THIS QUESTION IS KILLING ME
Calculate the volume of the object by using the triple integral.
Answers
The volume of the solid (call it S) in Cartesian coordinates is
[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
but I suspect converting to cylindrical coordinates would make the integral much more tractable.
Take
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]
Then
[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]
[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]
and the integral becomes
[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]
[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]
Related Questions
Let x = 8.99999 . (a) Is x < 9 or is x = 9? x < 9 It is neither; x > 9 x = 9 x < 9 and x = 9 It cannot be determined. (b) Sum a geometric series to find the value of x. x = (c) How many decimal representations does the number 9 have? decimal representations (d) Which numbers have more than one decimal representation? the integers the rational numbers except for 0 all rational numbers that have a terminating decimal representation except for 0 all integers except for 0 all real numbers
Answers
Answer: idk
Step-by-step explanation:
idk
Tameka can make 32 beads with 4 sheets of paper. Right now she only has 3 sheets of paper. How many beads can Tameka make?
Answers
Answer:
24 beads
Step-by-step explanation:
beads in 4 sheet=32
beads in 1 sheet=32/4=8
beads in 3 sheet=8*3=24
Answer:
Assuming that you can make the same number of beads with 1 sheet of paper, Tameka can make 24 beads with 3 sheets of paper.
Write the equation of a line that is perpendicular to y= -x - 6 and that passes through the point (-9, -4).
Answers
Answer:
y = x + 5
Step-by-step explanation:
Perpendicular slope is opposite inverse so the perpendicular slope to -1x would be 1x
Then find b in y=mx+b
Plug in all the number
y=-9
x=-4
m=1
So, -4=1(-9)+b
1×-9=-9
+9 to both sides
5=b
Therefore,
y=x+5
Help asap giving branlist!!!
Answers
Answer:
Option 2
Step-by-step explanation:
The first statement is false because the price for 10 gallons is about $37 from the graph. Using this same reasoning, the third statement is also false. The last statement doesn't make sense because the graph has nothing to do with the amount of miles driven. Therefore, the answer is the second statement. We can prove it by looking at the point (4, 15). This means that it costs $15 for 4 gallons, so then the price for one gallon will be 15 / 4 = $3.75.
An amount of money earned #24 in 4 years at a rate of 5% per year simple intrest. what was the amount of money
Answers
Answer:
4.8
Step-by-step explanation:
simple interest=Principal ×time×rate ÷100
=24×4×5÷100
=4.8
perimeter.
6) A quadrilateral can have 2
reflex angles.
Answers
Answer:
False
Step-by-step explanation:
Answer:
A quadrilateral can't have 2 reflex angles
Step-by-step explanation:
A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°
Determine the maximum r-value of the polar equation r = 3 + 3 cos theta
Answers
Answer:
Step-by-step explanation:
6
Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answers
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
which of the following expressions is equal to -3x^2-12??!!! please help him
Answers
Answer:
-3 ( x+2i) (x-2i)
Step-by-step explanation:
-3x^2-12
Factor out a -3
-3(x^2 +4)
Rewrite
-3 ( x^2 - -4)
-3 ( x^2 - (-2i)^2) This is the difference of squares ( a^2 -b^2 ) = (a-b)(a+b)
-3 ( x- -2i) (x+2i)
-3( x+2i) (x-2i)
c. Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade?
Answers
Answer:
A=12 feet²
Step-by-step explanation:
1/2*base*height=area
(1/2)*4*6=12
What is the distance from point N to line LM in the figure below?
Answers
Answer:
The correct answer would be F. 7.8
Step-by-step explanation:
the line is more or less a reflection of segment ON
so they are more or less the same.
I hope this helped you!
01
The list below shows the prices of T-shirts at a clothing store.
{8, 10, 10, 12, 15, 15, 18)
Which statement best describes the mean of this ser?
the difference between the least and greatest prices
the sum of the prices
the quotient of the difference between the least and greatest prices divided by 7
the sum of the prices divided by 7
dem
Answers
Answer:
the sum of the prices divided by 7
Step-by-step explanation:
The mean is the sum of the elements of a set, divided by the number of elements in the set. This set has 7 members, so its mean is ...
the sum of the prices divided by 7
The sum of two numbers is odd. Can the quotient of the two numbers be an odd number?
Answers
Answer: No.
