The triple integral is equal to ∫∫∫ f(x, y, z) dV using spherical coordinates is equal to 64π/21 .
Use spherical coordinates to evaluate this triple integral over the given region.
The region p < 2 is a sphere centered at the origin with radius 2.
In spherical coordinates, this region can be described by,
0 ≤ ρ ≤ 2
0 ≤ θ ≤ 2π
0 ≤ φ ≤ π
The volume element in spherical coordinates is ρ² sin φ dρ dφ dθ.
The triple integral can be written as,
∫∫∫ f(x, y, z) dV
= [tex]\int_{0}^{2}\int_{0}^{\pi}\int_{0}^{2\pi }[/tex] (ρ² sin φ)(ρ⁴ sin²φ cos²θ sin²θ) dρ dφ dθ
= [tex]\int_{0}^{2}\int_{0}^{\pi}\int_{0}^{2\pi }[/tex] (ρ⁶ sin³φ cos²θ sin⁵ θ) dρ dφ dθ
= [tex]\int_{0}^{2}[/tex](ρ⁶/7) [tex]\int_{0}^{\pi }[/tex] (sin³ φ) [tex]\int_{0}^{2\pi }[/tex] (cos² θ sin⁵θ) dθ dφ dρ
The innermost integral evaluates to π/8.
The second integral can be evaluated using the substitution u = cos φ, du = -sin φ dφ, which gives,
[tex]\int_{0}^{\pi }[/tex](sin³ φ) dφ
= -[tex]\int_{1}^{-1}[/tex](1-u²) du
= 4/3
The outer integral evaluates to (2⁷)/7.
Triple integral is equal to
∫∫∫ f(x, y, z) dV
= (2⁷/7) (4/3) (π/8)
= (32/7)π/6
= 64π/21
Therefore, the triple integral is equal to ∫∫∫ f(x, y, z) dV = 64π/21 .
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Caraline wants to compare the expression's -15-9 and 9-(-15) to determine which result is greater.How cab she do this without finding the value of rach difference? Explain your reasoning.
Answer:
9-(-15)
Step-by-step explanation:
because it would be changed to 9+15
radius:
diameter:32 meters
circumference:
area:
Given diameter is 32, radius would be 16 bc radius is always half of diameter, and circumference would be 2(pi)*radius, which would be 100.5309649.... and area is (pi)*radius^2 which would be 804.2477193........
I need this answered in 5 minutes!
Answer:
Step-by-step explanation:
a.19*5= 95
b.65*5= 325
c. 0*5=0
if my anwser helps please mark as brianliest.
Find the value of x. Round your answer to the nearest whole degree.
Answer:
68°
Step-by-step explanation:
arctan(x) = 5/2
Help please this is due in 10 minutes pleaseee I will mark you brainliest
Mori is building a cage for his pet guinea pig. The bottom is 8 inches
long and 8 inches wide. How big is the bottom of the cage?
[tex]area = lw[/tex]
[tex]area = (8)(8)[/tex]
[tex]area = 64 \: {inches}^{2} [/tex]
//
[tex]perimeter = 2(l) + 2(w)[/tex]
[tex]perimeter = 2(8) + 2(8)[/tex]
[tex]perimeter = 32 \: inches[/tex]
Ander makes a scale drawing of a tower. He uses scale of ' 1 cm represents 5 m. The tower in real life is 125 m high. How high is the tower on the scale drawing?
Answer:
25 cm
Step-by-step explanation:
125/5 = 25
hope this helped?
Please help!!!
Its an emergency
Answer: A
Step-by-step explanation:
The line 'd' separates the square into two triangles. Since the side lengths are equal, the angle is 45°. We need the line separating the two 90° angles, that I am going to define as 'z'. We can use the sine function.
[tex]\sin(45)=\frac{z}{5\sqrt{2} }[/tex]
z = 5
To solve for x, we can use sine again but for the 30 degree angle.
[tex]\sin(30)=\frac{5}{x} \\x=10[/tex]
Answer:
x=10
Step-by-step explanation:
The middle triangle has d as the hypotenuse and is an isosceles right triangle. The sides of such a triangle are in the ratio of y, y, and [tex]\sqrt{2}y[/tex].
For this triangle
[tex]\sqrt{2}y=5\sqrt{2}[/tex]
so y=5.
Tthe triangle on the right is a 30, 60, 90 triangle with sides in the ratio of
y, [tex]\sqrt{3}y[/tex], and 2y. So
2y=x=10
what is 2345653445353453463635746 divided by 34174182746542
Answer:
6.86381724×10 to the 10th power
Step-by-step explanation:
Philippe will read One-half of the number of pages that Rafael reads. How many pages will Rafael read?
Answer:
He will read 1/2 more than Philippe
Step-by-step explanation:This will be because is Rafael reads 1/2 and Philippe reads 1/2 of that it would still be 1/2
An item with an original price of p dollars is on sale at a 35% discount. Write an
expression that is equivalent to the price of the item with the discount.
Answer:
Step-by-step explanation:
Your answer
X =0.35 p
Mark it as Brainlist. Follow me for more answer.
ALGEBRA 15 POINTS please help will give 15 points
Answer:
angle FEX is 105
Step-by-step explanation:
x=30 just plug that in and check(i already did but if u want to u can do it too).
evaluate 4a + b2 for a = 4 b=3
Answer:
22
Step-by-step explanation:
We substitute the numbers for the letters to get 4*4 + 3*2 and then we multiply. 16 + 6 which equals 22. I hope this helps and please mark brainliest!
Answer:
22
Step-by-step explanation:
4a + b2
4(4) + (3)2
4 x 4 = 16
3 x 2 = 6
16 + 6 =
22
Expand- 2.5( - 3+ 4n + 8)
Answer:
10n + 12.5
Step-by-step explanation:
Find the two whole numbers that are the closest to √42. Explain your reasoning
The two whole numbers that are the closest to √42 are 6 and 7.
