Use either the shell method or the disk/washer method to find the volume of the solid (Calculus Help!!!)
Answers
Integrating with shells is the easier method.
V = 2π ∫₁³ x (√x + 3x) dx
That is, at various values of x in the interval [1, 3], we take n shells of radius x, height y = √x + 3x, and thickness ∆x so that each shell contributes a volume of 2π x (√x + 3x) ∆x. We then let n → ∞ so that ∆x → dx and sum all of the volumes by integrating.
To compute the integral, just expand the integrand:
V = 2π ∫₁³ (x ³ʹ² + 3x ²) dx
V = 2π (2/5 x ⁵ʹ² + x ³) |₁³
V = 2π ((2/5 × 3⁵ʹ² + 3³) - (2/5 × 1⁵ʹ² + 1³))
V = 4π/5 (9√3 + 64)
Related Questions
A long history of testing water samples in a certain lake has shown that the level of a certain pollutant is approximately normally
distributed with standard deviation 4.5 mg/L. What is the minimum number of samples required to estimate today's level to within 0.4
mg/L with 95% confidence? (Don't forget to round Zc to two decimal places!)
Answers
Answer:
The minimum number of samples required is 487.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation 4.5 mg/L.
This means that [tex]\sigma = 4.5[/tex]
What is the minimum number of samples required to estimate today's level to within 0.4 mg/L with 95% confidence?
This is n for which M = 0.4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.4 = 1.96\frac{4.5}{\sqrt{n}}[/tex]
[tex]0.4\sqrt{n} = 1.96*4.5[/tex]
[tex]\sqrt{n} = \frac{1.96*4.5}{0.4}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*4.5}{0.4})^2[/tex]
[tex]n = 486.2[/tex]
Rounding up
The minimum number of samples required is 487.
Ayoooo somebody please help me! 20pointss
Answers
Which shape is the base of the pyramid shown below?
A triangle
B square
Answers
hope that helps!
Answer:
B. it's a square pyramid so the base is a square.
Step-by-step explanation:
How to write -x^2+12-8x=-3 in standard form
Answers
Answer:
-x^2-8x+15=0
Please mark as brainliest
Answer:
give me a min if you can
Step-by-step explanation:
Which is a function?
O {(-3,5), (1,4), (3,7), (1,7), (4,9)}
O {(7.9), (13,-2), (8,4), (7,0), (4,12)}
O {(2,1), (-1,7), (6,-2), (10,3), (-6,0)}
O {(-2,4), (7,4), (-6,8), (-2,8), (1,1)
Answers
50000000000000000000000000000000000000000000
Answer:
{(7.9), (13,-2), (8,4), (7,0), (4,12)} is a function
Step-by-step explanation:
Twenty percent of 56 is 11.2
TRUE OR FALSE
FIRST TO ANSWER GET THE POINTS AND IM GONNA GIVE HIM A BRAINLIEST ANSWER. ORRRAYT
Answers
2. (MCC 6.5) Find the value of x. 77° (6x17)°
Answers
Answer:
x = 17
Step-by-step explanation:
77° + (6x + 1)° = 180° (angels on a straight line)
Solve for x
77 + 6x + 1 = 180
Add like terms
6x + 78 = 180
6x + 78 - 78 = 180 - 78
6x = 102
6x/6 = 102/6
x = 17
A 30-foot ladder was put up against a building. The ladder makes a 64° angle with the ground. How high up
on the wall does the top of the ladder reach?
Answers
Answer:
height = 26.96 feet
Step-by-step explanation:
sin 64° = height/30
0.8988 = height/30
height = 26.96 feet
Match each term with its notation.
___________ The number of treatment conditions
___________ The number of scores in each treatment.
___________ The total number of scores in the entire study.
___________ The sum of the scores for each treatment condition.
___________ The sum of all of the scores in the research study.
___________ The F-ratio
1. n
2. F
3. G
4. N
5. k
6. T
Answers
Answer:
_k_ The number of treatment conditions
_n_ The number of scores in each treatment.
