Use polar coordinates to find the volume of the given solid. Inside both the cylinder x2 y2 = 1 and the ellipsoid 4x2 4y2 z2 = 64
The Volume of the given solid using polar coordinate is:[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
V= [tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
What is Volume of Solid in polar coordinates?
To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.
Consider the cylinder,[tex]x^{2}+y^{2} =1[/tex] and the ellipsoid, [tex]4x^{2}+ 4y^{2} + z^{2} =64[/tex]
In polar coordinates, we know that
[tex]x^{2}+y^{2} =r^{2}[/tex]
So, the ellipsoid gives
[tex]4{(x^{2}+ y^{2)} + z^{2} =64[/tex]
4([tex]r^{2}[/tex]) + [tex]z^{2}[/tex] = 64
[tex]z^{2}[/tex] = 64- 4([tex]r^{2}[/tex])
z=± [tex]\sqrt{64-4r^{2} }[/tex]
So, the volume of the solid is given by:
V= [tex]\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta[/tex]
= [tex]2\int\limits^{2\pi}_ 0 \int\limits^1_0 \, r\sqrt{64-4r^{2} } r dr d\theta[/tex]
To solve the integral take, [tex]64-4r^{2}[/tex] = t
dt= -8rdr
rdr = [tex]\frac{-1}{8} dt[/tex]
So, the integral [tex]\int\ r\sqrt{64-4r^{2} } rdr[/tex] become
=[tex]\int\ \sqrt{t } \frac{-1}{8} dt[/tex]
= [tex]\frac{-1}{12} t^{3/2}[/tex]
=[tex]\frac{-1}{12} (64-4r^{2}) ^{3/2}[/tex]
so on applying the limit, the volume becomes
V= [tex]2\int\limits^{2\pi}_ {0} \int\limits^1_0{} \, \frac{-1}{12} (64-4r^{2}) ^{3/2} d\theta[/tex]
=[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta[/tex]
V = [tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
Since, further the integral isn't having any term of [tex]\theta[/tex].
we will end here.
The Volume of the given solid using polar coordinate is:[tex]\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta[/tex]
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Consider the parallelogram below.
Find the value of y.
Enter each line of work as an equation.
Answer: 10
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so [tex]17=y+7 \longrightarrow y=10[/tex]
The diameter of a circle is 26 millimeters. What is the circle's circumference?
Step-by-step explanation: the answer for this question should be 81.64 because to find the circumference you need to know the circumference formulas which is C=TT times d or C= 2 times TT times r.
C= 3.14 times 26 C= 2 times 3.14 times 13
C= 81.64
C= 81.64
so the answer is 81.64 for the circle's circumference so hopefully that is the correct answer and have a great day
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
The diameter of a circle is 26 mm. Find its circumference.
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
C=81.7mm
[tex]\blue{\textsf{\textbf{\underline{\underline{How to solve:-}}}}[/tex]
[tex]\implies{\sf{Circumference \:of \:a \:circle:\bigstar\:\:\:C=\pi d}}}[/tex]
Where:
C=Circumference
π=pi
d=diameter
Provided information:d=26 mm
Plug in the values:
[tex]\bf{C=26\pi }[/tex]
Multiply & round:
[tex]\bf{C=81.7mm}[/tex]
Good luck.
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wow lashes is a false eyelashes company. the companymade $50,000 in 2021. they have already sold enough lashes this year to make $5,500 in profit. this year, they plan to sell at least 800 more packs of lashes than the previous year. each pack of lashes makes the company $12
Answer:
whats the question
Step-by-step explanation:
If Alfonso increased his 401(k) plan contribution to 7%, how
much would be deducted each month for retirement?
Helpp
Answer:
20%
Step-by-step explanation:
sry if wrong byeeeeee
Taylor has a punch bowl shaped like a cylinder, with a diameter of 22 inches and a height of 20 inches, she pours 8.25 gallons of punch into the bowl.
