The value of the triple integral is π/4.
The given function is f(x,y,z) = z(x^2 + y^2 + z^2)^(-3/2).
We need to evaluate the triple integral over the part of the ball x^2 + y^2 + z^2 ≤ 1 defined by z ≥ 0.5.
Converting to spherical coordinates, we have x = ρsinφcosθ, y = ρsinφsinθ, and z = ρcosφ. The limits of integration are ρ = 0 to 1, φ = 0 to π/3, and θ = 0 to 2π.
So the integral becomes:
∫∫∫w f(x,y,z) dv = ∫₀^¹ ∫₀^(π/3) ∫₀^(2π) f(ρsinφcosθ, ρsinφsinθ, ρcosφ) ρ^2sinφ dθ dφ dρ
Substituting the function and limits, we have:
∫∫∫w z(x^2 + y^2 + z^2)^(-3/2) dv = ∫₀^¹ ∫₀^(π/3) ∫₀^(2π) (ρcosφ)(ρ^2)sinφ dθ dφ dρ
= ∫₀^¹ ∫₀^(π/3) ∫₀^(2π) ρ^3cosφsinφ dθ dφ dρ
= 2π ∫₀^¹ ∫₀^(π/3) ρ^3cosφsinφ dφ dρ
= π/4
Hence, the value of the given triple integral is π/4.
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what is (-2)( 3 4/7)
Answer:
-7 1/7
Step-by-step explanation:
Hope that helps!
Ms.Aluma is 165cm tall. She wants to find the square of her height In meters.
What is square of her height rounded to the nearest hundredth?
Height (m) x height (m) =height squared (m exponent 2)
Enter your answer in the box.
Answer:
2.72 cm2
Step-by-step explanation:
Height (m) x height (m) =height squared (m exponent 2)
The square of her height in meter² is 2.7225.
How to do decimal multiplication ?To multiply numbers with decimals one way is to multiply the given numbers without the decimal then in the obtained result put the decimal as many places before from the right as the sum of the digits after the digits which those decimal numbers had.
According to the given question Ms. Aluma is 165cm tall.
We know 165 cm is = (165/100)meter = 1.65meter.
As 1 meter is 100 centimeter.
∴ The square of her height is (1.65)² OR (1.65×1.65)m² which is
= 2.7225 m².
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Please please help :(((
Aubrey's dinner cost $85 She tips the waitstaff 30%, percent for excellent service.
Answer:
She tipped $25.50 and paid a total of $110.50
Step-by-step explanation:
hope this helps you out
The ratio of the number of baskets made by Tony to the number of baskets made by Colin is 2 to 3 Tony made 10 baskets how many baskets did Colin make
Answer:
15
Step-by-step explanation:
Answer: 15
Step-by-step explanation: 2:3. 10 baskets
10 -:- 2 = 5 so write 5 THREE times
5,5,5 Now Add.
5+5+5= 15 :) pls thanks this ty bye ❤️
can someone please explain number 5? please help merely if you know how to do this question
Step-by-step explanation:
The function/equation can be rewritten to fit the variables better. C=10t+2. C stands for the total cost, and t stands for the number of tickets. The total cost of tickets is the amount of tickets ($10 each) plus another $2 (probably some kind of fee).
please help me on this will give you brainliest
Answer:
ST =6.9
SR =15.9
Step-by-step explanation:
-10p - (1 - 2p)
(Distributive property[Expand] And combine like terms
Find the solution of y = 3x + 3 for x = –3.
(12, –3)
(–3, –6)
(–3, 0)
(–3, –2)
Answer:
B.
Step-by-step explanation:
Well, we know x=-3.
Substitute -3 for x in the equation, and solve. You should get -6.
(x,y)
(-3,-6)
find the missing value so that the line passing through the points has the given slope.
(10, y) and (3, 4); m= - 2/7
Answer:
y = 2
Step-by-step explanation:
use slope formula:
(4 - y) / (3 - 10) = -2/7
4-y / -7 = -2 /7
cross-multiply:
7(4 - y) = (-7)(-2)
28 - 7y = 14
-7y = -14
y = 2
pls help me out lol. I’m desperate
Answer:
x=3
Step-by-step explanation:
[tex]\frac{x}{9} =\frac{8}{21+x}[/tex]
x²+21x-72=0
(x-3)(x+24)=0
x=3 or x=-24(rejected)
∴x=3
True or False?
Is this the correct formula for using angles to see if a triangle is unique?
angle + angle <180
Answer: true
Step-by-step explanation:
. What is the ordered pair that satisfies the system 2x - 7y >5 and 3x-y S4?
A.(-1, -3)
B.(10, -1)
C.(-4, 6)
D.(-2,-8)
3. Which of the following is not a solution to this system?
Answer:
(-1, -3)
Step-by-step explanation:
What is the ordered pair that satisfies the system 2x - 7y >5 and 3x-y < 4?
Using the coordinate point (-1, 3)
If x = -1 and y = 3
Substitute into the expressions and check if they are true
2x - 7y >5
= 2(-1)-7(-3)
= -2 + 21
= 19
Since 19 is greater than 5, hence the inequality 19 > 5 is true
Substituting into 3x - y < 4
3(-1)-(-3)
= -3 + 3
= 0
Since 0 < 4, hence this is also true for the inequality.
The coordinate point that satisfies the inequality is therefore (-1, -3)
Please help me with this !!
Answer:
akismsksksialoalqoq kskw! sola skkss
Step-by-step explanation:
smksmskkwow!skkw
help me I keep getting it wrong
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{2}{3}[/tex] x - 6 ← is in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes , then
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (9, 2) into the partial equation
2 = 6 + c ⇒ c = 2 - 6 = - 4
y = [tex]\frac{2}{3}[/tex] x - 4 ← equation of parallel line
-------------------------------------------------------------------
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (9, 2) into the partial equation
2 = - [tex]\frac{27}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{27}{2}[/tex] = [tex]\frac{31}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ← equation of perpendicular line
a $528 video game console is on sale for 15% off. if sales tax is 6.25% what is total coast
The term "off" indicates that the price of the item is reduced by the percentage off. Sales tax is however, added to the price of the item.
The total cost of the video game console is: [tex]\$476.85[/tex]
Given that:
[tex]Game = \$528[/tex]
15% off means that, the price is reduced by 15%.
So, we have:
[tex]Sales =Game - Game \times 15\%[/tex]
[tex]Sales = \$528 - \$528 \times 15\%[/tex]
[tex]Sales = \$528 -\$79.2[/tex]
[tex]Sales = \$448.8[/tex]
The total cost (when the sales tax of 6.25% is added) is:
[tex]Total = Sales + Sales \times 6.25\%[/tex]
[tex]Total = \$448.8 + \$448.8 \times 6.25\%[/tex]
[tex]Total = \$448.8 + \$28.05[/tex]
[tex]Total = \$476.85[/tex]
Hence, the total cost of the video game console is: [tex]\$476.85[/tex]
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1. A number is 6 more than the average of, its half, its one-third and its one sixth
Find the number
Answer:
let no.be x
its half= x/2
its one third= x/3
its one sixth=x/6
atq.....avg of x= x/2+x/3+x/6//3=6x/6//3=x/3
now...x/3+6=x...as the no.is 6 more than its avg
x= 9
Calculate the value of the expression 44-(5x4)
Answer:
24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
44 - (5 x 4) = 44 - 20
= 24
HELLPPPP PLSSSS HELPPPPPPP
1. It is used to compare or determine the relation of a quantity, physical or not, with a certain
numerical value.
A measurement
C. weight
B. height
D. age
Answer:
A
Step-by-step explanation:
Measurement is the numerical quantification of the attributes of an object or event, which can be used to compare with other objects or events.
Measurement is used to compare or determine the relation of a quantity, physical or not, with a certain numerical value.
We have to determine, which is used to compare or determine the relation of a quantity, physical or not, with a certain numerical value
According to the question,
The process of measurement is required to measure or compare physical quantities in day-to-day life.
Thus, to measure each of the standard quantities, we choose certain units for them that are accepted worldwide.
Other similar quantities can also be expressed in terms of these units and can be measured accordingly.
The physical quantities are measured in terms of the unit and are known as a standard of that physical quantity.
The length of the foot, the width of a finger, and the distance between two different places were commonly measured by different units of measurements.
For unique measurement properties, scientists accepted standard units of measurement all over the world.
Hence, Measurement is used to compare or determine the relation of a quantity, physical or not, with a certain numerical value.
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Ayako claims that there are centers of dilations through which a dilation of line n by a factor leaves n changed. Determine whether each point below represents a center of dilation that supports ayako's claim
Answer:
The answer is below
Step-by-step explanation:
The question is not complete. The points are not given, but I can explain it.
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Dilation is the enlargement or reduction in the size of an object by a factor k. If a line AB is dilated by a factor k, with a center of dilation on the line AB, if the new line formed is A'B', then A'B' would lie on the same line AB irrespective of the dilating factor.
Dilation of a line segment is to smaller or larger a line with a specific scale factor. The line n when dilated with the center of dilation on the line, it will bring no change on the original line.
Given information
The line which is dilated is n.
DilationDilation of a line segment is to smaller or larger a line with a specific scale factor. If this scale factor is more than 1 then the line segment will larger otherwise smaller.
In the given problem a line n is dilated with the a scale factor that leaves the changed of n.
If the entire line is dilated and the point of this line passes through center of dilation then the change will be nothing. If dilated from the center of dilation the scale factor does not matter.
To find center of dilation which supports Ayako's claim the point below which represents the center of dilation are not given in the problem.
Hence, The line n when dilated with the center of dilation on the line, it will bring no change on the original line.
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Ellen and Bob went to Olive Garden for dinner. Ellen’s dinner costs $24.95 and Bob’s dinner costs $21.95. If they leave an 18% tip, what is the total cost of their dinner, including tip? (Round your answer to the nearest cent, and do not include the $ sign.)
Answer: 55.34
Step-by-step explanation:
24.95 + 21.95 = 46.90
46.90 x 18%
18% = .18
46.90 x 18 = 8.442
8.44 = cost of tip
8.44 + 46.90 = 55.34
PLEASE HELP ME!!!!!!!
Step-by-step explanation:
step 1. triangles ABG and ACF are similar.
step 2. triangle ACF is twice the size of triangle ABG.
step 3. if BG = 8 then CF = 16.
Price-club sells a 12-ounce box of crackers for $2.59 and Shop Mart sells 1- 1 2 pound box of crackers for $4.68.
The unit price at Price-Club is $
per ounce, and the unit price at Shop Mart is $
per ounce.
Answer:
Price club: = $0.216 per ounce
Shop Mart: = $0.195 per ounce
Step-by-step explanation:
Price club: 2.59 / 12 = 0.216 per ounce
Shop Mart: 4.68 / 24 = 0.195 per ounce (1 1/2 pounds & based on 16 ounces/pound)
Answer:
22
0.20
Step-by-step explanation:
A baseball team had 75 players show up for tryouts last year and this year had 90 players show up for tryouts. Find the percent increase in players from last year to this year.
Answer: 33.3%
Step-by-step explanation:
First find the difference between the players in try-outs over the years.
= 90 - 75
= 25
Then use this difference to find the percent increase:
= Difference / Players last years * 100%
= 25 / 75 * 100%
= 33.3%
SOMEONE PLEASE HELP!!!!!
Answer:
the answer is A and B
Step-by-step explanation:
hope it helps
(20 POINTS) PLZZZZZ HELPPPPPP
2. A diagonal shortcut across an empty
rectangular lot is 97 feet. The lot is 72
feet long. What is the other dimension of
the lot?
A 65 feet
C 120.8 feet
B 84.5 feet
D 169 feet
Answer:
65 ft (which is A)
Step-by-step explanation:
A² + B² = C²
72² + B² = 97²
B² = 4225
B = √4225
B = 65 ft
A. g(x) = f(x)+5
B. g(x) = f(x+5)
C. g(x) = f(x)-5
D. g(x) = f(x-5)
Answer:
-3 and 2Step-by-step explanation:
Te solutions of f(x) = g(x) are x-coordinates of points of intercept of the graphs.
Points of intercept are (-3, -8) and (2, -3)
So the solutions are: -3 and 2
Write as an addition problem: -49 - (-3)
Answer:
-49 + 3
Step-by-step explanation:
I think this ans may help you
Question below. Write an equation.
Answer:
16=3*2+5x
Step-by-step explanation:
3 is how many notebooks, 2 is cost per notebook, 5 is the cost of binders where x is the amount to bought, and 16 is how much you spent
Answer:
16 = 5x + 6
Step-by-step explanation:
You spend $16 on 3 notebooks and x binders. Notebooks cost $2 each and binders cost $5 each.
From this, we can see that our total amount of money spent is $16. This goes on one side of the equation.
T = 16
You have bought 3 notebooks that cost $2 each. An equation would be
n = 2x with x the number of notebooks bought. Plug 3 into x.
n = 2(3)
n = $6
You spent $6 on notebooks.
Your overall equation will be:
T = 5b + n
T is the total amount of money spent, x is the number of binders purchased, and n is the total amount of money spent on notebooks only.
Plug in the values you know.
16 = 5x + 6
To solve for x, subtract both sides by 6.
16 - 6 = 5x + 6 - 6
10 = 5x
Isolate x further by dividing both sides by 5.
x = 2
You bought 2 binders.
Hope this helps!