The given number is √42.
What is the square root of a number?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
The square root of √42 =6.48
The two whole numbers that are the closest to √42 are 6 and 7.
Therefore, the two whole numbers that are the closest to √42 are 6 and 7.
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Find the area of the figure below. 7 cm
Answer:
Area tells us the size of a shape or figure. It tells us the size ... The rectangle above has an area of 15 square units. The area of a ... Area = 7 cm x 6 cm = 42 cm2.
Step-by-step explanation:
Find the mean,median,mode, and range:5,2,5,2
Answer:
Mean = 3.5
Median = 3.5
Mode = 5, 2
Step-by-step explanation:
Hope that helps!
Mean: To find the mean, simply add the numbers together and divide by the amount of numbers in the set:
Mean: (5 + 2 + 5 + 2)/4
= (14)/4
= 3.5
Mean = 3.5
Median: To find the median, simply order from least to greatest, and find the middle number in the set. That is your median. In the case of an even amount of numbers in the set, find the mean with the two median numbers (as in this case):
Median: (2 + 5)/2
= 7/2
= 3.5
Median: 3.5
Mode: The Mode is the number that shows up the most frequently. As both given numbers show up the same amount of times (twice), there is no mode.
Mode: None.
Range: The Range is found by subtracting the greatest number with the least number:
5 - 2 = 3
Range: 3
Having trouble solving this
opt1.
667/1000
=66.7
hope u understand
Answer:
more like dividing the up ones with bottom ones
EX 717/1000=0.717
Question 4 (3 points)
What is the sum of the angle measures in this shape?
degrees
(I have to fill in the blank, please hurry I’ll give brainliest!!)
The sum of the angles in a triangle is 180°, If I remember correctly.
If your wages vary directly with how many hours you babysit, write the constant of
proportionality equation when w = 60 and h = 6.
W = wages
H = hours babysat
OPTIONS!!
1. W=1/10h
2. W=10H
3. H=10W
4. Y=1/10x
When I...
double my number ...
subtract six ...
take the square root and
add four
I get eight.
My number is:
Answer:
11
Step-by-step explanation:
Work backwards and reverse the operations to find the original number.
Reverse the operations for add four: 8 - 4 = 4
Reverse the operations for take the square root: 4² = 16
Reverse the operations for subtract six: 16 + 6 = 22
Reverse the operations for double the number: 22 ÷ 2 = 11
Please help!!!
I am failing math!!
Algebra 1
Answer:
Wouldnt the answer be "D"
Since it's negative number and multiplied
But still not sure.
2x - 5[4 + 3 (x + 2)] = 9
Step-by-step explanation:
i hope you will get the answer
Step-by-step explanation:
2x - 5 ( 4 + 3 ( x + 2 ) ) = 92x - 5 ( 4 + 3x + 6 ) = 92x - 5 ( 3x + 10 ) = 92x - 15x - 50 = 9-13x - 50 = 9-50 - 9 = 13x-59/13 = xMARK ME AS BRAINLISTx²+8x-84=0
Formúla General
Answer:
[tex]x_{1} =-14\\\\x_{2} =6[/tex]
Step-by-step explanation:
[tex]x^{2} +8x-84=0\\\\x=\dfrac{-b \pm \sqrt{b^{2}-4ac } }{2a} \\\\a=1; \: \: b=8; \: \: c=-84\\\\x=\dfrac{-8 \pm \sqrt{8^{2}-4 \cdot 1 \cdot (-84) } }{2 \cdot 1}=\dfrac{-8 \pm \sqrt{400 } }{2}=\dfrac{-8 \pm20}{2} =-4 \pm 10\\\\x_{1} =-14\\\\x_{2} =6[/tex]
QUESTIONS ARE DOWN BELOW!!! ALL HELP WILL BE APPRECIATED AND I WILL TRY TO MARK BRAINLIEST (IF I CAN)
Answer: 90 and 110
Step-by-step explanation:
plz help, just look at the picture
Answer:
<2, <3, <4
Step-by-step explanation:
You have parallel lines cut by a transversal, so alternate interior angles are congruent. Also, alternate exterior angles are congruent. Corresponding angles are congruent.
Vertical angles are always congruent.
I'll write each congruent angle and the reason.
<2, vertical
<3, corresponding
<4, alternate exterior angle
#every one when im in public be like
Answer:
lol
Step-by-step explanation:
Choose the answer that best represents the situation described below. George is climbing a mountain. He knows that the higher the mountain, the more time the climb will take.
A. The time to climb the mountain is a function of climbing speed.
B. The height of the mountain is a function of climbing speed.
C. The time to climb in the function of its height.
Can someone help me find the area of this ? If you can thank you so much , it's been awhile since I've done it
Answer:
185
Step-by-step explanation:
Hope this helps
iki sayının oranı 5/8 dir bu iki sayının farkı 24 olduğuna göre toplamı kaçtır
Answer:
x = -40 and y = -64
Step-by-step explanation:
The ratio of the two numbers is 5/8, since the difference of these two numbers is 24, what is the sum
Let two numbers be x and y.
ATQ,
x-y = 24 ..(1)
and
[tex]\dfrac{x}{y}=\dfrac{5}{8}[/tex]
or
8x-5y =0 ...(2)
Multiply equation (1) by 8.
8x-8y = 192 ...(3)
Subtract equation (3) from (2).
8x-5y -(8x-8y) = 0-192
-5y+8y = -192
3y = -192
y = -64
Put the value of y in equation (1).
x-(-64) = 24
x+64 = 24
x = -64+24
x = -40
So, the values of x and y are -40 and -64 respectively.