The required value of the triple integral is (16/3)π.
To evaluate the triple integral ∫∫∫E z dV, where E lies above the paraboloid z = x² + y² and below the plane z = 2y, we can use cylindrical coordinates.
In cylindrical coordinates, we have:
x = r cosθ
y = r sinθ
z = z
To determine the limits of integration, we need to find the bounds for r, θ, and z.
The paraboloid z = x² + y² can be expressed in cylindrical coordinates as z = r².
The plane z = 2y can be expressed in cylindrical coordinates as z = 2r sinθ.
To find the bounds for r, we set the two equations equal to each other:
r^2 = 2r sinθ
Simplifying the equation, we have:
r = 2 sinθ
Since the paraboloid lies above the xy-plane, the lower bound for r is 0.
To find the bounds for θ, we need to determine the range of θ that corresponds to the region of interest. This can be done by plotting the two surfaces and visualizing the region. From the equations, we can see that the region lies within the range 0 ≤ θ ≤ π.
To find the bounds for z, we need to determine the range of z between the two surfaces. The paraboloid is below the plane, so the lower bound for z is the equation of the paraboloid, z = r^2. The upper bound for z is the equation of the plane, z = 2r sinθ.
Therefore, the limits of integration are as follows:
0 ≤ r ≤ 2 sinθ
0 ≤ θ ≤ π
r² ≤ z ≤ 2r sinθ
Now, we can evaluate the triple integral:
∫∫∫E z dV = ∫[0,2π] ∫[0,∞] ∫[r²,(2r sin θ)] (r cos(φ) sin(θ)) dz dr dθ
= (16/3)π
Therefore, the value of the triple integral is (16/3)π.
Learn more about integral here:
https://brainly.com/question/33826941
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The surface area of a cube is 96 cm2. What is The volume of the cube in cm3
Answer:
64
Explination:
4 is the length of one side because 96/6(the ammount of faces)=16 and the square root of 16 is 4 and since the area of a cube is one side^3 this is the answer
Remember to mark brainliest
(c) Find the exact values of s and t.
Answer:
u have to use cos san and tan?
i think sorry if im wrong
Step-by-step explanation:
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 43 and 49
Answer:
P( 43 ≤ X ≤ 49) = 0.9545
Step-by-step explanation:
We are given mean of 46 and a standard deviation of 3
We want to find the percentage of daily phone calls numbering between 43 and 49. This can be written as;
P( 43 ≤ X ≤ 49)
Using the z-formula, we have;
z = (x - μ)/s
This transforms to;
P((43 - 46)/3)) ≤ Z ≤ ((49 - 46)/3))
This gives;
P(-2) ≤ Z ≤ P(2)
From z - table attached, P(-2) = 0.02275 and P(2) = 0.97725
Thus;
P( 43 ≤ X ≤ 49) = 0.97725 - 0.02275
P( 43 ≤ X ≤ 49) = 0.9545
What is the value of the expression 9(2)+1•8?
Answer:
19.8
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
When we find the values of questions like this, we have to remember to use "PEMDAS".
Because multiplication comes before addition, we have to multiply first.
(Since there are two multiplication parts in the question, we start off by the first one.)
When we multiply both parts, we'll get:
[tex](18)+(8)[/tex], which equals to 26.
So, your answer is 26.
Given: A = {(2, 3), (5, 1), (-3, -2), (0, 3)} What is the range of A?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ - 2 \: , \: 1 \: , \: 3 \: }}}}}[/tex]
Step-by-step explanation:
Given,
A = { ( 2 , 3 ) , ( 5 , 1 ) , ( -3 , -2 ) , ( 0 , 3 )
To find : Range
Range are set of all y - co-odinates.
So, Range = { - 2 , 1 , 3 }
Hope I helped!
Best regards!!
Answer:
(-2,1,3)
Step-by-step explanation:
ODY 2022
MAAM or SIR I AM FACING PROBLEM TO SOLVE THESE QUESTION WOULD YOU HELP ME WITH IT
Answer:
1. Kate travelled more by 83.87km 2. = 42.5, 85 3. a= 2570 b= 348.9 c= 0.0048 d= 0.765 4. = 15.25
Step-by-step explanation:
1. 320.25km- 236.38km = 83.87km.
2. 8.5x5= 42.5, 8.5x10 = 85.
3. a= 2570 b= 348.9 c= 0.0048 d= 0.765
4. 17.75- 2.5 = 15.25.
hope you found this helpful :)
X^2-2x-48
Factor the polynomial
Answer:
x=1
x=-6
Step-by-step explanation:
I used my ti-84 plus ce calculator and that is the answer I got
>download quadsolv
>prgm
>quadsolv
>enter the equation
>solve
Answer:
= (x + 6) (x - 8)
Step-by-step explanation:
x² - 2x - 48
break the expression into groups:
= (x² + 6x) + (-8x - 48)
= x (x + 6) - 8(x + 6)
= (x + 6) (x - 8)
Evaluate x(y-z)2 for =-1,y=5,and z=
Answer:
The value of [tex]x(y-z)^2[/tex] is -16.
Step-by-step explanation:
We need to evaluate [tex]x(y-z)^2[/tex] for x = -1, y = 5 and let us assume that z = 1
It can be simply done by putting the values of x,y and z in the given expression.
[tex]x(y-z)^2=(-1)(5-1)^2\\\\=-1(4)^2[/tex]
We know that the value of 4² = 16
So,
[tex]x(y-z)^2=16\times -1\\\\=-16[/tex]
So, the value of [tex]x(y-z)^2[/tex] is -16.
POSSIBLE
The temperature on Mars ranges from -68°F during the day to - 176°F at night. Which temperature is not likely to be measured on Mars?
-76F
-100°F
- 150 °F
PLEASE RESPONDDD
Answer:
49 -- No. 71 U.S. Naval Base, Guantanamo Bay, Cuba Wednesday, June 23, 1993 ... them while developing possible options for the future fo the Gen URL Community. ... The Independence Day from the fall of 1993 to the Throughout the day, after ... *MARS Station. ... Add 40 to original temperature (F or C, doesn't matter). 2.
Answer:
49 -- No. 71 U.S. Naval Base, Guantanamo Bay
Step-by-step explanation:
Two sides of a triangle measure 9 centimeters and 37 centimeters what could the length of the third triangle?
Step-by-step explanation:
One side of a triangle is 9 cm and other side is 37 cm. We need to find what could be the length of the third side of the triangle.
If we add one and other side i.e. 9 cm + 37 cm = 46 cm
If we subtract one and other side i.e. 37 cm - 9 cm = 28 cm
We know that, the length of the third side must be less than the sum of the other two sides and greater than the difference between the other two sides.
Thus, the third side could be between 46 cm and 28 cm.
Do we ever use numbers to describe the values of a categorical variable?
Answer:
Yes
Step-by-step explanation:
Because A categorical variable can bexpressed as a number when statistical evaluation is intended, However, these numbers do not mean the same as a numerical value e.g giving numbers to waist sizes, test scores, grade level etc
The cafeteria sells each apple at one price and each banana at another price. For 5 apples and 3 bananas Dan pays $5.70. For 3 apples and 5 bananas Chris pays $4.70. The price of one apple is how much more then the price of one banana, in cents?
Answer:
50
Step-by-step explanation:
a = # of apples
b = # of bananas
5a + 3b = 570
3a + 5b = 470
Solve with substitution or elimination. To solve by elimination, multiply the first equation by 5 and the second equation by 3.
25a + 15b = 2850
9a + 15b = 1410
Subtract:
16a = 1440
a = 90
Plug into either equation to find b.
5(90) + 3b = 570
450 + 3b = 570
3b = 120
b = 40
So apples are 90 cents, and bananas are 40 cents. Therefore, apples are 50 cents more than bananas.
Solve: -3= 12x - 5(2x - 7)
X = -19
19
71 =
=-11
10
11
I= 19
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 19}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 3 = 12x - 5(2x - 7)}[/tex]
Distribute 5 through the parentheses
⇒[tex] \sf{ - 3 = 12x - 10x + 35} [/tex]
Collect like terms
⇒[tex] \sf{ - 3 = 2x + 35}[/tex]
Swap the sides of the equation
⇒[tex] \sf{2x + 35 = - 3}[/tex]
Move 45 to right hand side and change it's sign
⇒[tex] \sf{2x = - 3 - 35}[/tex]
Calculate
⇒[tex] \sf{2x = - 38}[/tex]
Divide both sides of the equation by 2
⇒[tex] \sf{ \frac{2x}{2} = \frac{ - 38}{2} }[/tex]
Calculate
⇒[tex] \sf{x = - 19}[/tex]
Hope I helped!
Best regards!!
solve for z? 2x-4y+4z-6w=4 6w-4x+4y-4z=-12 6w+4x-2y+6z=64 4z+2w+6y-4x=56
Answer:
9.22
Step-by-step explanation:
The calculation of z is shown below:-
Given that
2x-4y+4z-6w=4 .... (1)
6w-4x+4y-4z=-12 ..... (2)
6w+4x-2y+6z=64 ...... (3)
4z+2w+6y-4x=56 .... (4)
Here we need to decrease the equations with the help of canceling out a few variables.
Now we need to add equations 1 and 2 that is
(2x - 4x) + (-4y + 4y) + (4z - 4z) + (-6w + 6w) = 4 + 12
Now we solve the above equation
-2x + 0 = 16
-2x = 16
x = -8
Now, equation 2 minus 3
6w - 6w + (-4x - 4x) + 4y + 2y + (-4z - 6z) = 12 - 64
-8x + 6y - 10z = -52
Now we will put the value of x
-8(-8) + 6y - 10z = -52
64 + 6y - 10z = -52
6y - 10z = -52 - 64
6y - 10z = -116
3y - 5z = -58 ... 5
Equation 3 × 1 and equation 4 × 3
6w + 4x - 2y + 6z = 64 ..... (3)
4z + 2w + 6y - 4x = 56 .... (4)
6w + 4x - 2y + 6z = 64
12z + 6w + 18y - 12x = 168
Now we will subtract both equations that are
16x - 20y - 6z = -104
8x - 10y - 3z = -52
8(-8) - 10y - 3z = -52
-64 - 10y - 3z = -52
-10y - 3z = -52 + 64
-10y - 3z = 12 ....... (6)
equating 5 and 6 and solving that is
3y - 5z = -58 ... 5 × 10
-10y - 3z = 12 ....... 6 × 3
30y - 50z = -580
-30y - 9z = 36
we will add both equation
-50z - 9z = -580 + 36
-59z = -544
z = -544 ÷ -59
After solving z value we will get
= 9.22
If s(x) = x - 7 and t(x) = 4x2 – x + 3, which expression is equivalent to
to (t•s )(x)?
Answer:
(t•s )(x) = 4x^3 - 29x^2 + 10x - 21
Step-by-step explanation:
(t•s )(x) is the product of functions s and t:
(t•s )(x) = ( 4x^2 - x + 3)(x - 7). Applying the Distributive Property of Multiplication, we get:
(t•s )(x) = 4x^3 - 28x^2 - x^2 + 7x + 3x - 21
which needs to be simplified by combining like terms:
(t•s )(x) = 4x^3 - 29x^2 + 10x - 21
Refer to the accompanying TI-83/84 Plus calculator display of a 95% confidence interval. The sample display results from using a simple random sample of the amounts of tar (in milligrams) in cigarettes that are all king size, non-filtered, non-menthol, and non-light. Express the confidence interval in the format of E.
(23.305,25.075)
mean = 23.69
n = 30
The confidence interval is__?__ + or -___?___.
Answer:
[tex]22.805 < \mu < 24.575\\[/tex]
Step-by-step explanation:
Given parameters
Z interval E = (23.305,25.075)
mean xbar = 23.69
number of samples n = 30
Required
we are to find the confidence interval for the Z interval given.
The formula for finding the confidence interval is expressed as shown below;
[tex]\overline x - E < \mu < \overline x + E[/tex] where;
xbar is the mean = 30
E is the margin of error
[tex]E = \frac{U-L}{2}[/tex]
U = upper limit = 23.305
L = lower limit = 25.075
[tex]E = \frac{25.075-23.305}{2}\\E = \frac{1.77}{2}\\E = 0.885[/tex]
The confidence interval is therefore expressed as [tex]23.69 - 0.885 < \mu < 23.69+ 0.885\\22.805 < \mu < 24.575\\[/tex]
Hence the confidence interval is expressed as [tex]22.805 < \mu < 24.575\\[/tex]
Refer to Exercise probabilities. Find the following probabilities.
a. Two heads
b. One head
c. At least one head
d. At least two heads
Required:
Draw a probability tree to describe the flipping of three fair coins.
Answer:
Step-by-step explanation:
Probability is defined as the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
probability = n{E}/n{S}
n(E) is the total number of events
n{S} is the total number of sample space.
For a coin that is tossed 3times, the possible outcome are:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
The total number of sample space is n(S) = 2³ = 8
n{S} = 8
a) probability of getting two heads.
Events E = {HHH, HHT, HTH, THH}
n(E) = 4
Pr(getting two heads) = 4/8 = 1/2
b) probability of getting one head.
Events E = {HTT, THT, TTH}
n(E) = 3
Pr(getting one head) = 3/8
c) probability of getting at least one head means probability of getting 1 head and more but not less than a head.
Events E = {HHH, HHT, HTH, HTT, THH, THT, TTH}
n(E) = 7
Pr(getting at least one head) = 7/8
d) probability of getting at least two heads means probability of getting 2 head and more but not less than 2 head.
Events E = {HHH, HHT, HTH, THH}
n(E) = 4
Pr(getting at least two head) = 4/8 = 1/2
Find the tree diagram in the attachment below.
Terry bought a television set, a digital camera and a DVD recorder.
The average cost of the digital camera and the DVD recorder was
$925. He spent an average amount of $1985 on the 3 items. How
much did the television set cost?
Answer:
$1060
Step-by-step explanation:
as the average amount of DVD and digital camera is $925 so the television cost:
$1985-$925
=$1060
A tap leaks at the rate of 2cm³ per second.How long will it take the tap to fill a container of 45litres capacity.
Answer:
6 hours 15 minutes
Step-by-step explanation:
1 litre = 1000cm³
45 litres = 45000cm³
Volume = rate × time
45000 = 2 × t
t = 22500 secs
= 375 mins
BRAINLIEST PLEASE
All time values listed above are equivalent, so you only need to pick one value to write as the answer.
======================================================
Work Shown:
1 liter = 1000 cubic cm
45 liters = 45*1000 = 45000 cubic cm
The container has a capacity of 45000 cubic cm
It will take 45000/2 = 22500 seconds to fill the container since the rate is 2 cubic cm per second.
-----------------
Convert from seconds to minutes
22500 seconds = (22500)*(1 min/60 sec)
22500 seconds = (22500/60) min
22500 seconds = 375 min
-----------------
Convert to hours
375 min = (375)*(1 hr/60 min)
375 min = (375/60) hr
375 min = 6.25 hr
----------------
Converting to hours,minutes
6.25 hr = 6 hr + 0.25 hr
6.25 hr = 6 hr + (0.25*60) min
6.25 hr = 6 hr + 15 min
6.25 hr = 6 hr, 15 min
Marlene is given 7 feet of fabric to design a dress. She uses 6 feet of fabric. How much fabric is left?
Answer:
Amount of fabric left = 1 ft
Step-by-step explanation:
Given:
Amount of fabric Marlene had = 7 ft
Amount of fabric Marlene used = 6 ft
Find:
Amount of fabric left
Computation:
Amount of fabric left = Amount of fabric Marlene had - Amount of fabric Marlene used
Amount of fabric left = 7 ft - 6 ft
Amount of fabric left = 1 ft
Some friends decided to equally split the cost of gas on their trip. The expression 3g/4 represents how much money each person had to pay in dollars for g gallons of gas. What does the expression 3g in the numerator represent?
A the cost per person
B the number of people splitting the cost of the gas
C the total cost of the gas before it was split among the friends
D the cost per gallon of gas
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Answer: The total cost of the gas before it was split among the friends.
Explanation: If they split it equally, they divide. 3g is divided by 4 so you know that there are 4 friends/people.
Since they are splitting the [total] amount of gas for 4 people, 3g must be the total cost of the gas.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Answer:
c
Step-by-step explanation:
i took the quiz
What is a square matrix
Answer:
A square matrix is a matrix with the same number of rows and columns.
Step-by-step explanation:
In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order. Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation.
For this item, any answers that are not whole numbers should be entered as a decimal, rounded to the tenths place. In the figure below, line AB, line CD, and line EF intersect at point Q. Line AB is perpendicular to line CD. Complete the following equations.
x =
m∠CQF =
m∠AQE =
Answer:
[tex] x = 10 [/tex]
m<CQF = 32°
m<AQE = 32°
Step-by-step explanation:
m<CQB = m<CQA = 90° (right angle)
m<CQB = m<CQF + m<FQB
m<CQF = 3x + 2
m<FQB = 58°
Therefore,
[tex] 90 = 3x + 2 + 58 [/tex]
Solve for x:
[tex] 90 = 3x + 60 [/tex]
[tex] 90 - 60 = 3x + 60 - 60 [/tex]
[tex] 30 = 3x [/tex]
[tex] \frac{30}{3} = \frac{3x}{3} [/tex]
[tex] 10 = x [/tex]
[tex] x = 10 [/tex]
m<CQF = 3x + 2
Plug in the value of x to find m<CQF
m<CQF = 3(10) + 2 = 30 + 2
m<CQF = 32°
m<CQF and m<AQE are vertical opposite angles, therefore, they are congruent.
Thus,
m<AQE = 32°
Answer:
x = 10
m∠CQF = 32
m∠AQE = 58
Step-by-step explanation:
Suppose that a defined population is all men who are 50 or younger, and a survey is being conducted. Which of these is an example of selection bias? A. Excluding men over 50 from the selection process of the survey B. Including men under 30 in the selection process of the survey C. Excluding men under 30 from the selection process of the survey
Answer: C
Step-by-step explanation:
Excluding men under 30 from the selection process of the survey makes it bias because all mean 50 or younger are supposed to be included.
A student is growing two plants for a science experiment. Each plant was a different height at the start of the experiment. Plant A was given only water and plant B was given water and food. The system of equations show how the heights of the plants, y, in inches have change over x weeks. Plant A: y = 8 + ½ x Plant B: y = 4 + (5/4) x
Answer:
A: 12.5 per week B= 12.75
Step-by-step explanation:
1/2 times 7 (days in a week) is 3.5. So A is 8+3.5=12.5. 7 times 5/4 is 8.75. So B is 4+8.75=12.75
3 • { [ 4 ÷ 2 ] + 2 answer
Answer:
6+2=8
3×2+2=
6+2=8
good luck
Identify the slope and line intercept for y = 3x + 1
Answer:
Intercept - 1
Slope - 3
Step-by-step explanation:
in y=mx+b
m is the slope and b is the y intercept
Reduce these answers to simplest form 13/41 + 27/82
Answer:
53/82
Step-by-step explanation:
Answer:
13/41 + 27/82
We reduce to the same denominator.
The common denominator is 82
=(13×2)/(41×2) + 27/82
= 26/82 + 27/82
to calculate the sum of two fractions that have the same denominator, just add the numerators between them .
= 53/82
I screenshot the question.
Answer:
17 34
24 58
31 89
38 127
45 172
52 224
59 283
62 345
69 414
76 490
83 573
Step-by-step explanation:
Filling up the chart, you will get 227 at the 15 score mark. (You can just continuously add)
Then at the final answer you add the results to total pushups you get 573.
There is a faster way to do this using a formula, but probably will go over your head.
Write the point-slope form of a linear equation that passes through the two point (3, −5) and (−1, 8)
Answer:
y + 5 = (-13/4)(x - 3)
Step-by-step explanation:
Going from (-1, 8) to (3, -5), x (the 'run') increases by 4 and y (the 'rise') decreases by 13. Thus, the slope of the desired line is m = rise / run = -13/4.
The point-slope formula is
y - k = m(x - h), and here m = -13/4, k = -5 and h = 3:
y + 5 = (-13/4)(x - 3)