Step-by-step explanation:
I guess that here we have the statement:
If the sum of two numbers is odd----> can their quotient be an odd number?
first, for n an integer number, we have that:
an odd number can be written as 2n + 1
an even number can be written as 2n.
The sum of two numbers is only odd if one of them is odd and the other even.
Then we have a number that is 2n and other that is 2k + 1, for n and k integer numbers.
Now, let's see if the quotient can also be an odd number.
One way to think this is:
There is an odd number such that when we multiply it by another odd number, the result is an even number?
no, and i can prove it as:
let 2k + 1 be an odd number, and 2j + 1 other.
the product is:
(2k + 1)*(2j + 1) = 2*(2*k*j + k + j) + 1
and as k and j are integers, also does 2*k*j + k + j, so:
2*(2*k*j + k + j) + 1 is an odd number.
This says that the product of two odd numbers is always odd, then we never can have that the quotient between an even number and an odd number is odd.
The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width. What is the length and width in yards?
Answers
Answer:
160 yards
Step-by-step explanation:
P=2l+2w
P=2(3w-8)+2(w)
432=2(3w-8)+2(w)
432=6w-16+2w
432=8w-16
432+16=8w
448=8w
w=448/8
w=56yards
l=3(56)-8
l=168-8=160yards
A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off. Assuming both promotions can be applied at the same time how much more would you pay if you applied the coupon first?
Answers
Answer:
[tex]\$0.26[/tex] has to be paid more if the coupon is applied first
Step-by-step explanation:
Given: A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off.
To find: how much more would be paid if the coupon is applied first
Solution:
Let $ x denotes cost of hand soap
Case 1:
If the discount is given first,
cost of hand soap = [tex]x-\frac{13}{100} x=\$ \frac{87}{100}x[/tex]
If the coupon for $2.00 off is applied,
Final cost of the hand soap = [tex]\$\,(\frac{87}{100}x-2)[/tex]
Case 2:
If the coupon for $2.00 off is applied first,
cost of hand soap = [tex]\$(x-2)[/tex]
If the discount is given then,
final cost of the hand soap = [tex](x-2)-\frac{13}{100}(x-2)=\frac{87}{100}(x-2)[/tex] = [tex]\frac{87}{100}x-\frac{87}{50}[/tex]
Here,
[tex]\frac{87}{100}x-\frac{87}{50}-\frac{87}{100}x+2=\frac{13}{50}=\$0.26[/tex]
So, [tex]\$0.26[/tex] has to be paid more if the coupon is applied first.
Answer:
$0.26
Step-by-step explanation: I took the test
During your journey, you develop an abscessed tooth and have to visit the dentist. You are prescribed an antibiotic with a dosage of 7.5 mg/kg every six hours. If you weigh 128 pounds and the antibiotic comes in 250 mg tablets, how many tablets should you take each day?
Answers
Answer:
I should take 10.44 tablets in a day, approximately 10.5 tablets.
Step-by-step explanation:
In order to solve this problem we need to convert the weight from pounds to kilograms, to do that we need to divide it by 2.205.
[tex]w = \frac{128}{2.205}\\w = 58.05 \text{ kg}[/tex]
Since I need to take 7.5 mg per kg of body weight, then in order to find the dosage we need to multiply the weight in kg by 7.5.
[tex]\text{dosage} = 58*7.5 = 435 \text{ mg}[/tex]
Since I need to take it every six hours and there are 24 hours in a day, we will have to take 4 dosages in a day, therefore we need:
[tex]\text{dosage(day)} = 435*6 = 2,610 \text{ mg}[/tex]
The antibiotic comes in 250 mg in tablets, therefore the number of tablets is:
[tex]tablets = \frac{2610}{250} = 10.44[/tex]
I should take 10.44 tablets in a day, approximately 10.5 tablets.
A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained:
Smokers: 69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8
Non-Smokers: 28.6 25.1 26.4 34.9 28.8 28.4 38.5 30.2 30.6 31.8 41.6 21.1 36.0 37.9 13.9
Which group having greater value of relative dispersion and why?
Answers
Answer:
The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.
CV smokers: 0.387
CV non-smokers: 0.234
Step-by-step explanation:
We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).
Then, first we calculate the mean and standard deviation for the smokers data:
Mean: 43.7
Standard deviation: 286.5
[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]
The mean and standard deviation for the non-smokers is:
Mean: 30.3
Standard deviation: 50.9
[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]
Now, we can calculate the coefficient of variation:
CV smokers:
[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]
CV non-smokers:
[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]
Which one of the following numbers is an irrational number?
