Answer:
a) Minimize Z =30 X1 +25 X2+18 X3
subject to following constraints
[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]
b) Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.
c) As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.
Step-by-step explanation:
Step 1:-
a)
Let's take
X1 to be the number of hours assigned to Lisa
X2 to be the number of hours assigned to David
X3 to be the number of hours assigned to Sarah.
The objective function is to attenuate the entire cost of the project by deciding an optimum number of hours for every person. the target function is given by -
Minimize Z =30 X1 +25 X2+18 X3
subject to following constraints
[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]
Constraints and explanation:
1. Lisa must be assigned a minimum of 40% of the entire number of hours assigned to the 2 senior designers.
2. Sarah must be assigned a minimum of 15% of the entire project time.
3. The corporate estimates that 150 hours are going to be required to finish the project.
4. The number of hours assigned to Sarah must not exceed 25% of the entire number of hours assigned to the 2 senior designers.
5. Lisa features a maximum of fifty hours available to figure on this project.
6. Non-negative condition.
Step 2:-
b)
From the above equations, we get
The number of hours assigned to Lisa is 48 hours
The number of hours assigned to David 72 hours
The number of hours assigned to Sarah 30 hours.
Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.
Step 3:-
c)
As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.
Samantha acored 15 points in her laat
basketball game. She made 3 free throwa
that are worth 1 point each. The rest of
her pointa came on 2 point field goala,
Write an equation that can be used to find
the number of 2 point field goals that
Samantha made
(uae p as your variable)
Help fasttt
Answer:
15=2p+3
Step-by-step explanation:
A coin is tossed times and comes up heads times. Use the Empirical Method to approximate the probability that the coin comes up heads. Round your answer to four decimal places as necessary.
Answer:
[tex]P(head) = 0.5600[/tex]
Step-by-step explanation:
Given
[tex]n = 500[/tex] -- number of toss
[tex]head = 280[/tex] --- outcomes of head
See comment
Required
Empirical probability of head
This is calculated as:
[tex]P(head) = \frac{n(head)}{n}[/tex]
[tex]P(head) = \frac{280}{500}[/tex]
[tex]P(head) = 0.5600[/tex]
(7+3i)-(3-9i)complex numbers
Answer:
C
Step-by-step explanation:
For this, you want to treat i like any other variable, and combine like terms. However you need to keep in mind that there is a negative sign before the second set of parentheses. This means everything inside it should have a negative before it. So we can write it like this:
(7 + 3i) - (3 - 9i)
7 + 3i -3 +9i
4 + 12i
Hope that helps!
Anyone know this question?
Answer:
All of these
Step-by-step explanation:
Given
[tex]f(5) = 11[/tex]
[tex]f(x)[/tex] at [tex](5,11)[/tex]
Required
Interpret
[tex]f(5) = 11[/tex] mean that: the function is at [tex](5,11)[/tex]
In other words:
[tex]x = 5; y = 11[/tex]
It also means:
Substitute 5 for x and the result will be 11
Hence, all options are true
SOMEONE HELP PLEASE! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Sebastian is going to choose the color pattern
Answer:
use blue red blue red
Step-by-step explanation:
Find the domain and range of the relation
Answer:
The domain is "all real numbers" and the range is x more than -3
NFL Pre-Season Teams in the National Football League (NFL) in the US play four pre-season games each year before the regular season starts. Do teams that do well in the pre-season tend to also do well in the regular season? We are interested in whether there is a positive linear association between the number of wins in the pre-season and the number of wins in the regular season for teams in the NFL.
Required:
a. What are the null and alternative hypotheses for this test?
b. The correlation between these two variables for the 32 NFL teams over the 10 year period from 2005 to 2014 was 0.067. Use this sample (with n=320) to calculate the appropriate test statistic and determine the p-value for the test.
c. State the conclusion in context, using a 5% significance level.
Answer:
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic = 1.197
Pvalue = 0.2335
There is no correlation between the two variables
Step-by-step explanation:
The null and alternative hypothesis :
H0 : No correlation exist,
H1 : Correlation exist
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic, T = r / √(1 - r²) / (n - 2)
T = 0.067 / √(1 - 0.067²) / (320 - 2)
T = 0.067 / √(0.995511 / 318)
T = 0.067 / 0.0559512
T = 1.197
The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335
α = 5% = 0.05
The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.
