Answer:
it is C
Step-by-step explanation:
Which is NOT the graph of a function?
Οε:
te
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)
Answer:
[tex]r = 1.34[/tex]
Step-by-step explanation:
Given
Solid = Cylinder + 2 hemisphere
[tex]Volume = 10cm^3[/tex]
Required
Determine the radius (r) that minimizes the surface area
First, we need to determine the volume of the shape.
Volume of Cylinder (V1) is:
[tex]V_1 = \pi r^2h[/tex]
Volume of 2 hemispheres (V2) is:
[tex]V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3[/tex]
[tex]V_2 = \frac{4}{3}\pi r^3[/tex]
Volume of the solid is:
[tex]V = V_1 + V_2[/tex]
[tex]V = \pi r^2h + \frac{4}{3}\pi r^3[/tex]
Substitute 10 for V
[tex]10 = \pi r^2h + \frac{4}{3}\pi r^3[/tex]
Next, we make h the subject
[tex]\pi r^2h = 10 - \frac{4}{3}\pi r^3[/tex]
Solve for h
[tex]h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}[/tex]
[tex]h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}[/tex]
[tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]
Next, we determine the surface area
Surface area (A1) of the cylinder:
Note that the cylinder is covered by the 2 hemisphere.
So, we only calculate the surface area of the curved surface.
i.e.
[tex]A_1 = 2\pi rh[/tex]
Surface Area (A2) of 2 hemispheres is:
[tex]A_2 = 2\pi r^2+2\pi r^2[/tex]
[tex]A_2 = 4\pi r^2[/tex]
Surface Area (A) of solid is
[tex]A = A_1 + A_2[/tex]
[tex]A = 2\pi rh + 4\pi r^2[/tex]
Substitute [tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]
[tex]A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2[/tex]
Open bracket
[tex]A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]
[tex]A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]
[tex]A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2[/tex]
[tex]A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2[/tex]
Take LCM
[tex]A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}[/tex]
[tex]A = \frac{20}{r} + \frac{4\pi r^2}{3}[/tex]
Differentiate w.r.t r
[tex]A' = -\frac{20}{r^2} + \frac{8\pi r}{3}[/tex]
Equate A' to 0
[tex]-\frac{20}{r^2} + \frac{8\pi r}{3} = 0[/tex]
Solve for r
[tex]\frac{8\pi r}{3} = \frac{20}{r^2}[/tex]
Cross Multiply
[tex]8\pi r * r^2 = 20 * 3[/tex]
[tex]8\pi r^3 = 60[/tex]
Divide both sides by [tex]8\pi[/tex]
[tex]r^3 = \frac{60}{8\pi}[/tex]
[tex]r^3 = \frac{15}{2\pi}[/tex]
Take [tex]\pi = 22/7[/tex]
[tex]r^3 = \frac{15}{2 * 22/7}[/tex]
[tex]r^3 = \frac{15}{44/7}[/tex]
[tex]r^3 = \frac{15*7}{44}[/tex]
[tex]r^3 = \frac{105}{44}[/tex]
Take cube roots of both sides
[tex]r = \sqrt[3]{\frac{105}{44}}[/tex]
[tex]r = \sqrt[3]{2.38636363636}[/tex]
[tex]r = 1.33632535155[/tex]
[tex]r = 1.34[/tex] (approximated)
Hence, the radius is 1.34cm
The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.
Given :
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters.The volume of a cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
The total volume of the two hemispheres is given by:
[tex]\rm V' = 2\times \dfrac{2}{3}\pi r^3[/tex]
[tex]\rm V' = \dfrac{4}{3}\pi r^3[/tex]
Now, the total volume of the solid is given by:
[tex]\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]
Now, substitute the value of the total volume in the above expression and then solve for h.
