Please help fast! I need the answer along with step by steps explaining to I can learn it thanks I’ll give brainlist to who does it for me I appreciate it!
Answers
Answer:
?
Step-by-step explanation:
Related Questions
Use spherical coordinates to evaluate the
triple integral x2 + y2 + z2 DV, where E
is the ball: x2 + y2 + z2 = 16.
1/S22+
Answers
Answer:
4096π / 5
Step-by-step explanation:
∫∫∫ (x² + y² + z²) dV
In spherical coordinates, x² + y² + z² = r², and dV = r² sin φ dr dθ dφ.
E is the range 0 ≤ r ≤ 4, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π.
∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r²) (r² sin φ dr dθ dφ)
∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r⁴ sin φ) dr dθ dφ
Evaluate the first integral.
∫₀ᵖⁱ∫₀²ᵖⁱ (⅕ r⁵ sin φ)|₀⁴ dθ dφ
∫₀ᵖⁱ∫₀²ᵖⁱ (¹⁰²⁴/₅ sin φ) dθ dφ
¹⁰²⁴/₅ ∫₀ᵖⁱ∫₀²ᵖⁱ (sin φ) dθ dφ
Evaluate the second integral.
¹⁰²⁴/₅ ∫₀ᵖⁱ (θ sin φ)|₀²ᵖⁱ dφ
¹⁰²⁴/₅ ∫₀ᵖⁱ (2π sin φ) dφ
²⁰⁴⁸/₅ π ∫₀ᵖⁱ sin φ dφ
Evaluate the third integral.
²⁰⁴⁸/₅ π (-cos φ)|₀ᵖⁱ
²⁰⁴⁸/₅ π (-cos π + cos 0)
²⁰⁴⁸/₅ π (1 + 1)
⁴⁰⁹⁶/₅ π
Answer:
[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV = \frac{4096 \pi}{5}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Triple Integrals
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Spherical Coordinate Conversions:
[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]Integral Conversion [Spherical Coordinates]:
[tex]\displaystyle \iiint_T {f( \rho, \phi, \theta )} \, dV = \iiint_T {\rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]
Step-by-step explanation:
*Note:
Recall that φ is bounded by 0 ≤ φ ≤ 0.5π from the z-axis to the x-axis.
I will not show/explain any intermediate calculus steps as there isn't enough space.
Step 1: Define
Identify given.
[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV[/tex]
[tex]\displaystyle \text{Region E (Ball):} \ x^2 + y^2 + z^2 \leq 16[/tex]
Step 2: Integrate Pt. 1
Find ρ bounds.
[Ball] Substitute in Spherical Coordinate Conversions:[tex]\displaystyle \rho^2 \leq 16[/tex]Solve:
[tex]\displaystyle \rho \leq 4[/tex]Define limits:
[tex]\displaystyle 0 \leq \rho \leq 4[/tex]
Find θ bounds.
[Ball] Substitute in z = 0:[tex]\displaystyle x^2 + y^2 \leq 16[/tex][Circle] Graph [See 2nd Attachment][Graph] Identify limits [Unit Circle]:
[tex]\displaystyle 0 \leq \theta \leq 2 \pi[/tex]
Find φ bounds.
[Circle] Substitute in Cylindrical Coordinate Conversions:[tex]\displaystyle r^2 \leq 16[/tex]Solve:
[tex]\displaystyle r \leq 4[/tex]Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle \rho \sin \phi \leq 4[/tex]Solve:
[tex]\displaystyle \phi \leq \frac{\pi}{2}, \frac{3 \pi}{2}[/tex]Define limits:
[tex]\displaystyle 0 \leq \phi \leq \pi[/tex]
Step 3: Integrate Pt. 2
[Integrals] Convert [Integral Conversion - Spherical Coordinates]:[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV = \iiint_E {(x^2 + y^2 + z^2) \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex][dρ Integrand] Rewrite [Spherical Coordinate Conversions]:
[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV = \iiint_E {\rho^4 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex][Integrals] Substitute in region E:
[tex]\displaystyle \iiint_E {x^2 + y^2 + z^2} \, dV = \int\limits^{2 \pi}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^4_0 {\rho^4 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]
We evaluate this spherical integral by using the integration rules, properties, and methods listed above:
[tex]\displaystyle \begin{aligned}\iiint_E {x^2 + y^2 + z^2} \, dV & = \int\limits^{2 \pi}_0 \int\limits^{\pi}_0 \int\limits^4_0 {\rho^4 \sin \phi} \, d\rho \, d\phi \, d\theta \\& = \int\limits^{2 \pi}_0 \int\limits^{\pi}_0 {\frac{\rho^5}{5} \sin \phi \bigg| \limits^{\rho = 4}_{\rho = 0}} \, d\phi \, d\theta \\& = \int\limits^{2 \pi}_0 \int\limits^{\pi}_0 {\frac{1024}{5} \sin \phi} \, d\phi \, d\theta\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\iiint_E {x^2 + y^2 + z^2} \, dV & = \int\limits^{2 \pi}_0 {\frac{-1024}{5} \cos \phi \bigg| \limits^{\phi = \pi}_{\phi = 0}} \, d\theta \\& = \int\limits^{2 \pi}_0 {\frac{2048}{5}} \, d\theta \\& = \frac{2048}{5} \theta \bigg| \limits^{\theta = 2 \pi}_{\theta = 0} \\& = \frac{4096 \pi}{5}\end{aligned}[/tex]
∴ we have evaluated the given integral in spherical coordinates.
---
Learn more about spherical coordinates: https://brainly.com/question/17166987
Learn more about multivariable calculus: https://brainly.com/question/4746216
---
Topic: Multivariable Calculus
Unit: Triple Integrals Applications
The blue dot is at what value on the number line?
Answers
Answer: The blue dot is at -22
Step-by-step explanation:
The distance between two line is shown to be 6, so you subtract six from -16 to find the value of the dot.
Answer:
-22
Step-by-step explanation:
the distance between -10 and -16 is 6 and 6 divided by 2 is 3. I add -6 to -16 to get -22
find the slope of the line passing through the points (-9,-6) and (-4,5)
Answers
Answer:
11/5
Step-by-step explanation:
its 11/5
Answer:
[tex]m=\frac{11}{5} \\\\m=2\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-9,\:-6\right),\:\\\left(x_2,\:y_2\right)=\left(-4,\:5\right)\\\\m=\frac{5-\left(-6\right)}{-4-\left(-9\right)}\\\\m = \frac{5+6}{-4+9}\\\\m=\frac{11}{5} \\\\m=2\frac{1}{5}[/tex]
The Math Team sells crunchy and fruity trail mixes to raise money. The ratio of fruit to nuts in each mix and the price they charge for an 8-oz (or -cup) bag of each mix are given in the table below. [Hint: The ratio of fruit to nuts in the crunchy trail mix is 1:3. So, of each bag is fruit and of each bag is nuts.]
Ratio of fruit to nuts Price of an 8-oz (or cup) bag
Crunchy trail mix 1:3 $2.50
Fruity trail mix 5:3 $3.50
They have 30 cups of fruit and 50 cups of nuts to use in their trail mixes. So, they need to know how many bags of each type of mix they should they make. They let c represent the number of bags of crunchy trail mix and f represent the number of bags of fruity trail mix. Which set of inequalities below represents the conditions?
Answers
The conditions would be represented by the following set of inequalities:
c + 5f ≤ 60.3c + 3f ≤ 100.c ≥ 0. f ≥ 0.What is an inequality?An inequality can be defined as a mathematical relation for comparing two (2) or more integers or variables in an equation based on any of the following:
Greater than (>).Less than (<).Greater than or equal to the other (≥).Less than or equal to the other (≤).In this scenario, the ratio of fruit to nuts in the crunchy trail mix is equal to 1:3. Therefore, 1/4 of each bag contain fruits while 3/4 contain nuts.