The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x. Suppose each of the x objects increases its sound power by 10 decibels, so that the new total sound power, in decibels, is given by the function g(x) = f(x) + 10. Which shows the graphs of f(x) and g(x)? On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60). On a coordinate plane y = f (x) starts at (0, 50) and curves up through (10, 60). y = g (x) starts at (0, 40) and curves up through (10, 50). On a coordinate plane, y = f (x) starts at (0, 50) and curves up through (10, 60). Y = g (x) starts at (10, 50) and curves up through (20, 60). On a coordinate plane, y = g (x) starts at (negative 10, 50) and curves up through (0, 60). Y = f (x) starts at (0, 50) and curves up through (10, 60). Mark this and return
Answer:
Graph A
Step-by-step explanation:
correct answer on edge :)
The statement that represents the graphs of the functions f(x) and g(x) : On a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).
What is a function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."For given question,
The total sound power, in decibels, from x objects each producing 50 decibels of sound power is given by the function f(x) = 50 + 10 log x.
If each of the x objects increases its sound power by 10 decibels, then the new total sound power, in decibels, is given by the function
g(x) = f(x) + 10.
The graph of the function f(x) would starts at (0, 50)
For x = 10 the value of the function f(x) would be,
f(10) = 50 + 10 log (10)
f(10) = 50 + 10 (1)
f(10) = 60
This means, the graph of the function f(x) passes though point (10, 60)
Also, the graph of the function g(x) would starts at (0, 60)
For x = 10 the value of the function g(x) would be,
g(10) = f(10) + 10
g(10) = 60 + 10
g(10) = 70
This means, the graph of the function g(x) passes though point (10, 70)
Therefore, on a coordinate plane y = g (x) starts at (0, 60) and curves up through (10, 70). Y = f (x) starts at (0, 50) and curves up through (10, 60).
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You have been doing research for your statistics class on the prevalence of severe binge drinking among teens. You have decided to use 2011 Monitoring the Future (MTF) data that have a scale (from 0 to 14) measuring the number of times teens drank 10 or more alcoholic beverages in a single sitting in the past 2 weeks.
a. According to 2011 MTF data, the average severe binge drinking score, for this sample of 914 teens, is 1.27, with a standard deviation of 0.80. Construct the 95% confidence interval for the true averse severe binge drinking score.
b. On of your classmates, who claims to be good at statistics, complains about your confidence interval calculation. She or he asserts that the severe binge drinking scores are not normally distributed, which in turn makes the confidence interval calculation meaningless. Assume that she or he is correct about the distribution of severe binge drinking scores. Does that imply that the calculation of a confidence interval is not appropriate? Why or why not?
Answer:
(1.218 ; 1.322)
the confidence interval is appropriate
Step-by-step explanation:
The confidence interval :
Mean ± margin of error
Sample mean = 1.27
Sample standard deviation, s = 0.80
Sample size, n = 914
Since we are using tbe sample standard deviation, we use the T table ;
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 914 - 1 = 913
Tcritical(0.05, 913) = 1.96
Margin of Error = 1.96 * 0.80/√914 = 0.05186
Mean ± margin of error
1.27 ± 0.05186
Lower boundary = 1.27 - 0.05186 = 1.218
Upper boundary = 1.27 + 0.05186 = 1.322
(1.218 ; 1.322)
According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate
At a local university the students have been overdosing on caffeine to help them study for exams. However, many students have been getting quite sick from taking too much coffee and cola.
A. How many cups of coffee would be too much and at the dangerous level (3.00 g)? You know that coffee contains 21.5 mg caffeince per ounce and a cup is 8 oz.
B. How many cans of cola would be too much and at the dangerous level? You know that cola contains 4.20 mg per ounce and a soft drink can contain 12.0 oz.
Answer:
A) Hence, the number of coffee cups that are risky = 17.4 Cups.
B) Here, the number of coffee cups that are risky = 59.5 Colas.
Step-by-step explanation:
A)
In 1 cup coffee =[tex]8\times21.5mg= 172.0 mg[/tex]
Hence one cup of coffee contains 172 mg of caffeine. The risky level is 3000mg.
Therefore, the number of coffee cups that are risky
[tex]= 3000/172\\ \\=17.4 cups[/tex]
Here, the number of coffee cups that are risky = 17.4 cups.
B)
[tex]1 cola=12\times4.2mg\\\\ = 50.4mg / day[/tex]
Hence, one can cola contains 50.4 mg of caffeine.
The dangerous level is 3000 mg.
Therefore, the number of cola cans that are risky [tex]=3000/50.4= 59.5[/tex] cola is risky.
Today, 11:50
Sawing and cutting. Level
Arjun cut a loaf of bread and made
sandwiches. How many sandwiches did he
make if he made 10 cuts?