_N_ The total number of scores in the entire study.
_T_ The sum of the scores for each treatment condition.
_G_ The sum of all of the scores in the research study.
_F_ The F-ratio
Step-by-step explanation:
These notations are ANOVA (Analysis of variance) notations, where
k is the number of treatment conditions
n is the number of scores in the treatment
N is the total number of scores in the entire study
T is the sum of scores for a specific treatment
G is the sum of all scores in the study
and F is the F-ratio.
Now, for the question, we will match each term with its notation
_k_ The number of treatment conditions
_n_ The number of scores in each treatment.
_N_ The total number of scores in the entire study.
_T_ The sum of the scores for each treatment condition.
_G_ The sum of all of the scores in the research study.
_F_ The F-ratio
ILS.
Carnival visitors
50
70
90
110
130
150
What fraction of the days did the carnival have 70 or fewer visitors?
Submit
Answers
Answer:
its 1/4 :)
Step-by-step explanation:
After observing the number of visitors, the fraction of the days that the carnival has 70 or fewer visitors is 1/3.
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction.
It can be written in the form of p:q, which is equivalent to p / q.
Given that,
There are 2 days with 70 or fewer visitors.
To find the required fraction,
Determine how many days out of the given total had 70 or fewer visitors.
Since there are 2 days with 70 or fewer visitors,
To calculate the fraction,
Divide the number of days with 70 or fewer visitors (2) by the total number of days (6).
So, the fraction is 2/6.
Simplifying this fraction yields 1/3.
Hence, the required fraction is 1/3.
To learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ4
9. Are there any outliers in the data from question #7?
A. Yes; Week 10 is an outlier since it is the greatest data point.
B. Yes; Week 1 is an outlier since it is the lowest data point.
C. Yes; Week 7 is an outlier since it does not fit the general trend of the data.
D. No; there are not any outliers in the data.
Answers
Answer:
A) Yes; Week 10 is an outlier since it is the greatest data point.
PLEASE HELP, 80 POINTS!!!!
1. Write as a function of an acute angle. sec(11 pi/4)
A): sec45
B): -sec45
C): -sec(-45)
D): sec(-45)
2. If cot0=5.671, find a point on the terminal side of 0.
A): (5.671, 1)
B): (1, 5.671)
C): (5.671, -1)
D): (-1, 5.671)
3. Convert to degrees. 2^R
A): 360
B): 180
C): 114.592
D): 1.570
Answers
Answer:
I think it's
1. C
2. B
3. A
Step-by-step explanation:
PLS HELP DUE SOON SHOW YOUR WORK!
Answers
9514 1404 393
Answer:
615.8 square feet9 truckloadsStep-by-step explanation:
The area of the circular ring is given by the formula ...
A = πr²
where r is the radius, or half the diameter.
A = π(14 ft)² = 196π ft² ≈ 615.752 ft²
The area of the training area is about 615.8 square feet.
__
The number of truckloads of dirt required for coverage will be ...
(615.8 ft²)/(75 ft²/truckload) ≈ 8.21 truckloads
Since the dirt comes only in whole truckloads, Hilary needs 9 truckloads.
If you wanted to put a fence around your garden, would you find the perimeter or the area of the garden??
Answers
Answer:
U would find the perimeter.
Step-by-step explanation:
Wanda drove 392 miles in 14 hours. What is her unit rate of miles per hour?
Answers
40 pts please help! picture below!
Answers
Answer:
B. 135
Step-by-step explanation:
CB is 45
AB= half of circle or 180*
So, 180-45=135
Therefore, the answer is 135* or b
hope this helps
Answer:
135 degrees
Step-by-step explanation:
Since the angle is measured from the center, the arc is the same as the angle measurement.
ACB = 180
AC + CB = 180
AC + 45 = 180
AC = 180-45 = 135
Which number is a multiple of 7? A 27 B 48 C 56 ET D 74
Answers
Answer:
C. 56
Step-by-step explanation:
7*8=56
peggy drives for 3 hours at an average speed of 61 miles per hour. Then when she crosses over into the next state she is able to drive the next 2.5 hours at an average speed of 72 miles per hour.
what was her average speed for the entire trip?
Answers
Answer:
65 miles per hour
Eli gave out a survey to some students in his school about their favorite color. 880 of those surveyed said their favorite color was red. If 88% of the students surveyed said their favorite color was red, how many students were surveyed in total?
Answers
Answer:
The answer is 1000.
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!
Answers
Answer:
Your answer would be B
Step-by-step explanation:
a way to remember it is:
a food web= think of a spiders web and how it goes multiple waysa food chain= think of a metal chain, they only link on one another and go only on direction or pathIf x=2 and y=5 Evaluate this expression: 6x +5 y
Answers
Answer:
12 + 25 = 37
Step-by-step explanation:
If we have the value for each of the variables, we can plug them in, and be done with it.
when we plug them in, we get
6(2) + 5(5)
12 + 25
37
Which statement is true
Answers
Answer:
D
Step-by-step explanation:
hey man. trust me. quack
Answer:
i think that the answer might be d
Solve the system of equations and choose the correct answer from the list of options. d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (4 points) Question 3 options: 1) (0, 0) 2) (10, −5) 3) (5, 10) 4) (10, 5)
Answers
Answer:
3) (5, 10)
Step-by-step explanation:
d + e = 15
-d + e = -5
e = -5 + d
substitude e for -5 + d
d + -5 + d = 15
2d = 10
d = 5
figure out e
5 + e = 15
e = 10
22, 17. 12, 7... O Arithmetic
O Geometric
O Neither
Answers
Arithmetic means that the numbers are increased or decreased by the same number each time. This does not include multiplication.
And since all of these are subtracted by 5, it would be Arithmetic.
Could use help on this please. No wrong answers! I NEED to get an A on this otherwise I'll have to literally repeat the year.
Answers
Answer:
blank 1: 0.75b
black 2: 2/5p
3|2z-4|-6>12
Solve for z
Answers
Answer:
312z-41-6>12
subtract -41-6
312z-47>12
add it on both sides
312z-47>12
+47 +47
312z>59
divide 312 to both sides
z<0.189
Answer:
can someone help me pls i dont know 2x=4=
Step-by-step explanation:
PLEASE HELP I WILL MARK
BRIANLIST Caitlin has $24 to spend. She spent $8.50, including tax, to buy a book. She needs to save $6.25, but she wants to buy some candy. If each piece of candy costs $0.25 including tax, what inequality would show the maximum number of pieces Caitlin can buy? Let x represent the cost of one piece of candy.
Solve your inequality by showing your work and steps.
Answers
Answer: 37 pieces of candy
Step-by-step explanation:
24-8.50 is 15.50 she wants to save 6.25, so, 15.50-6.25 is 9.25. 9.25 divided by the cost of each candy (0.25) is 37
An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length
the pond is two times its width.
Find the length and width of the pond to the nearest tenth.
Answers
Answer:
Should be
Width: 38.7
Length: 77.5
Please give me Brainliest and like
Name:
Date:
Class:
Test: Lessons 18-1 Slicing Solids and 18-2 Lateral and Surface Area of Prisms
Circle the term or phrase that best completes each sentence.
1. The figure on the left is a ...
triangular prism.
triangular pyramid.
2. The figure on the right is a...
three-dimensional figure.
two-dimensional composite figure.
3. Another name for the shapes that make up any three-dimensional
figure is ...
faces.
edges.
4. For any three-dimensional figure, the sum of the areas of all its
faces is its ...
surface area.
area.
Answers
Answer:
?????????
Step-by-step explanation:
that is a lot
Please help me not sure
Answers
Question:
What is the probability that a card drawn from a deck of 52 cards is not back?
Answer:
1/2 and if not it will be 25/52
Step-by-step explanation:
A card game has each even cards