[tex]\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]
[tex]\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}[/tex]
Now, the surface area of the curved surface is given by:
[tex]\rm A = 2\pi r h[/tex]
Now, the surface area of the two hemispheres is given by:
[tex]\rm A'=2\times (2\pi r^2)[/tex]
[tex]\rm A'=4\pi r^2[/tex]
Now, the total area is given by:
[tex]\rm A_T = 2\pi rh+4\pi r^2[/tex]
Now, substitute the value of 'h' in the above expression.
[tex]\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2[/tex]
Simplify the above expression.
[tex]\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}[/tex]
Now, differentiate the total area with respect to 'r'.
[tex]\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]
Now, equate the above expression to zero.
[tex]\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]
Simplify the above expression in order to determine the value of 'r'.
[tex]8\pi r^3=60[/tex]
r = 1.34 cm
For more information, refer to the link given below:
https://brainly.com/question/11952845
Hell and thanks please
Answer:
A
Step-by-step explanation:
In San Diego, the weather was sunny 90% of the says this past June. How many days was it sunny
Answer:
27 days
Step-by-step explanation:
June has 30 days, So our equation looks like this:
30*0.9=27 days.
3)m I really need help
====================================================
Explanation:
We'll use the angle addition postulate. This is basically the idea where we can break any angle into smaller parts, or go in reverse to build up larger angles based on smaller pieces.
In this case, we can see that the smaller angles KLU and ULM combine to form the largest angle KLM. Think of it like puzzle pieces.
Let x be the measure of angle ULM
We can say the following
(angle KLU) + (angle ULM) = angle KLM
(36) + (x) = 156
36 + x = 156
To solve for x, we subtract 36 from both sides
36+x-36 = 156-36
x = 120
Angle ULM is 120 degrees.
-------------------
As a check,
(angle KLU) + (angle ULM) = 36 + 120 = 156
which matches with angle KLM, so the answer is confirmed.
2. Multiply the following:
a. 3.5(x)
Answer:
3.5x
Step-by-step explanation:
3.5(x)=3.5x
write 13.28 as a fraction in the lowest term
Answer:
13 wholes and 7/25
Step-by-step explanation:
write 28 over 100 and just simplify but don't forget 13
At a university, Todd deposits $100 into his cafeteria account. He spends $5 on dinner every day. Seth deposits $140 into his account. He spends $5 on lunch and $5 on dinner every day. After how many days will Todd and Seth have the same amount of money in their accounts? 16 8 4 2
Answer:
The answer is 8 days.
Step-by-step explanation:
By applying the correct equations to Todd and Seth's balances for each day we end up with Todd and Seth having an equal balance in their accounts by day 8, alternatively, we can show that Todd and Seth have the same amount of money in their accounts by day 8 with this table
Day - Todd - Seth
1 - 95 - 130
2 - 90 - 120
3 - 85 - 110
4 - 80 - 100
5 - 75 - 90
6 - 70 - 80
7 - 65 - 70
8 - 60 - 60
After collecting the data, Christopher finds that the total snowfall per year in Reamstown is normally distributed with mean 94 inches and standard deviation 14 inches. What is the probability that, in a randomly selected year, the snowfall was greater than 52 inches?
Answer:
0.9987
Step-by-step explanation:
Using Z score formula
z = (x-μ)/σ, where
x is the raw score = 52 inches
μ is the population mean = 94 inches
σ is the population standard deviation = 14 inches
z = 52 - 94/14
z =-3
Probability value from Z-Table:
P(x<52) = 0.0013499
P(x>52) = 1 - P(x<52)
P(x>52) = 1 - 0.0013499
= 0.99865
Therefore, the probability that, in a randomly selected year, the snowfall was greater than 52 inches is approximately 0.9987
Answer:
Step-by-step explanation:
99.87 for Knewton Alta
JUAN VIAJO DE SALAMANCA A CELAYA Y RECORRIO 25 CM. ¿CUÁNTOS METROS
RECORRIO?
Answer:
0.025
Step-by-step explanation:
Answer:
0.25 metros.
Step-by-step explanation:
cada centimetro es 0.01 metro.