Answer:
5 sandwiches he made in bread
Quadrilateral A'B'C'D'A
′
B
′
C
′
D
′
A, prime, B, prime, C, prime, D, prime is the result of dilating quadrilateral ABCDABCDA, B, C, D about point AAA by a scale factor of \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction.
Answer:
[tex]A' = (2,0)[/tex]
Step-by-step explanation:
Given
See attachment for ABCD
[tex]k = \frac{1}{2}[/tex] --- the scale factor
Required
The coordinates of A'
From the attachment, we have:
[tex]A = (4,0)[/tex]
So:
[tex]A' = k * A[/tex]
[tex]A' = \frac{1}{2} * (4,0)[/tex]
[tex]A' = (2,0)[/tex]
Answer:
on khan, both are false
Step-by-step explanation:
The graph of a line goes through the points (-4,3) and (6,8). What is the equation of the line in slope-intercept form?
Enter the correct answer in the box by replacing m and b with the appropriate values.
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+
a, sin cos tan sin costan!
μ ρ Φ
CSC seccot log log. In
ΖΔ
Σ
U (0)
X
5
A
>
S
2
II
1
y = mx + b
I
Submit
Reset
Type here to search
73°F Mostly cloudy
327 PM
7/3/2001
Answer:
[tex]y=\frac{1}{2}x+5[/tex]
Step-by-step explanation:
Hi there!
Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that lie on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug the given points (-4,3) and (6,8) into the equation
[tex]m=\frac{8-3}{6-(-4)}\\m=\frac{8-3}{6+4}\\m=\frac{5}{10}\\m=\frac{1}{2}[/tex]
Therefore, the slope of the line is [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex] :
[tex]y=\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2}x+b[/tex]
Plug in one of the given points and solve for b
[tex]8=\frac{1}{2}(6)+b\\8=3+b[/tex]
Subtract 3 from both sides to isolate b
[tex]8-3=3+b-3\\5=b[/tex]
Therefore, the y-intercept is 5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x+5[/tex]
I hope this helps!
Acellus
First, find the surface area of the yellow prism.
3 cm 3 cm
: ?
4 cm
3 cm
front: [?]
back: [ ]
right: [ ]
left: [ ]
3cm
3cm
4cm
top:[]
5 cm
TOTAL: [ ]
Note: The bottom will not be
included because this is whern
5 cm
Answer:
57 cm²
Step-by-step explanation:
Surface area of the yellow prism = front + back + right + left + top
✔️Area of the front = L * W
L = 4 cm
W = 3 cm
Area of the front = 4*3 = 12 cm²
✔️Area of the back = L * W
L = 4 cm
W = 3 cm
Area of the back = 4*3 = 12 cm²
✔️Area of the right face = L * W
L = 4 cm
W = 3 cm
Area of the right face = 4*3 = 12 cm²
✔️Area of the left face = L * W
L = 4 cm
W = 3 cm
Area of the left face = 4*3 = 12 cm²
✔️Area of the top = L * W
L = 3 cm
W = 3 cm
Area of the top = 3*3 = 9 cm²
✅Total = 12 + 12 + 12 + 12 + 9 = 57 cm²
Given the functions below, find f(x)+g(x)
CHECK MY ANSWERS PLEASE
The answer is (a)..........
A 19 in. monitor has a length of 16 in. What is its width?
10.25 in.
14.64 in.
16.51 in.
18.91 in.
Find the volume of the cement block in the figure shown.
Please help :)
9514 1404 393
Answer:
1240 in³
Step-by-step explanation:
The overall dimensions of the block are ...
10 in by 11 in by 17 in
The volume of that space is ...
V = LWH = (10 in)(11 in)(17 in) = 1870 in³
The volume of each of the three identical holes is similarly found:
V = (10 in)(3 in)(7 in) = 210 in³
Then the volume of the block is the overall volume less the volume of the three holes:
= 1870 in³ - 3(210 in³) = 1240 in³
Which of the following is a secant on the circle below?
Н
G
13-
125
K
o
A.
B. JK
C. HG
D. K
Answer:
D. KI
Step-by-step explanation:
KI intersects a minimum of two points meaning it is the definition of a secant.
4) Write the equation of the line passing
through (-5, 6 ) and has slope equal to 4.
Answer:
y = 4x + 26
Step-by-step explanation:
y = mx + b
The slope (m) is equal to 4.
y = 4x + b
To find the y-intercept (b), plug in the point given.
6 = 4(-5) + b
6 = -20 + b
26 = b
The answer is y = 4x + 26.
Answer:
The equation of the line passing through (-5, 6) with a slope of 4 is
y = 4x + 26
Step-by-step explanation:
An equation of a line would always have the following structure...
y = mx + b
In this equation, "y" is the y coordinate of the point, "x" is the x coordinate of the point, "m" is the slope, and "b" is the y coordinate of the y-intercept. We know all the values except "b", but we can find the value of "b" by substituting all the other values into the equation...
y = mx + b
6 = 4(-5) + b
6 = b - 20
b = 6 + 20
b = 26
Therefore, the equation of the line passing through (-5, 6) with a slope of 4 is y = 4x + 26
Find the circumference of a circle in terms of u with a radius of 10 ft.
100n ft
10 ft
5 ft
62.87 ft
20 ft
Answer:
[tex]2 \times \frac{22}{7} \times 10 = 62.87 [/tex]
Which of the following is a like radical to cube rt of 7x
Answer:
[tex]\sqrt[3]{7x}[/tex]
Step-by-step explanation:
Given
[tex]7x[/tex]
Required
The radical statement
Cube root is represented as:
[tex]\sqrt[3]{}[/tex]
Considering [tex]7x[/tex], the expression is:
[tex]\sqrt[3]{7x}[/tex]
Assuming the probability of a single sample testing positive is 0.15, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
Answer:
[tex]P(Positive\ Mixture) = 0.2775[/tex]
The probability is not low
Step-by-step explanation:
Given
[tex]P(Single\ Positive) = 0.15[/tex]
[tex]n = 2[/tex]
Required
[tex]P(Positive\ Mixture)[/tex]
First, we calculate the probability of single negative using the complement rule
[tex]P(Single\ Negative) = 1 - P(Single\ Positive)[/tex]
[tex]P(Single\ Negative) = 1 - 0.15[/tex]
[tex]P(Single\ Negative) = 0.85[/tex]
[tex]P(Positive\ Mixture)[/tex] is calculated using:
[tex]P(Positive\ Mixture) = 1 - P(All\ Negative)[/tex] ---- i.e. complement rule
So, we have:
[tex]P(Positive\ Mixture) = 1 - 0.85^2[/tex]
[tex]P(Positive\ Mixture) = 1 - 0.7225[/tex]
[tex]P(Positive\ Mixture) = 0.2775[/tex]
Probabilities less than 0.05 are considered low.
So, we can consider that the probability is not low because 0.2775 > 0.05
Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?
Enter the exact answer.
Hint: The distance formula is that distance = rate * time, so for example in one and a half hours, Ben has walked 3 * 1.5 miles.
Amanda catches up to Ben in ____________ hours.
Answer:
1.125 hours
Step-by-step explanation:
Given :
Ben's speed = 3 mi/hr
Time before Amanda starts = 1.5 hours
Amanda's speed = 7 mi/hr
Time before Amanda catches up with Ben
Recall :
Distance = speed * time
Distance already covered by Ben before Amanda starts :
(3 * 1.5) = 4.5
Hence, we can setup the equation :
Ben's distance = Amanda's distance
Let time taken = x
4.5 + 3x = 7x
4.5 = 7x - 3x
4.5 = 4x
x = 4.5 / 4
x = 1.125 hours
1.125 * 60 = 67. 5 minutes
I need help solving this problem. Thanks
Answer:
Step-by-step explanation:
they say by noon 4 inches of rain has fallen, then the say that it's falling at 1/4 inch per hour
f(x) = 1/4x +4
where x is in hours, and f(x) represents the linear graph of the amount of rain that has fallen after noon :)
so by 2:30 or 2.5 hours.... then
f(2.5) = 1/4x +4
y = 1/4 (2.5) +4 ( i moved to the y b/c now there is an answer)
y =[tex]\frac{5}{8}[/tex] + 4
y =4[tex]\frac{5}{8}[/tex] inches of rain
Answer:
a) y = 1/4x + 4
b) 4.625 inches
Step-by-step explanation:
a) y(0) = 4 inches
slope = 1/4 rate
y = 1/4x + 4
b) 12:00pm (noon) to 2:30pm = 2 hours 30 mins = 2.5 hours
y = 1/4x + 4
y = (1/4)(2.5) + 4
y = 0.625 + 4
y = 4.625 inches
What iis 155 plus 33 minus 4 divided by 2
Answer:
155+33-4÷2155+33-2188-2186hope it is helpful to you
The simplified form of statement 155 plus 33 minus 4 divided by 2 is
186.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
The given statement is 155 plus 33 minus 4 divided by 2 which can be numerically expressed as,
155 + 33 - 4 ÷ 2.
PEMDAS rule states the correct order of simplifying an expression is as follows, Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.
155 + 33 - 2.
= 188 - 2.
= 186.