Mathematically, these conditions would be represented by the following set of inequalities:
1/2 × (c + 5f) ≤ 30 ⇒ c + 5f ≤ 60.
1/2 × (3c + 3f) ≤ 50 ⇒ 3c + 3f ≤ 100.
c ≥ 0. f ≥ 0.
Read more on inequality here: https://brainly.com/question/24372553
#SPJ2
Lenny buys a popcorn and soda at the movies. A large popcorn is $7 and the drink is $3.50. Lenny has to also pay tax of 6%. How much will he pay in total?
Answers
Answer:
i think its 10.71 i dont know if i got it right your welcome
Step-by-step explanation:
Answer:
$10.71
Step-by-step explanation:
How to solve this additional problem
1/(x+2)+x^2+x-2
Answers
Answer:
1/x^2+2x
Step-by-step explanation:
Which statement shows how to compute the area of a circle with a radius of 4 feet?
a. 7 times 4 squared
b. 7 times 2 squared
C. 7 times 8 squared
d. 7 times 16 squared
Answers
Answer:
I think its C......Yea C..................
Step-by-step explanation:
Determine the intercepts of the line.
2x + 5y = -6
Answers
Step-by-step explanation:
x-intercept: 2x + 5(0) = -6
2x = -6
x = -3
y-intercept: 2(0) + 5y = -6
y = -6/5
topic: coordinate geometry
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
HELP PLEASE!!
Mrs. Newman has $15 to buy birthday cards that cost $1.40 each.
Create a set of five ordered pairs that shows the amount of money she spends as a function of the number of birthday cards she buys.
( ____, ____ ), ( ____, ____ ), ( ____, ____ ), ( ____, ____ ), ( ____, ____ ),
Can Mrs. Newman buy 12 birthday cards? Why or why not?
What are 12 times 1.40? Is $16.80 less than $15?
Challenge: Write a function rule (equation) that shows the relationship between the number of cards she buys (x) and the amount of money she spends (y).
Answers
Answer:
I'm dumb hwhsbdbshagebsvxv
Help me please ASAP will mark brainliest!!
Answers
Hey you’ve got it right on ur screen.
A rectangle has a length of 12 yards less than 3 times its width. If the area of the rectangle is 135 square yards, find the length of the rectangle.
Answers
Answer:
The length is 15 yards
Step-by-step explanation:
Given
Represent the width with W and length with L: So
[tex]Area = 135yd^2[/tex]
[tex]L=3W - 12[/tex]
Required
Determine the length of the rectangle:
Area is calculated as thus:
[tex]Area = L * W[/tex]
Substitute 3W - 12 for L and 135 for Area
[tex]135= (3W - 12) * W[/tex]
[tex]135= 3W^2 - 12W[/tex]
Reorder:
[tex]3W^2 - 12W - 135= 0[/tex]
Divide through by 3
[tex]W^2 - 4W - 45 = 0[/tex]
Expand:
[tex]W^2 - 9W + 5W - 45 = 0[/tex]
[tex]W(W - 9) + 5(W - 9) = 0[/tex]
[tex](W + 5)(W-9) = 0[/tex]
[tex]W + 5 = 0[/tex] or [tex]W - 9 = 0[/tex]
[tex]W = -5[/tex] or [tex]W = 9[/tex]
But width can't be negative
So:
[tex]W = 9[/tex]
Recall that: [tex]L=3W - 12[/tex]
[tex]L = 3 * 9 - 12[/tex]
[tex]L = 15[/tex]
Hence, the length 15 yards
Mireya has breakfast at a restaurant. Her bill was $9.00. Mireya plans to leave a 20% tip. How much does she need to leave for the tip?
Answers
9 * .20 = 1.80
What is the sum of 4 - 7i and the conjugate of 2 + 3i ?
A.6 - 4i
B.8 - 21i
C.8 - 4i
D.6 - 10i
Answers
The conjugate of a complex number z = a + b i is z * = a - b i. So
(4 - 7i ) + (2 + 3i )* = (4 - 7i ) + (2 - 3i )
… = (4 + 2) + (-7i - 3i)
… = 6 - 10i
and the answer is D.
the ruiz family is exchanging euros for us dollars the exchange rate is 1 euro 1.35261
Answers
Answer:so what is the question
Step-by-step explanation:
Helped needed having difficulty
Answers
Answer:
1. 1/4 cup of molasses.
2. 72 1/2 strips.
3. 7 1/2 hours.
Step-by-step explanation:
What is the product of (–22.1)(–5.6)?
–123.76
–27.7
27.7
123.76
Answers
Answer:
d) 123.76
Step-by-step explanation:
hope this helps :)
3. A solid cylinder has a radius of 6cm and a height of 20cm.
a. Calculate the volume of the cylinder. Give your answer correct to 3 significant figures.
b. The cylinder is made of a material that has a density of 1.5g/cm3. Calculate the mass of the cylinder. Give your answer correct to 3 significant figures.
4. The diagram shows a right-angled triangular prism.
Answers
Answer:
a) 2260 cm³
b) 3390 grams
Step-by-step explanation:
3.
a)The radius of the solid cylinder = 6cm
The height of the cylinder is =20 cm
The volume = π*r²*h
The volume = 3.14 * 6²*20 =2260 cm³
b) Density of the material = 1.5 g/cm³
Volume of the cylinder = 2261 cm³
Mass of the cylinder = Density * Volume
Mass of the cylinder = 1.5 * 2261 = 3390 grams
The population in a certain town is increasing linearly each year. The population at time t=3 is 1160 and at time t=5 is 1520, where t is the number of years after 1990.
Answers
Answer:
1999
Step-by-step explanation:
At a local hospital, 35 babies were born. If 28 were boys, what percentage of the newborns were boys? Express your answer to the ones place.
Answers
Answer:
80% of the newborns were boys
Step-by-step explanation:
is 141.3 more than 141.05
Answers
Answer:
Yes
Step-by-step explanation:
Since the base numbers (141) is the same, we can ignore that.
Now, let's look at .3 and .05.
.3 is the same as .30.
If we remove the decimal point, we're looking at 30 and 5. 30 is greater than 5, so 141.3 is greater than 141.05.
There are twelve shirts in your closet, three blue, five green, and four red. You randomly select one to wear. It is blue or green.
Answers
Answer:
green
Step-by-step explanation:
green has a higher possible of being picked over blue
A 7-foot piece of cotton cloth costs $7.56. What is the price per inch?
Answers
Answer:
$.09 per inch
Step-by-step explanation:
1 foot = 12 inches
Multiply each side by 7
7 ft = 12*7 = 84 inches
Take the cost and divide by the number of inches
$7.56 / 84 inches
$.09 per inch
Answer: 0.09 per inch because multiply that by 12 and thats a foot and multiply that by 7 and you'll get 7.56
Step-by-step explanation:
A train travels 16.8 km in 25 mins. find the speed of the train in
(i)km/h (ii) m/s.
Answers
i. Distance = 16.8 km
Time = 25 mins = 5/12hours
Speed = distance/time
= 16.8÷(5/12)
= 16.8 × 12/5
= 40.32 km/h
ii. In m/s = 40.32/3.6
= 11.2 m/s
The speed of the train is 11.2 m/s.
The speed of the train is 40.32 km/h.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Distance.
= 16.8 km
= 16.8 x 1000
= 16800 m
Time.
= 25 minutes
= 25 x 60 seconds
= 1500 seconds
Speed.
= Distance / Time
= 16800 / 1500
= 16800 / 1500
= 11.2 m per second
Speed.
Distance = 16.8 km
Time = 25/60 hours
Speed = (16.8 x 60) / 25 = 40.32 km per hour.
Thus,
The speed is 40.32 km per hour.
The speed is 11.2 meters per second.
Learn more about speed here:
https://brainly.com/question/7359669
#SPJ2
Solve for x.
Enter the solutions from least to greatest.
(-5x + 4)(x – 3) = 0
Answers
Answer:
x = 4/5, and x = 3
Step-by-step explanation:
set both parts of the equation equal to 0
-5x+4 =0
-5x= -4
divide by -5
x= 4/5
x-3 = 0
x=3
Alice has two bags of marbles: Bag A contains 8 red and 3 blue marbles, and Bag B contains 5 red and 7 blue marbles. She randomly selects a bag and then draws one marble at random. It is blue. What is the probability that it came from Bag B?
Can you explain why the answer is 77/113? and actually answer the question if you don't know, dont post an answer
1
Answers
It might help to draw out a probability tree. Check out the diagram below. The first two branches at the top represent bags A and B. The probability of picking either bag is 1/2 assuming each bag is equally likely to be picked.
If we go with bag A, then the probability of getting blue is 3/11 since there are 3 blue out of 8+3 = 11 total. The probability of getting bag A and a blue marble is (1/2)*(3/11) = 3/22 which I've marked in the diagram as well.
If we go with bag B, then the probability of getting blue is 7/12 since there are 7 blue out of 5+7 = 12 total. The probability of getting bag B and blue is (1/2)*(7/12) = 7/24
Add up the results found getting
P(blue) = P(blue & bag A) + P(blue & bag B)
P(blue) = 3/22 + 7/24
P(blue) = 36/264 + 77/264
P(blue) = 113/264
This is shown in the diagram as well.
--------------------------------------------------
Recall that conditional probability in general is defined as follows
P(A given B) = P(A and B)/P(B)
In this problem, we'll have
P(bag B given blue) = P(bag B and blue)/P(blue)
Therefore, we can say...
P(bag B given blue) = P(bag B and blue)/P(blue)
P(bag B given blue) = (7/24)/(113/264)
P(bag B given blue) = (7/24)*(264/113)
P(bag B given blue) = (7*264)/(24*113)
P(bag B given blue) = (7*24*11)/(24*113)
P(bag B given blue) = (7*11)/(113)
P(bag B given blue) = 77/113
In short, the probability of getting bag B, given the marble is blue, is 77/113.
HELP IS THIS PROPORTIONAL
Answers
683,004 and 3,854.927to nearest hundredths
Answers
Answer:
683004.00
3854.93
Step-by-step explanation:
Solve the equation: -68 = 5y - 3
Answers
Answer:
-13
Step-by-step explanation:
-68 = 5y-3 First you move the -3 by adding 3 to both sides to get -65 =5y
Then you divide 5 by both sides to get y=-13
Answer:
y = -13
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-68 = 5y - 3
Step 2: Solve for y
Add 3 to both sides: -65 = 5yDivide both sides by 5: -13 = yRewrite: y = -13Step 3: Check
Plug in y to verify it's a solution.
Substitute: -68 = 5(-13) - 3Multiply: -68 = -65 - 3Subtract: -68 = -68And we have our final answer!
kaitlyn and brian are ordering stickers. a carton has 20 packets wythe 600 stickers in each packet. If Kaitlyn and brian ordered 20 cartons. How many stickers did they order
Answers
Answer:
240000
Step-by-step explanation:
20x600=12000
12000x20=240000
Determine whether the following triangles are congruent. If they are congruent, give a congruency statement.
Answers
Answer:
Congruent, ASA Congruency Theorem
Step-by-step explanation:
HGI and KJI are vertical angles, therefore equalAngle H and K are congruentGJ bisects HK at Point I, therefore segments HI and KI are congruent