(note 1 gallon = 231 cubic inches)
How far from the top of the punch bowl is the top of the punch?
Answer:
1 gal =231 cu/in
r^2pi*ht=area
36pi*7= 791.68cu/in
231*3.25=750cu/in
41.68/(r^2pi)
=41.65/113.1=.368"
Step-by-step explanation:
Note that 1 gallon = 231 cubic inches.
Volume of liquid = 231 cubic inches = PI*R^2*H (equation for volume of a cylinder)
We have a radius (half diameter), so we can figure out the height of the liquid.
To figure how far below the top the liquid is, we subtract the height of the liquid from the height of the punch bowl (7 inches).
does somebody know how to do this??
Answer:
95
Step-by-step explanation:
65+66+90+95=316
316/4=79
find the area of the shaded region, round to the nearest tenth. I will give brainliest
Answer: 17.4
Step-by-step explanation: Area of a Square
Area of a rectangle = s².
s is the side length.
Area of Circle
4 quarter circles equals a full circle.
Area of a full circle = πr².
There are four quarter circles in the diagram given, therefore:
Area of the shaded region = area of square - area of full circle
= 9² - π(4.5²)
= 17.38.
Therefore, the area of the shaded region, to the nearest tenth, is about: 17.4 m².
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What is the area of the rectangle?
2 om
3 cm
А
6 cm
B
23 cm
с
17 cm
D
31 cm
Area
Length ×Breadth3(2)6cm²Find an angle
x where sin x = COS x.
Answer:
[tex]x = \frac \pi4 + k\pi (k \in \mathbb{Z})[/tex]
Step-by-step explanation:
If [tex]cos\ x = 0 \rightarrow sin\ x = \pm1[/tex], which is obviously not a solution. At this point we can divide both sides by [tex]cos\ x[/tex] to get
[tex]\frac {sin\ x}{cos\ x} = 1 \rightarrow tan\ x = 1[/tex]
which has solutions [tex]x = \frac \pi4 + k\pi (k \in \mathbb{Z})[/tex]
A study you are reading gives the results of a 2 X 2 MANOVA with 6 dependent variables. Authors found significant omnibus main effects, but no significant interactions. What would be an appropriate next step according to materials covered in this course
The appropriate next step according to materials covered in this course is to examine post hoc pairwise comparisons.
What is a post hoc pairwise comparison?Pairwise Comparisons is known to be a kind or type of post-hoc analysis, where a person can compare the mean differences to that of a critical value.
Note that a post hoc tests tell a person, the key differences that exist between three or more set of means when an analysis of variance (ANOVA) F test is said to be significant just as in the case above.
See options below
Examine post hoc pairwise comparisons
Examine Levene’s test of equality of variance
Examine the results for each DV with 6 ANCOVAs
Examine the results for each DV with 6 ANOVAs
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help statistics
no spam
Answer:
P = 20
Step-by-step explanation:
Mean
18.75 = 10(5) + 15(10) + P(7) + 25(8) + 30(2) / 3218.75 × 32 = 50 + 150 + 7P + 200 + 60600 = 460 + 7P7P = 140P = 20URGENT HELP
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 66%. What is the probability that it will rain on exactly one of the five days they are there? Round your answer to the nearest thousandth.
Question 2 options:
.362
.227
.044
.109
Answer:
.82^5 = ? I dont think it helps
Step-by-step explanation:
3. If A and B are complements, then which of the following is true about the probability of B based on the probability of A?
(1) P(B)=P(A)+1
(3) P(B) =1/P(A)
(2) P(B)=1-P(A)
(4) P(B)=P(A)-1
Reason:
Complementary events have their probabilities add to 1.
P(A)+P(B) = 1
P(B) = 1 - P(A)
For example,
P(A) = the chance it rains = 30% = 0.30
P(B) = the chance it doesn't rain
P(B) = 1 - P(A) = 1 - 0.30 = 0.70 = 70%
The equation that relates the probability of A and B is P(B) = 1 - P(A).