One part of Clare’s job at an environmental awareness organization is to answer the phone to collect donations. The table shows the number of hours she worked each week, \small x, and the amount of donations in dollars, \small y, that the organization collected each week for 10 weeks. The data in the scatter plot suggest a linear association. A line to model the data is given by \small y=12x+41.
Describe the correlation between the variables as either strong or weak and as either positive or negative. Explain your reasoning.
Answer:
The more hours she worked the more donations she would receive.
Step-by-step explanation:
In the chart the higher the number of how many hours she worked resulted in a higher amount of donations
The association between the variables is strong and positive.
The equation of a straight line is given by y = mx + c. can easily make use of a regression line to ascertain the nature of the relationship between two variables as we can see in the graph shown in the question.
From the graph shown in the question, it is easy to ascertain that the association between the variables is strong and positive. The association is strong because the points lie together and positive because the plot increases linearly.
Learn more about association of variable: https://brainly.com/question/2426761
brian earns 420 a daywotking at a convenience store. write an algebraic expression to represent the money hre in will earn in d days
Answer:
420d
Step-by-step explanation:
If triangle ABC is equilateral, and side AC is 7m long, how long is side BC?
Answer:
7m
Step-by-step explanation:
In an equilateral triangle all the sides and angles are the same
Find the range of the following piecewise function. [27,3) (-22,3] (27,3] [-22,3)
Answer:
The answer is "(27,3]"
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\to f(-5) = (-5)^2 + 2 = 25 +2 =27\\\\\to f(7)= 7-4 = 3\\\\answer \ is = ( 27, 3]\[/tex]
Answer
(27,3]
Step-by-step explanation:
Correct In HW
(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ
Answer:
See below
Step-by-step explanation:
[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]
Thus proved
the mass of a rock same is 25 g and its density is d5d/cm cubed. What is the volume of the rock?
Answer:
וודי מסיפור הצעצועים יזיין אותך בלילה
Step-by-step explanation:
Resuelve la ecuación de la recta
que pasa por el punto (2 , 8 ) y tiene una pendiente de -3.
ayudaaaa
Answer:
SPANISH TALK ENGLISH OK
Step-by-step explanation:
OKKK
Graph: f (x)=−2/3 x−3
Answer:
-2/3 x-3 graphed will look whit the line going down the negative side (bottom left) of the graph and also passing the (right bottom side of the graph) the points will be (0,-3)
Step-by-step explanation:
A company finds that on average, they use 43 minutes for each meeting. An employee sketches a graph to show the total amount of time in minutes, T, used for m meetings. The graph shows the value of T for 1 to 5 meetings. If the employee counts by 10's, what should be the largest value on the T-axis of his or her graph so that the scale is the most appropriate for the given information? Drag and drop the correct number into the box. Response area
Answer:
220 just took the test
Step-by-step explanation:
Answer:
your answer is 220 :)
The data from the U.S. Census Bureau for 1980-2010 shows that the median weekly earnings of full-time
male employees who have at least a bachelor's degree can be modeled by the function
M(x) = 0.009x3 - 0.29x2 + 30.7x + 439.6 where x Is the number of years after 1980 and M(x) Is the
median weekly earnings in dollars. The median weekly earnings of all full-time employees who have at
least a Bachelor's degree can be modeled by the function T(x) = 0.012x3 - 0.46x2 + 56.1x + 732.3 where
x Is the number of years after 1980 and T(x) Is the median weekly earnings in dollars.
Estimate the median weekly earnings of a full-time female employee with at least a Bachelor's degree in
