time required to processed 100 units is equal to 1120 minutes.
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even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from the population mean. what outcome is likely if this happens?
Answers
The outcome is Reject H0 and make a Type 1 error
What is H0?
When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H0.
Here type 1 error is defined as Rejecting H0 when H0 is true.
Therefore, the outcome is Reject H0 and make a Type 1 error.
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PLEASE HELP ASAP
Part A: A 30-kilogram mass is moving across a horizontal surface at 5.0 m/s. The mass comes to
a stop over 6 seconds. What is the acceleration?
Part B: What is the magnitude of the force required to bring the object to a stop?
Answers
Answer:
Below
Step-by-step explanation:
acceleration = Δv / Δt = - 5/6 m/s^2
( negative sign shows it to be a deceleration)
F = ma
= 30 ( -5/6) = -25 N or 25 N in the direction opposite of the velocity ( like a frictional force)
help i give brainless its not that hard I just need help pls
Answers
Answer:
A. Linear
B. Non-linear
C. Linear
Step-by-step explanation:
A linear line has a consistent slope either going down (negative) or going up (positive.)
A. The x values are increasing by a constant rate of 1, and the y values are decreasing at a constant rate of 1. Therefore it is a linear relation.
B. The x values are increasing by a constant rate of 1, but the y-value repeats itself twice in the second and third column. Therefore it does not have a consistent slope and is not a linear relation.
C. The x values are increasing by a constant rate of 1, and the y- values increase by a constant rate of 2 except in column 4 making it a non-linear relation.
I need the answer please.
Answers
Apple pies are $5 and pumpkin pies are $15
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
5a+12p=205............(1)
2a+1p=25.................(2)
Now, Multiply (2) by -12 to get
-24a-12p=-300
and, 5a+12p=205
-24a-12p=-300
Adding above Equations together
-19a=-95
a= 5
and, 2(5)+p=25
10+p=25
p=15
Hence, Apple pies are $5 and pumpkin pies are $15
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Please help! Just Simplify the expression!
Answers
1. Simplified Solution: [tex]a^9[/tex]
2. Simplified Solution: [tex]x^1^0[/tex]
3. Simplified Solution: [tex]1024a^1^0b^1^5[/tex]
4. Simplified Solution: [tex]x^2[/tex]
5. Simplified Solution: [tex]\frac{1}{x^3}[/tex]
6. Simplified Solution: [tex]1[/tex]
7. Simplified Solution: [tex]\frac{4a^6}{b^8}[/tex]
8. Simplified Solution: [tex]32768x^1^0[/tex]
9. Simplified Solution: [tex]\frac{1}{x^1^2y^2^1}[/tex]
10. Simplified Solution: [tex]x^1^4y^1^1[/tex]
11. Simplified Solution: [tex]-\frac{3}{x^4}[/tex]
12. Simplified Solution: [tex]\frac{xy^1^1}{4}[/tex]
13. Simplified Solution: [tex]x^7[/tex]
14. Simplified Solution: [tex]xy^2[/tex]
15. Simplified Solution: [tex]1[/tex]
16. Simplified Solution: [tex]\frac{1}{1000x^1^5y^9}[/tex]
17. Simplified Solution: [tex]\frac{y^3}{x^2}[/tex]
18. Simplified Solution: [tex]\frac{1}{16x^4y^1^0}[/tex]
19. Simplified Solution: [tex]\frac{xy^2}{3}[/tex]
20. Simplified Solution: [tex]-\frac{y^1^2}{9x^4}[/tex]
21.Simplified Solution: [tex]3x^2y^2[/tex]
____________________________________________________
Hope this helps! And good luck! :D
write a question of interest for which a two-sided t test for the difference in populations means can be used to answer example
Answers
To determine whether the mean weight of two distinct turtle species is equal. It would take too much time and money to weigh each turtle because there are thousands of them in each group.
A two-sample t-test is used to determine whether or not genuine population means are equal.
The accompanying null hypothesis is usually used in a two-sample t-test:
[tex]H_0[/tex]: The two population averages are equivalent when 1 = 2.
The alternative hypothesis might have two tails, a left or right tail, or none at all:
Two-tailed [tex]H_1[/tex]: μ1 ≠ μ2 Neither of the two population means is equal.
(Left-tailed) [tex]H_1[/tex]: Population 1 mean is lower than population 2 mean by a factor of 1.
[tex]H_1[/tex] (right-tailed): Populations 1 and 2 have mean values that are higher than each other.
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