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
As per the given data:
We are given two events, event A and event B.
We are also given the relationship between the two events.
It's given that A and B are complements of each other.
Let's assume that the probability of the event B is P(B).
The sample space for this situation when only 2 events are there will be
(A, B)
We are given that A and B are complements of each other.
This means that the complement of A is equal to the probability of event B.
P(A') = 1 - P(A)
P(B) = P(A')
∴ P(B) = 1 - P(A)
The equation that relates the probability of A and B is P(B) = 1 - P(A).
Hence, The equation that relates the probability of A and B is P(B) = 1 - P(A).
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What is the equation of the line that passes through the point (4,7) and has an
undefined slope?
Answer:
Step-by-step explanation:
use the point slope formula
y - y1 = m(x -x1)
where "m" is an undefined slope
and plug in the given point (4,7) it's form is (x1,y1)
y-7 = m(x - 4)
y = m(x - 4 ) + 7
Is the following linear or nonlinear?
m = n 2 - 7n - 54
a) linear
b) nonlinear
I NEED HELP ASAP
====================================
[tex]\large \sf \underline{Problem:}[/tex]
Is the following linear or nonlinear?
m = n 2 - 7n - 54
a) linear
b) nonlinear
====================================
[tex]
\large \sf \underline{Answer:}[/tex]
A. Linear
====================================
[tex]\large \sf \underline{Explanation:}[/tex]
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
====================================
is the equation y=1/7x an example of direct variation
Answer:
no
Step-by-step explanation:
k=1(constant)
y varies inversely with x
Simplify Negative 3 over 2 divided by 9 over 6.
−4
−1
4
1
BEST ANSWER :
(( -3/2 ) 9 ) / 6.
= -0.02777777777
HURRY PLS!!!!!The heights, in feet, of the trees for sale at two nurseries are shown below. Yard Works: 7, 9, 7, 12, 5 The Grow Station: 9, 11, 6, 12, 7 Which statements are true regarding the measures of center and variability of these data sets? Select three choices. The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station. The median of the tree heights at Yard Works is greater than the median of the tree heights at The Grow Station. The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. The mean absolute deviation of the tree heights at Yard Works is greater than the mean absolute deviation of the tree heights at The Grow Station. The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.
The statement first, statement third, and the statement fifth are correct because the mean absolute deviation are the same.
What is mean absolute deviation?It is defined as the measure to show the variation in data set in other words between the mean and every data value, the distance known as the MAD.
We have data:
Yard Works: 7, 9, 7, 12, 5
Grow Station: 9, 11, 6, 12, 7
The mean for yard works = 40/5 = 8
The mean for grow station = 45/5 = 9
The mean absolute deviation for yard work = 2
The mean absolute deviation for grow station = 2
The correct statements are:
The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Growth Station.The range of the tree heights at Yard Works is greater than the range of the tree heights at The Growth Station. The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Growth Station.Thus, the statement first, statement third, and the statement fifth are correct because the mean absolute deviation are the same.
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Answer: A, C, E.
Step-by-step explanation: I got it right on the test
Suppose that a good has an income elasticity of demand of -2. 0. This means that the good is
The good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.
What are the characteristics of inferior goods?An inferior good occurs when an increase in income causes a fall in demand.
An inferior good has a negative income elasticity of demand. (YED) Inferior goods are characterized by low quality – and are goods with better alternatives.
Suppose that good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.
An inferior good is one whose demand drops when people's incomes rise. When incomes are low or the economy contracts, inferior goods become a more affordable substitute for more expensive goods.
Inferior goods are the opposite of normal goods, whose demand increases even when incomes increase.
Hence, the good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.
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identify b on the following diagram not really important but 8 would love for someone to help me
Answer: A origin
Step-by-step explanation:
Luca made a scale drawing of the auditorium. in real life, the stage is 45 feet long. it is 18
inches long in the drawing. what is the scale of the drawing?
Answer:
30:1
Step-by-step explanation:
45*12 = 540
540/18 = 30
Find the output for the graph
y = -6x + 25
when the input value is 3.
=
y = [?]
Answer
[tex]x=\frac{11}{3}[/tex]
Explanation
Based on the given conditions, formulate:: [tex]y=3[/tex]
Substitute [tex]y=3[/tex] into [tex]y=-6x+25[/tex] :: [tex]3=-6x+25[/tex]
Rearrange variables to the left side of the equation: [tex]6x=25-3[/tex]
Calculate the sum or difference: [tex]6x=22[/tex]
Divide both sides of the equation by the coefficient of variable: [tex]x=\frac{22}{6}[/tex]
Cross out the common factor: [tex]x=\frac{11}{3}[/tex]
what’s the answer to this problem , figure out the area and perimeter of this triangle please and thank you
Answer:
P=2.66m
A=.3318m
Step-by-step explanation:
P=1.0+.79+.87
A=.79 * .84
A sweater is $45 and 10% off. What is the discount? HTML EditorKeyboard Shortcuts
Answer:
Discount = $4.50
Discounted Price = $40.50
Step-by-step explanation:
First you need to find what 10% of $45 is. To do that you need to divide $45 by 10 or just move the decimal point one space to the left. The answer would be $4.50. Then, you need to subtract $4.50 from $45 as we are calculating the discounted price. The answer would be $40.50.
Equation:
$45 ÷ 10 = $4.50 (discount)
$45 - $4.50 = $40.50 (discounted price)
There are 36 pieces of building blocks in a bag: 9 each of blue, green, red, and yellow. Four pieces are chosen at random. Identify the probability that all four of the pieces are red.
Answer:
2/935
Step-by-step explanation:
I have attached an image of the equation to use. Assuming that this is without replacement, we'll be taking out one piece out of the bag every time that one is chosen.
Therefore, for probability, the fraction is part/whole. We first have 9 red to 36 pieces in total, but if we take one out, we'll get 8 red left in the bag, and 35 pieces in total. This continues until we fulfill the prophecy (I don't know. qualifications?) that 4 of the pieces are red.
You can try this for yourself, but once simplified, it should be 3024/1413720, which simplifies to 2/935.
Please let me know if you need more clarification or have issues! probability can be confusing :)
Answer:
2/935
Step-by-step explanation:
dito^
There are 6 athletes at a track meet. How many different ways can they finish first or second?
(8-b) + (5b + 6) what is the answer?
Answer: [tex]4b+14[/tex]
[tex]2*(2b+7)[/tex]
Step-by-step explanation:
[tex](8-b)+(5b+6):8-b+5b+6[/tex]
[tex]-b+5b+8+6[/tex]
[tex]-b+5b+14[/tex]
[tex]=4b+14[/tex]
Therefore your answer is [tex]2*(2b+7)[/tex], in other words, 4b+14Sebastian is going to choose design elements that include color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 10 colors, 14 patterns, 12 fonts, and 9 images for him to choose from. (He will choose only one of each.)
How many different sweatshirt designs are possible?
Answer:
Sebastian is going to choose design elements that include color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 10 colors, 14 patterns, 12 fonts, and 9 images for him to choose from. (He will choose only one of each.)
How many different sweatshirt designs are possible?
Step-by-step explanation:
It's 4320
direction. The number b varies directly with the number a. For example b = 2 when a = -2
-2. Which equation
=
4
represents this direct variation between a and b?
b = -a
-b = -a
ОООС
b-a= 0
b(-a) = 0
Answer:
b = - a
Step-by-step explanation:
given b varies directly with a then the equation relating them is
b = ka ← k is the constant of variation
to find k use the condition b = 2 when a = - 2 , then
2 = - 2k ( divide both sides by - 2 )
- 1 = k
then
b = - a ← equation of variation