Question 20 options:
A)
134∕675
B)
3.
C)
7.676767…
D)
8.12131415…
Answers
Answer:
B
Step-by-step explanation:
rational number means comparison between two numbers
eg: 1:3 or 1/3 or 0.333
irritional number does not
The one of the numbers is an irrational number that is A) 134 / 675
What are rational numbers, and irrational numbers?Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.
Irrational numbers are those real numbers which are not rational numbers.
Noted that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
For example
: 1:3 or 1/3
or 0.333
But irrational number does not.
The rational number means the comparison between two numbers
A) 134 / 675 = 0.19
B) 3.
C) 7.676767…
D) 8.12131415…
So, A) 134 / 675
This is an irrational number
Learn more about numbers here;
https://brainly.com/question/3151755
#SPJ2
Want Brainliest? Get this Correct The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y
Answers
Answer:
Option (A).
Step-by-step explanation:
We choose a point from table of f(x), that is (-2, -31)
1). If this point is reflected across x-axis, rule to be followed,
(x, y) → (x, -y)
That means y coordinate of the point gets changed with opposite notation.
If (-2, -31) is reflected over the x-axis,
(-2, -31) → (-2, 31) ----------(1)
2). When a point is reflected over the y-axis,
Rule to be followed,
(x, y) → (-x, y)
(-2, -31) → (2, -31) ----------(2)
3). When a point is reflected over the line y = x
Rule to be followed,
(x, y) → (y, x)
(-2, -31) → (-31, -2) -----------(3)
By comparing f(x) and g(x) we find the relation between the functions as,
f(-2, -31) → g(2, -31)
Rule between the functions f and g matches with the rule number (2).
Therefore, function 'f' has been reflected across y axis to get the function 'g'.
Option (A) will be the answer.
Solve for w: 2w<9+5w
Answers
Answer:
w > -3
Step-by-step explanation:
2w<9+5w
Subtract 5w from each side
2w-5w<9+5w-5w
-3w <9
Divide each side by -3 remembering to flip the inequality
-3w/-3 > 9/-3
w > -3
Answer:
w>-3
Step-by-step explanation:
Factorize (3x-2y)2 + 3(3x-2y)-10
Answers
Answer:
[tex]5(3x-2y-2)[/tex] i think. i am sorry if i am wrong
Step-by-step explanation:
The radius of a circle is 10.7 m. Find the circumference
to the nearest tenth.
Answers
Answer:
2 x [tex]\pi[/tex] x 10.7 = 67.2
Step-by-step explanation:
Step-by-step explanation:
c=2πr
c=2×π×10.7m
c=67.2m
so about 67
What is the value of the expression 1/7 ÷8 A 1/12 B 1/35 C 5/7 D 6/7
Pss. Its multiple choice okay dont get confused
Answers
Answer:
Looks like it's none.
Step-by-step explanation:
[tex]\frac{1}{7}*\frac{1}{8}=\frac{1}{56}[/tex]
Answer:
Step-by-step explanation:B and D I belive.
Nike sells 20,000 pairs of shoes for $200 each pair. How much revenue did Nike make?
Answers
Answer:
$4,000,000
Step-by-step explanation:
20,000*200=4,000,000
Find tan x if sec x = sort 37/6 and sin x <0
Answers
Answer:
tan(x) = -1/6
Step-by-step explanation:
We can use the relation between tan and sec:
[tex]\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}[/tex]
The tangent of x is -1/6.
solve for x
x/9=3
whats x
Answers
Answer:
x = 27
Step-by-step explanation:
x/9 = 3
Multiply each side by 9
x/9 * 9 = 3*9
x = 27
Answer:
27
Step-by-step explanation:
x/9= 3
Carry over the 9 and make x the subject.
x= 3*9
x= 27
Therefore x is 27.
To check if the answer is correct, replace the x with the value of what it is in brackets. The value of x is 27.
(27)/9= 3
= 27/9
= 3
We got back the 3 so that means the answer is correct
If P(-2, 1) is rotated 90°, its image is
Answers
Which number is irrational
Answers
Answer:
Can you give the question. Can you post the picture. I can help solve. I will edit this answer once you have given the question/picture.
Please answer this correctly
Answers
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326
Please answer this correctly without making mistakes
Answers
Answer:
508
Step-by-step explanation:
use l x w
40x7
10x18
8x6
508