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The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 15.3% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
Answer:
[tex]Pr = 0.153[/tex]
Step-by-step explanation:
Given
[tex]p = 15.3\%[/tex]
Required
Probability of alarm not working
[tex]p = 15.3\%[/tex] implies that the alarm has a probability of not working on a given day.
So, the probability that the alarm will not work on an exam date is:
[tex]Pr = 15.3\%[/tex]
Express as decimal
[tex]Pr = 0.153[/tex]
This assignment has a value of 10 points. You will have two (2) questions to answer and one (1) attempt to send this assignment. Refer to the calendar in Blackboard for due dates. Your calendar is available under the Tools menu > Calendar. Once you have built the Excel tables, with all the changes in different tables, and answered all the questions you have to send the work (Excel sheets and answered questions) to the professor using the Attach File function in Black Board to attach your document and send it to the professor. To use the Attach File enter the Course Content in Black Board. Select the Assignment Module 5, attach the file and submit. Solve the following problem and compute the probability of the Binomial and Poisson distributions. What is the probability of finding two defects in a Binomial distribution, with a sample size of 30, and probability of 0.2
Answer:
0.0337 = 3.37% probability of finding two defects.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
What is the probability of finding two defects in a Binomial distribution, with a sample size of 30, and probability of 0.2?
This is [tex]P(X = 2)[/tex], with [tex]n = 30[/tex] and [tex]p = 0.2[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 30) = C_{30,2}.(0.2)^{2}.(0.8)^{28} = 0.0337[/tex]
0.0337 = 3.37% probability of finding two defects.
Please Help NO LINKS
Suppose that
R
is the finite region bounded by
f
(
x
)
=
4
√
x
and
g
(
x
)
=
x
.
Find the exact value of the volume of the object we obtain when rotating
R
about the
x
-axis.
V
=
Find the exact value of the volume of the object we obtain when rotating
R
about the
y
-axis.
V
=
Answer:
Part A)
2048π/3 cubic units.
Part B)
8192π/15 units.
Step-by-step explanation:
We are given that R is the finite region bounded by the graphs of functions:
[tex]f(x)=4\sqrt{x}\text{ and } g(x)=x[/tex]
Part A)
We want to find the volume of the solid of revolution obtained when rotating R about the x-axis.
We can use the washer method, given by:
[tex]\displaystyle \pi\int_a^b[R(x)]^2-[r(x)]^2\, dx[/tex]
Where R is the outer radius and r is the inner radius.
Find the points of intersection of the two graphs:
[tex]\displaystyle \begin{aligned} 4\sqrt{x} & = x \\ 16x&= x^2 \\ x^2-16x&= 0 \\ x(x-16) & = 0 \\ x&=0 \text{ and } x=16\end{aligned}[/tex]
Hence, our limits of integration is from x = 0 to x = 16.
Since 4√x ≥ x for all values of x between [0, 16], the outer radius R is f(x) and the inner radius r is g(x). Substitute:
[tex]\displaystyle V=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx \\\\ &=\pi\int_0^{16} 16x-x^2\, dx \\\\ &=\pi\left(8x^2-\frac{1}{3}x^3\Big|_{0}^{16}\right)\\\\ &=\frac{2048\pi}{3}\text{ units}^3 \end{aligned}[/tex]
The volume is 2048π/3 cubic units.
Part B)
We want to find the volume of the solid of revolution obtained when rotating R about the y-axis.
First, rewrite each function in terms of y:
[tex]\displaystyle f(y) = \frac{y^2}{16}\text{ and } g(y) = y[/tex]
Solving for the intersection yields y = 0 and y = 16. So, our limits of integration are from y = 0 to y = 16.
The washer method for revolving about the y-axis is given by:
[tex]\displaystyle V=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy[/tex]
Since g(y) ≥ f(y) for all y in the interval [0, 16], our outer radius R is g(y) and our inner radius r is f(y). Substitute and evaluate:
[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy \\\\ &=\pi\int_{0}^{16} (y)^2- \left(\frac{y^2}{16}\right)^2\, dy\\\\ &=\pi\int_0^{16} y^2 - \frac{y^4}{256} \, dy \\\\ &=\pi\left(\frac{1}{3}y^3-\frac{1}{1280}y^5\Bigg|_{0}^{16}\right)\\\\ &=\frac{8192\pi}{15}\text{ units}^3\end{aligned}[/tex]
The volume is 8192π/15 cubic units.
Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming pool with an area of 1,000 square feet can be installed for $50,000, whereas the installation of an 800 square foot swimming pool costs $35,000. Select the correct graph that models the given relationship.
Answer:
$35,000
Step-by-step explanation:
if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain