Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, and below the cone z = x^2 + y^2.
Answer:
The volume of the solid is 243[tex]\sqrt{2} \ \pi[/tex]
Step-by-step explanation:
From the information given:
BY applying sphere coordinates:
0 ≤ x² + y² + z² ≤ 81
0 ≤ ρ² ≤ 81
0 ≤ ρ ≤ 9
The intersection that takes place in the sphere and the cone is:
[tex]x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81[/tex]
[tex]2(x^2 + y^2) =81[/tex]
[tex]x^2 +y^2 = \dfrac{81}{2}[/tex]
Thus; the region bounded is: 0 ≤ θ ≤ 2π
This implies that:
[tex]z = \sqrt{x^2+y^2}[/tex]
ρcosФ = ρsinФ
tanФ = 1
Ф = π/4
Similarly; in the X-Y plane;
z = 0
ρcosФ = 0
cosФ = 0
Ф = π/2
So here; [tex]\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}[/tex]
Thus, volume: [tex]V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi[/tex]
[tex]V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho[/tex]
[tex]V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}[/tex]
[tex]V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ][/tex]
V = 243[tex]\sqrt{2} \ \pi[/tex]
Please I need help???
Answer:14
Step-by-step explanation:
14
f(x) = 4x + 2 and g(x) = x2–2, find the value of f(2) +g(3)
Answer:
14
Step-by-step explanation:
f(2)=4(2)+2
f(2)=10
g(3)=2(3)-2
g(3)=6-2
g(3)=4
10+4=14
Answer:
17
Step-by-step explanation:
f(x) = 4x + 2
g(x) = x² - 2
f(2) = 4(2) + 2 = 10
g(3) = 3² - 2 = 7
10 + 7 = 17
On average, 2.8 babies are born each day at a local hospital. Assuming the Poisson distribution, what is the probability that no babies are born today?
Answer:
The probability is [tex]P(X = 0) = 0.6997[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 2.8[/tex]
Generally the Poisson distribution constant [tex]\lambda[/tex] is mathematically represented as
[tex]\lambda = \frac{1}{\mu }[/tex]
=> [tex]\lambda = \frac{1}{2.8 }[/tex]
=> [tex]\lambda = 0.3571[/tex]
Generally the probability distribution for Poisson distribution is mathematically represented as
[tex]P(X = x) = \frac{(\lambda t)^x e^{-t \lambda}}{x!}[/tex]
Here t = 1 day
Generally the probability that no babies are born today is mathematically represented as
[tex]P(X = 0) = \frac{(0.3571 * 1 )^0 e^{-1 * 0.3571}}{0!}[/tex]
=> [tex]P(X = 0) = 0.6997[/tex]
Sammy deposits $200 in an account at his bank.The simple interest rate is 8%.How much interest will he earn in three years
Answer:
$48
Step-by-step explanation:
Multiply 200 by 0.08 or 8%. That is how much interest he will earn in a year. Then multiply the product by 3.
Help anyone 5th grade math
Answer:
Equal???
Step-by-step explanation:
How many metres and centimetres are in 3080mm
Answer:
3080mm = 3.08 meters
3080mm = 308 centimeters
Step-by-step explanation:
1 meter = 1000 mm
3080mm = 3080/1000 = 3.08 meters
1 centimeter = 10 mm
3080mm = 3080/10 = 308 centimeters
what is the slope and the y-intercept for the equation y = -3 + 6x?
Answer:
slope-6
y-intercept-(0,-3)
Step-by-step explanation:
Determine the total number of roots of each polynomial function using the factored form.
f (x) = (x + 1)(x - 3)(x - 4)
Answer:
3 roots
Step-by-step explanation:
The roots of a function is the x intercepts.
x=-1
x=3
x=4
Help please I’ll mark as brainliest!
Answer:
I think its B cause i was solving it and my answer came close to letter B
Step-by-step explanation:
i tried
I Need help fast What is 18/1.69= because i don't want to fail and please give the right answer
Answer:
10.650887574
Step-by-step explanation:
Hope this helps. Good luck!
Answer: 10.6508
If you get the app Socratic, it tells you the answers from all different websites
Find the percent the first number is of the second 7 ft, 7 yd
Answer:
33 1/3
Step-by-step explanation:
7/21=1/3
1/3*100=100/3
100/3=33 1/3
con las medidas de los lados 8cm , 9cm ,2cm se existe un triángulo ?
Answer:
si
Step-by-step explanation:
la longitud mayor es menor que la suma de las otras 2 longitudes que es 10
I believe SAS is the correct answer but SSS is also possible so which one is it?
PLSSSSSS HELPPPPPPPPPPPPPP I HAVE BEEN STUCK ON THIS PROBLEM IN MY HOMEWORK
Write the expression as a square of a monomial:
[tex]100x^{2} *0.36y^{4}[/tex]
Please help!!!
If h(x)= -3x-10, find h(-3)
Please give an explanation too. Thank you.
Answer:
h(-3)=-1
Step-by-step explanation:
Replace all x in h(x)= -3x-10 by -3:
h(-3)=-3(-3)-10
Now multiply -3 and -3:
h(-3)=9-10
Simplify 9 and -10 (aka add 9 and -10 together):
h(-3)=-1
Answer: h(-3)=-1
Hope this helps!
Answer:
-1
Step-by-step explanation:
If h(x)= -3x-10 and we want to solve for h(-3) then we have to plug in -3 for all x variables. h(-3)= -3(-3)-10, then solve using PEMDAS.
First multiple h(-3)= 9-10, multiple -3*-3 to get 9.
Then subtract, h(-3)=-1
A restaurant offers delivery for their pizzas. The total cost is a delivery fee added to the price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. How many pizzas are delivered to a customer who pays $80
Answer:
7 pizzas
Step-by-step explanation
First we subtract 58-25=33
Then we subtract 5-2=3
Now, we have 33 over 3 so we divide them and we get 11
So, that means that each pizza costs $11 and the fee that they charge for each pizza is 3.
So if the customer pays $80 that means that he bought 7 pizzas and he payed $3 fee.
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another
right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS SSS
SAS
HL
Answer:
the answer is hl
Step-by-step explanation:
its d
Answer:
the d
Step-by-step explanation:
HL
a+b+c=88
b+c=84
a=2xb
Help!
Answer:
C=84∘, a=2, c=7
Step-by-step explanation:
Answer:
Sorry, but i need to do my homework as well. The answer is: a=4, b=2, c=82
Al cuadrado de un número se lo aumenta en 7 unidades y se obtiene el número 56.
¿Cuál es dicho número?
Answer:
Hola, me no Espanol.
Step-by-step explanation:
How many times larger is 4 x 10 ^16 than 4 x 10^6?
Answer:
10^10 timesStep-by-step explanation:
To find it we will divide:
4 x 10^16 / 4 x 10^6 = 4/4 x 10^(16 - 6) = 1*10^10=10^10 timesThe first number is 10^10 times larger
Answer:
1e+16 and 1000000 multiply it then divide...
Step-by-step explanation:
Which equation is the inverse of y = 9x2 – 4?
Answer:
C
Step-by-step explanation:
For edge
Answer:
correct C on e2021
Step-by-step explanation:
Your friend says that 14.5% is same as the fraction 29/200. explain whether your friend is correct or incorrect by comparing the two values
14.5% = 0.145
Step-by-step explanation:
The term 'percent' (%) actually means per 100. So when you say 14.5% it means 14.5 per 100. So when you put that into an equation it actually means:
So when you solve it, 14.5% is actually 0.145 and not 14.5.
Your friend is then incorrect because:
14.5% ≠ 14.5
Answer:
Your friend would be correct. 14.5% divided by 100 is equal to 0.145. When you divide 29/200 you also get 0.145, if you multiply it by 100 you get 14.5%.
7. You bought three erasers and a magazine for $6. You spent a total of $18. How much did
each eraser cost?
Answer:
each eraser cost $4
Step-by-step explanation:
Answer:
$12
Step-by-step explanation:
ONLY DO THE THE ONES THAT HAVE BLUE NEXT TO THEM!!!
Answer:
You need to have an attachment or question for us to help you. :3
Step-by-step explanation:
PLEASE
Solve for x and y by graphing the system of linear equations.
y=-7/2x+3
y=-3/2x-1
Answer:
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).
Step-by-step explanation:
hope its right
If 900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box?
Answer:
1400
Step-by-step explanation:
During a period of 112 minutes, a music station played 40 minutes of commercials. What
is the ratio of music they played to commercials they played?
Answer:
9:5
Step-by-step explanation:
112 - 40 = 72. 112 represents the total time, but you are comparing music to commercials, so you have to subtract the commercial time from the total time.Find the GCF of 72 and 40, which is 8. Divide 72 and 40. The simplified ratio is 9:5.A) -2/3
B) -1/3
C) 1/3
D) 2/3
Answer:
D
Step-by-step explanation:
(0, -3), (6,1) these are the points
Using the slope formula:
1+3/6-0= 4/6=2/3
Thus, it is D
Triangle ABC is congruent to Triangle A’B’C’. Describe a sequence of transformations on triangle ABC that would result in triangle A’B’C’.
Answer:A
Step-by-step explanation:
The triangle ΔABC is rotated 180° about the origin, then the ΔA'B'C' is obtained.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Triangle ABC is congruent to Triangle A’B’C’.
ΔABC ≅ ΔA'B'C'
The triangle ΔABC is rotated 180° about the origin, then the ΔA'B'C' is obtained.
More about the transformation of a point link is given below.
https://brainly.com/question/27224339
#SPJ2