2006. Round to the nearest dollar.
The median weekly earnings of a female employee in 2006 is about
Answer:
890.908
Step-by-step explanation:
Given that :
Median weekly salary for males :
M(x) = 0.009x3 - 0.29x2 + 30.7x + 439.6
x = number of years after 1980
Median weekly salary for all employees :
T(x) = 0.012x3 - 0.46x2 + 56.1x + 732.3
Estimate the median weekly earnings of a full-time female employee with at least a Bachelor's degree in 2006
Estimated median weekly earning for a full time female employee with at least bachelor's degree ; F(x)
F(x) = T(x) - M(x)
F(x) = (0.012x3 - 0.46x2 + 56.1x + 732.3) - (0.009x3 - 0.29x2 + 30.7x + 439.6)
F(x) = (0.012 - 0.009)x3 + (-0.46 + 0.29)x2 + (56.1 - 30.7)x + (732.3 - 439.6)
F(x) = 0.003x³ - 0.17x² + 25.4 + 292.7
x = 2006 - 1980 = 26
F(26) = 0.003x³ - 0.17x² + 25.4x + 292.7
0.003(26)^3 - 0.17(26)^2 + 25.4(26) + 292.7 = 890.908
=
Minus one thousand ,eight hundred and five point nine six as a number
Answer:
-1805.96
Step-by-step explanation:
I think that is the answer
Answer:
-9805.96 this is the answer
find the equation of circle whose centre is at (3,4) and passing through (1,5)
Answer:
Step-by-step explanation:
Answer:
[tex](x-3)^{2} + (y-4)^{2} = r^{2} \\\\(1-3)^{2} + (5-4)^{2} = r^{2}\\r^{2} = 5 \\so the equation is \\(x-3)^{2} + (y-4)^{2} = 5[/tex]
Step-by-step explanation:
Find the GCF of 32, 64, and 96. The GCF is _______.
Answer:
128
Step-by-step explanation:
If you multiply you get it.
Answer:
The GCF of these numbers are 32.
Step-by-step explanation:
All of these integers are able to be divided, and by the first number.
Hope this helps! :3
Which set of data is most accurately represented by a logarithmic model?
What is the slope of the line?
Answer:
slope = 7/4
Step-by-step explanation:
slope is found by figuring the change in y-values over the change in x-values. Look for points on the line that go through an intersection of the graph lines exactly. I found the points (3, 4) and (-1, -3)
difference of y/difference of x = 4-(-3) / 3-(-1) = 7/4
3/8 of the homes have a red door how many homes have a red door
Answer:
three out of the eight homes have red doors. so 3 homes have red doors
Step-by-step explanation:
7 cards are drawn from a standard deck of 52 playing cards. How many different 7-card hands are possible if the drawing is done without replacement?
Answer:
The number of different 7 card hands possibility is 133784560
Step-by-step explanation:
The computation of the number of different 7 card hands possibility is shown below:
Here we use the combination as the orders of choosing it is not significant
So,
The number of the different hands possible would be
= [tex]^{52}C_7[/tex]
= 52! ÷ (7! × (52 - 7)!)
= 133784560
Hence, the number of different 7 card hands possibility is 133784560
Helllppppppp. A wheelbarrow has a wheel with a diameter of 10 in. What is the distance, in
inches, that the wheelbarrow moves after 16 full rotations of the wheel?
Answer:
160 in.
Step-by-step explanation:
10 * 16 = 160
Find the deposit required to accumulate $7700 after investing 3 years in an account that pays an APR of 5% compounded quarterly. How much is earned in interest?
Answer:
The deposit required is $6633.62 and the interest earned is $366.38
Step-by-step explanation:
Compound interest occurs when the interest earned is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It's given the final amount A=$7700 after t=3 years of investment in an account that pays an APR of r=5%=0.05. Since the interests compound quarterly and there are 4 quarters in a year, then n=4.
To find the principal P, we solve the previous equation for P as follows:
[tex]{\displaystyle P=A\left(1+{\frac {r}{n}}\right)^{-nt}}[/tex]
Substituting:
[tex]{\displaystyle P=7700\left(1+{\frac {0.05}{4}}\right)^{-4\cdot 3}}[/tex]
[tex]{\displaystyle P=7700\left(1+0.0125}\right)^{-12}}[/tex]
P=$6633.62
The interest earned is:
I = A - P = $7700 - $6633.62 = $366.38
The deposit required is $6633.62 and the interest earned is $366.38
hellpppppp please I will give brainliest
Answer:
y=3x+4
Step-by-step explanation: