Find the volume of the solid generated by revolving the region about the
A.)-axis (use washer method)
B.)-axis (use cylindrical shell method)
Answers
Answer:
Step-by-step explanation:
The region R is bounded below by y=1 and above by f(x) where
[tex]f(x)=\begin{cases}3,&1\leq x\leq 2\\\\-x+5,&2\leq 3\end{cases}[/tex]
and we integrate the R over the interval [1,3]
A.
[tex]V=\int_1^3 \pi(f(x)^2-1^2)\, dx\\V=\int_1^2 \pi(3^2-1^2)\, dx +\int_2^3 \pi((-x+5)^2-1^2)\, dx\\=9\pi + \int_2^3 \pi(x^2-10x+24)\, dx\\=9\pi +\pi\left({[(1/3)x^3-5x^2+24x]_2^3\right)\\=9\pi + \pi( (19/3) -25 +24)\\=9\pi +(16/3)\pi=43/3 \pi.[/tex]
For part B
[tex]V=\int_1^3 2\pi x(f(x)-1)\, dx[/tex]
and you can compute the integral similarly as above, just split the integral into two integrals, one over [1,2] and the other is over [2,3].
Related Questions
Use the laws of logarithms to expand and simplify the expression.
ln( (x^4)/square root of x(1 + x)^2)
Answers
Answer:
Step-by-step explanation:
[tex]\ln\left(\frac{x^4}{\sqrt{x(1+x)^2}}\right)\\=\ln(x^4)-\ln\sqrt{x(1+x)^2}\\=4\ln x - \ln \sqrt{x} - \ln (1+x)\\=4\ln x-(1/2)\ln x -\ln(1+x)\\=(9/2)\ln x - \ln(1+x)\\=\ln x^{9/2}-\ln(1+x}\\=\ln (x^{9/2}/(1+x))[/tex]
You lose 2 points every time you forget to write your name on a test. You have forgotten to write your name 6 times. What integer represents your change in points from forgetting to write your
Answers
Answer:
I'm not sure I completely understand what is being asked but this is what I'm going with......
2 every test you have lost 2 points per test on 6 tests so that is a total of 12 lost??
Step-by-step explanation:
Hope I helped even a little Have a great day!!!
please help me please please please please please please please
Answers
Answer:
picture
Step-by-step explanation:
That my answer.
m,n,o
Find the midpoint of the line segment joining the points (5,6) and (-1,-6).
The midpoint is
(Type an ordered pair. Use integers or simplified fractions for any numbers in the expression.)
Answers
Answer:
The midpoint is (2,0)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
(5+-1)/2 =4/2 =2
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(6+-6)/2 =0/2 =0
The midpoint is (2,0)
Each chef at "Sushi Emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On Tuesday, each customer ate 2 regular rolls and 3 vegetarian rolls. By the end of the day, 4 regular rolls and 1 vegetarian roll remained uneaten. How many chefs and customers were in "Sushi Emperor" on Tuesday?
Answers
9514 1404 393
Answer:
2 chefs13 customersStep-by-step explanation:
Let x and y represent the numbers of chefs and customers, respectively. We can write equations for the different kinds of rolls made and eaten:
15x -2y = 4 . . . . . 4 regular rolls were uneaten
20x -3y = 1 . . . . . 1 vegetarian roll was uneaten
Using the "cross multiplication method", the solution can be found to be ...
Δ1 = (15)(-3) -(20)(-2) = -5
Δ2 = (-2)(-1) -(-3)(-4) = -10
Δ3 = (-4)(20) -(-1)(15) = -65
1/Δ1 = x/Δ2 = y/Δ3, so we have ...
x = Δ2/Δ1 = -10/-5 = 2 . . . . there were 2 chefs
y = Δ3/Δ1 = -65/-5 = 13 . . . there were 13 customers
_____
Additional comment
The version of the "cross multiplication method" I use for solving two linear equations is this. Write the equations in general form. List the coefficients in two rows, repeating the first column so there are 4 columns. Form "cross products" of the coefficients taking columns pairwise. Use these cross products to find the variable values.
In general form, these equations are ...
15x -2y -4 = 020x -3y -1 = 0Then the rows of coefficients are ...
[ 15, -2, -4, 15 ]
[ 20, -3, -1, 20 ]
The "cross multiplication" subtracts the product on the up-diagonal from the product on the down-diagonal. If we label the results Δ1, Δ2, Δ3, we get the results shown above. These "cross products" are used in the equation ...
1/Δ1 = x/Δ2 = y/Δ3
to find the values of x and y.
Some videos I have seen of this method write the two rows of coefficients shifted to the left, and use a different final equation for the solution. The result is the same. I find the extra shifting to make the process confusing and difficult to remember.
I prefer this method when there is no simple way to do substitution or elimination. In the end, it takes slightly fewer math operations than would be required by either of those methods in such cases.
__
A graphing calculator provides another simple way to find the solution.
One of the legs of a right triangle measures 12cm and its hypotenuse measures 17 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
12
Step-by-step explanation:
3. From noon to midnight, how many times do the hands of a clock form a
straight line
Answers
Step-by-step explanation:
The hands of a clock point in opposite directions ( in the same straight line) 11 times in every 12 hours.
Choose two statements that are true for this expression.
Answers
Answer: A and C
Step-by-step explanation: Brainliest please?
300 words in 4 minutes
a. 80 words per minute
b. 75 words per minute
c. 70 words per minute
d. 134 words per minute
Answers
The area of a square is 36. A rectangle whose length is 1 more than twice
its width has the same area. What are the dimensions of the rectangle?
Answers
L 70, h89, w56!
hope this helps <3
4(1 - p) = -4 + 4 show work please
Answers
Problem: 4(1 - p) = -4 + 4
First solve parenthesis:
4 - 4p = -4 + 4
Cancel terms:
-4p = -4
Divide terms:
p = 1
Answer:
p = 1
4(1 - p) = -4 + 4
4(1 - p) = 0
Distribute the 4 across the numbers in the parentheses:
4 - 4p = 0
Minus four from both sides
-4p = -4
Then divide negative four by both sides
p = 1
Pllllzzzz heeeelllppp
Answers
Answer:
a. circumference
b. area
c. area
d. circumference
Step-by-step explanation:
a. You are using the circumference formula to find the distance around a CIRCULAR track, if you used area, that would include the space in between the track as well. You are only trying to find the track line. ( you can draw a picture of a track and show what you are finding. )
b. You are trying to find the amount of area that the tiles make up in the circular floor, how much of the floor the tiles take up.
c. You are trying to find how much of the oil takes up of the WHOLE bottom of the frying pan.
d. Finding the circumference of your wheel can help determine the distance the car traveled. If you used area, it would not be useful.
Evaluate the expression x + (-5) +5 when x=-3
4x12
Answers
Answer:
2045
Step-by-step explanation:
-34×12(-5)+5
-405(-5)+5
2040+5
2045 is the answer
Please help me with the question!!!!!!
Answers
Now We know
[tex]\\ \sf\longmapsto tan30=\dfrac{7}{B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{\sqrt{3}}=\dfrac{7}{B}[/tex]
[tex]\\ \sf\longmapsto B=7\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto B=7(1.732)[/tex]
[tex]\\ \sf\longmapsto B\approx 12[/tex]
Now
Using pythagorean theorem
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto H^2=7^2+12^2[/tex]
[tex]\\ \sf\longmapsto H^2=144+49[/tex]
[tex]\\ \sf\longmapsto H^2=193[/tex]
[tex]\\ \sf\longmapsto H=\sqrt{193}[/tex]
[tex]\\ \sf\longmapsto H\approx 13[/tex]
I’m so sorry I’m really bad at math please help!!
Answers
5×3=15
4×8=32
6×3/2=9
12×1/4=3
Referring to the figure, find the value of x
Answers
The distance between two towns on that map is 6cm, therefore in reality there’s 6 * 50 000 = 300 000 centimetres, which is equal to 3 000 metres, which is equal to 3 kilometres.
Answer:
Step-by-step explanation:
By the triangle angle-sum theorem, all the angles of a triangle have to add up to equal 180°. Thus,
72° + 5x° + x° = 180° and
72° + 6x° = 180° and
6x° = 108° so
x = 18°
PLS ANSWER HELP IF U SEE THIS I GIVE FREE BRAINLY
Answers
Answer:
2
Step-by-step explanation:
64 ÷ 32 = 2
2 × 32 = 64
Answer:
2
Step-by-step explanation:
you do 64 divided by 32 which you would get the same answer as 6 divided by 3 which is 2
Number 67.89 is rational or irrational
Answers
Answer:
rational
Step-by-step explanation:
The elevation of Lake Baikal is about 1,494 feet below sea level. Which integer represents this elevation?
Answers
Answer:
-1,494
Step-by-step explanation:
If sea level is 0, the on a scale below sea level would be a negative integer.
G(x,y)={mod((x),2)>0,-1}
im doing a puzzle and this is a equation in the puzzle, i know the equation might be incomplete but the only other numbers i have for this is -6, -6 please do not answer "this answer might be spelled incorrectly" only comment that and i might be able to help
Answers
Answer:
the integer is a possible coordinate plane
Step-by-step explanation:
.
5.) -3(12 – 25) + 7 please
Answers
Answer:
46
Step-by-step explanation:
−3(12−25)+7
=(−3)(−13)+7
=39+7
=46
Sample annual salaries (in thousands of dollars) for employees at a company are listed.
41 54 61 48 27 27 41 54 61 31 48 41 47
(a) Find the sample mean and sample standard deviation.
(b) Each employee in the sample is given a 5% raise. Find the sample mean and sample standard deviation for the revised data set.
(c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set.
(d) What can you conclude from the results of (a), (b), and (c)?
Answers
Answer:
Down
Step-by-step explanation:
List from low to high
27 27 31 41 41 41 47 48 48 54 54 61 61
a. Mean = sum of sample/2
Mean = 581 / 2 = 290.5
b. Mean + 5%
290.5 + 5% = 305.025
c. 305.025 / 12 = 25.41875
d. Mean is ratio. Thus the adding and dividing with anything will affect the mean overall
Find the measures of the missing angles g, h, k, and m
Answers
Answer:
Angle g = 29 degrees
Angle h = 180-29 = 151 degrees
Angle k = 61 degrees
Angle m = 180 - 61 = 119 degrees
Step-by-step explanation:
The midpoint of CD is M (-3, -7). If the coordinates of C are (-2, -10), what are the coordinates of D?
Answers
Answer:
Answer: (-4, -4)
Step-by-step explanation
2(-3) = -2 + X 2(-7) = -10 + Y
-6 = -2 + X -14 = -10 + Y
+2 +2 +10 +10
-4 = X -4 = Y
7m-4-9m-35=0
Solving linear equation
please help me
Answers
Step-by-step explanation:
-2m-39=0
-2m=0+39
-m= 39/2
m= -19.5
Answer:
[tex]7m - 4 - 9m - 35 = 0 \\ 7m - 9m = 35 + 4 \\ - 2m = 39 \\ 2m = - 39 \\ m = \frac{( - 39)}{2} \\ \boxed{m = - 19.5}[/tex]
m = -19.5 is the right answer.I need these answers
Answers
Answer:
You are correct with all of your answers so far,...
Step-by-step explanation:
5) = 0 (-17 + 20 = 3,... 3 + -3 = 0)
6) = -34 (-34 + 25 = -9,... -9 + -25 = -34)
9) = -4 (7 + -11 = -4)
Chow,...!
Answer:
for question 5 the answer is 0.
for question 6 the answer is -34.
for question 9 the answer is -4.
Step-by-step explanation:
question 5: -17+20 can also be written as 20-17 which is equal to 3. Next, we have to add 3 with -3. 3+(-3) is the same as 3-3 which equals 0.
question 6: 25-25 = 0, and the remainder is -34.
question 9: 7-11 can also be written as -11+7, which is equal to -4.
Try to fill in the missing numbers
Answers
9514 1404 393
Answer:
[[274][895][136]]
Step-by-step explanation:
Starting with the middle row, we need a product of two single-digit numbers that is between 53-1 = 52 and 53-9 = 44. Possible products are 5×9=45 and 6×8=48. This means the number in the middle position in the left column must be 8 or 5.
The middle number in the left column cannot be 5, because we must be able to get -5 by subtracting that number from a sum that is at least 3 = 1+2. So, the middle number in the left column is 8, the other two numbers in that column are 1 and 2, and the other two numbers in the middle row are 5 and 9.
There is no product of single-digit numbers that is 30-1 = 29, so the upper left number must be 2, and the bottom left number must be 1. The other two numbers on the top row must be 4 and 7, so that row's equation is 2+4×7=30.
The only remaining digits are 3 and 6. In order to have -3 on the bottom row, the equation there must be 1×3-6 = -3. Then the middle digit must be divisible by 3, so must be 9.
Our solution is ...
row 1: 2 + 7 × 4 = 30
row 2: 8 + 9 × 5 = 53
row 3: 1 × 3 - 6 = -3
And that makes the column equations be ...
col 1: 2 - 8 + 1 = -5
col 2: 7 + 9 / 3 = 10
col 3: 4 × 5 - 6 = 14
What is the answer to
(9)(-2)=
Answers
Answer:
-18
Step-by-step explanation:
9 x -2 = -18
You multiply like normal and then for the answer just add a neg sign if there is an ODD amount of neg signs in the overall problem and then add no neg sigh if there are an EVEN number of neg signs (they cancel out),...
Hope it helps,... Chow,...!
Question 5: A car used 1164 gallon of gas to drive ya of a mile. At this rate, how many miles can the car travel using 1
gallon of gas?
I
Answers
Answer:
Hello! Your answer is BELOW
Step-by-step explanation:
Car will cover 16 miles in 1 gallon of the gas.
We can solve this question by unitary method.
∵ A car used [tex]\frac{1}{64}[/tex] gallons of gas to drive the distance = [tex]\frac{1}{4}[/tex] miles
∴ Car used 1 gallons to drive the distance = [tex]\frac{1}{4} \\\\\frac{1}{64}[/tex]
= [tex]\frac{64}{1} X \frac{1}{4}[/tex]
= [tex]\frac{64}{4}[/tex]
= 16 miles
Therefore, car will cover 16 miles in 1 gallon of the gas.
Hope I helped! Hope you make an 100%.
-Amelia♥
When six is multiplied by a number the result is 30
Answers
Answer:
the number is 5
30/6 = 5.
Step-by-step explanation:
