The region inside the cylinder with the radial distance r must range from 3 to √(16 - z²).
In polar coordinates, we express points in terms of a radial distance (r) and an angle (θ). To find the volume of the solid, we need to determine the limits of integration for r, θ, and z.
The equation of the sphere x² + y² + z² = 16 can be expressed in polar form as r² + z² = 16. This implies that the radial distance r ranges from 0 to √(16 - z²). The angle θ spans from 0 to 2π, representing a complete revolution around the z-axis. The height z ranges from -4 to 4, as the sphere extends from -4 to 4 along the z-axis.
The equation of the cylinder x² + y² = 9 translates to r = 3 in polar form. However, we need to exclude the region inside the cylinder. Therefore, the radial distance r must range from 3 to √(16 - z²).
To find the volume, we integrate the expression r dz dθ dr over the given limits of integration. The volume is calculated by evaluating the triple integral using the appropriate limits.
It is important to note that without further information about the region of interest, such as any boundaries or additional constraints, a more precise volume calculation cannot be provided.
Learn more about polar coordinates here:
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Ming's school is selling tickets to a play. On the first day of ticket sales the school sold 8 adult tickets and 1 student ticket for a total of $95. The school took in $71 on the second day by selling 2 adult tickets and 7 student tickets. Define two variables for this situation. Write a system of equations to represent this situation. What is the price each of one adult ticket and one student ticket?
Answer:
Your answer.
8x + y = 95.........(1)
2x + 7y = 71........... (2)
Y = 95-8x........ (3)
Put this value in eq 2
Then x = 11
Put x value in eq 3
Y = 7
Thank you. And give my answer as Brainlist answer. Follow me for more
Step-by-step explanation:
Find the length of y
Answer:
25 cm
Step-by-step explanation:
-3/4x=-5
Please help fast!!!
Answer:
x=3.75
Step-by-step explanation:
-3/4x=-5
x-3 x-3
4x=15
/4 /4
x=3.75
Answer:
x = 3.75
Step-by-step explanation:
-3/4x = -5
(-3/4) -3/4x = -5(-3/4)
x = 3.75
Factor the following expression completely.
2x^2y-18y
Answer:
Since both terms are perfect squares, factor using the difference of squares formula,
a2-b2=(a+b)(a−b) where a=x and b=3.2y(x+3)(x−3)
Step-by-step explanation:
hope this helps!!!
What is the next term of the geometric sequence?
20, -10,5,
Answer:
0
Step-by-step explanation:
Answer: -2.5
Step-by-step explanation:
8r2 in fraction form
8r^2 eight r squared hope this is right
It is the simplest fraction form
13. Town officials are putting a pathway around a pool as shown below.
(4x+3)
pool
(2x-5) ft
deck
a) Determine the perimeter of the pool in terms of x. Write your answer in simple form and
include units. Show or explain your work.
b) Determine the area of the pool in terms of x. Write your answers as a trinomial and include
units. Show or explain your work.
Answer:
ghcfgnxfgxgfmvjbnjghjbnmxfhcgxfgcxgchmvjm
Step-by-step explanation:
good day
Tyler has $415 in his savings Tyler has $415 in his savings account account. He earns $45 a week mowing lawns. Write and solve an equation.using b for the variable to find how many weeks will he to work to have $1315 saved?
Answer:
20 weeks
Step-by-step explanation:
1315$-415$=900$
900/45=20
Hence 20 weeks
Answer: 45b
Step-by-step explanation: Divide 1315 with 45xb.
What multiplication fact could help me find out 24 ÷ 8 ?
Answer:
Step-by-step explanation:
That would be 8 x 3. It would help because 24/8 = 3.
5/2k+1=-9
What does k equal?
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
If you mean,
[tex] \frac{5}{2k} + 1 = - 9[/tex]
Then the answer would be,
[tex]k = - \frac{1}{4} [/tex]
But, if you mean
[tex] \frac{5}{2} k + 1 = - 9[/tex]
Then the answer would be,
[tex]k = - 4[/tex]
The candy store has a stock of candy. They have 15 bags of tootsie rolls, 10 boxes of nerds, 12 bags of gummy
bears, 5 bags of M&M's and 22 bags of skittles. Find the ratio of tootsie rolls to total candy in the store. Be sure
to simplify
Answer:
15:49
Step-by-step explanation:
15 : 10+12+5+22
15 : 49
Can't be simplified further.
Find the surface area of the
triangular prism.
10 ft.
3 ft.
3 ft
Given:
The figure of a triangular prism.
To find:
The surface area of the triangular prism.
Solution:
We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.
Triangles have base 3 ft and height 2 ft.
Area of a triangle is
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_1=\dfrac{1}{2}\times (3)\times (2)[/tex]
[tex]A_1=3[/tex]
Area of congruent triangles are congruent. So,
[tex]A_1=A_2=3\text{ sq. units}[/tex]
Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.
Area of a rectangle is
[tex]Area=Length\times width[/tex]
[tex]A_3=10\times 3[/tex]
[tex]A_3=30[/tex]
Dimensions of all three rectangles are same, therefore there areas are equal.
[tex]A_3=A_4=A_5=30[/tex]
Now, the total surface area of the prism is
[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]
[tex]A=3+3+30+30+30[/tex]
[tex]A=96[/tex]
Therefore, the total surface area of the prism is 96 sq. ft.
plz I need help on this really bad :(
Answer:
x+3y=4x+y
Step-by-step explanation:
¿Sera cierto que existe una fraccion con numerador 20 equivalente a la fraccion 100/55?Justifica tu respuesta
Answer:
si porq si porq si si dices si es si
In the figure shown the sum of the measures yxz and wxv is 75 degrees . what is the measure of zxw
Answer: 105 = WXZ
Step-by-step explanation:
180 = WXZ + 75
subtract both sides by 75 and you get WXZ is equal to 105
I'm not 100% sure, lmk if I'm wrong
a²-a² what is the answer
Answer:
a² - a² = 0
hope it helps
Answer:
a ² - a ²= 1 a ² - 1 a ² = 0
you understand ?
Your class earned $120.00 Saturday afternoon by washing cars to raise money for the class trip. This is 1/4 of the money needed for the trip. What is the total amount needed?
Answer:
$360.00
(I hope this was helpful)
What is the difference from congruent figures and similar figures
Answer:
similar = only the angles are the same
congruent = angles and sides are the same
Please help:
Find the class width of this graph
Answer:
The biggest one is 32 to 38
Step-by-step explanation:
hope it helps
Order the angles in each triangle from smallest to largest.
how to the medium in the dot line????!! I don't want my mom to be mad at my grade please!!!!!!
Thank you whoever helps me!
Answer: To find the median, count the dots from left to right until you find the middle value.
Step-by-step explanation:
Ok so first it's not a dot line it's a dot plot. Second, let's define what a medium is. The medium is the "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. The middle number is 15, so the median is 15. Tip to find the median from a list of value ordered numbers every time cross a number from each side. For example, if you cross 13 from above also cross 26 and if you cross 23 then also cross 10.
Back to your original question of how to find the medium on a dot plot you need to take all the numbers from your dotted line put them in order even if they are repeated and then cross each one on each side from right to left. Also remember if you cross out all the numbers right and left and end up with two numbers left then take them and add them and then divide by 2 and that will be the median.
An example is attached on here in order to help you understand what I am saying. Hope this helps. Your welcome and I hope you make your mama proud.
Was wondering if anyone knows the answer to part A and B for this question?
Answer:
no idea
Step-by-step explanation:
Answer:
k so from my opinion
I think the answer is gonna be a
There are 9 counters in a bag.
7 of the counters are green.
2 of the counters are blue.
Ria takes at random two counters from the bag.
Work out the probability that Ria takes one counter of each colour.
Perry's bikes rent bikes for $18 plus $4 per hour. Lea paid $42 to rent a bike for how many hours did she rent the bike?
Answer:
10.5 hours!
Step-by-step explanation:
A gymnast scores a total of 125 points in the first 4 meets of the season. At this rate, how many points will she score by the end of 14 meets
Answer:
i dont know but will u date me
Step-by-step explanation:
A medical provider is doing a study to determine the average time spent waiting before an appointment. The current average wait time is 34 minutes, which is 15% shorter than the average was when the study started. What was the average wait time then?
Answer:
39.1 minutes
Step-by-step explanation:
Given that:
Current wait time = 34 minutes
Current wait time is 15% shorter than average wait time when study started.
Average wait time when study started :
15% of current wait time :
0.15 * 34
= 5.1 minutes
Average wait time when study started :
34 minutes + 5.1 minutes
= 39.1 minutes
Maria ha invitado a 18 de sus compañeros de clase a su fiesta de cumpleaños .Si en total tiene 30 compañeros ,¿que porcentaje de la clase ha ido a su fiesta?
Answer:
59.9%
Step-by-step explanation:
100/30 = 3.3
3.3*18 = 59.9%
Which of the following is equivalent to 3^-8 × 3^4
3^-4
3^-2
3^-12
3^-32
PLZ HELP ME & ANSWER CORRECTLY!!!!! NEED ANSWER ASAP!!!!!
Mica and Joy are standing at corner A of the rectangular field shown below.
Mica walks diagonally across the field, from A to corner C. Joy walks from corner A to corner B, and then to corner C. To the nearest hundredth of a mile, how much farther did Joy walk the Mica?
Answer:
0.54 miles more
Step-by-step explanation:
1. Find the Diagonal. d=w2+l2=1.252+0.752≈1.45774
2. 3/4+1 and 1/4=2 miles
3. 2 miles-1.46 estimate.
4. Solution...0.54
What is the volume of this?
Answer:
270 m³
Step-by-step explanation:
[tex]A_{triandle}[/tex] = [tex]\frac{5*12}{2}[/tex] = 30 m²
[tex]V_{triangular prism}[/tex] = 30 × 9 = 270 m³