Use spherical coordinates. evaluate (9 − x2 − y2) dv, where h is the solid hemisphere x2 + y2 + z2 ≤ 4, z ≥ 0.
To solve the given task, change the Cartesian coordinates into spherical coordinates. Rewrite the integrand and the solid hemisphere limits according to these new variables. Evaluate the final triple integral using standard techniques.
Explanation:To solve the given problem, the first step is to convert the Cartesian coordinates into spherical coordinates. In spherical coordinates, a point in three dimensions is represented by three parameters: ρ (rho) for the radial distance, θ (theta) for the azimuthal angle, and φ (phi) for the polar angle.
Here, given x² + y² + z² ≤ 4, z ≥ 0, the given region corresponds to a solid hemisphere centered at the origin and radius 2 in spherical coordinates, goes as 0 ≤ ρ ≤ 2, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ π/2. Our spherical coordinates are x = ρsin(φ)cos(θ), y = ρsin(φ)sin(θ), and z = ρcos(φ).
Then, rewrite the integrand using spherical coordinates, (9 - x² - y²) becomes (9 - ρ²sin²(φ)) and dv becomes ρ²sin(φ)dρdφdθ.
The final integral that needs to be evaluated will read: ∫₀^2 ∫₀^π/2 ∫₀^2π (9 - ρ²sin²(φ))ρ²sin(φ) dθ dφ dρ. This is a triple integral in spherical coordinates that you can now solve using standard integration techniques.
Learn more about Spherical Coordinates here:https://brainly.com/question/31745830
#SPJ3
Can someone please answer this?
Which is the equation of the line with slope 5 that contains point (-2, -3)
A. y + 2 = 5(x – 3) B. y + 3 = 5(x + 2) C. y – 3 = 5(x – 2) D. y – 2 = 5(x – 3)
The answer is y = 5x + 7
here's how you get it:
Start with the base y = mx + b
then imput the points and the slope:
-3 = 5 ( -2 ) + b
Then solve for b
-3 = 5 ( -2 ) + b
-3 = -10 + b
-b = -7
b = 7
so the equation is:
y = 5x + 7
14,000 acres of 40,000 acre forest burned in a forest fire. What percentage of the forest was damaged?
if f(x)=3/x+2 -√x-3, complete the following statement (round your answer to the nearest hundredth) f(7)=
The given function [tex]f(x) = \dfrac{ 3}{x + 2} -\sqrt{x-3}[/tex] The value of f(7) would be -1.67.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
The given function
[tex]f(x) = \dfrac{ 3}{x + 2} -\sqrt{x-3}[/tex]
By substitute x = 7 to find f(7)
[tex]f(7) = \dfrac{ 3}{7 + 2} -\sqrt{7-3}\\\\f(7) = \dfrac{ 3}{9} -\sqrt{4}\\\\f(7) = \dfrac{ 1}{3} -2\\\\f(7) = \dfrac{ 1 - 6}{3}\\\\f(7) = \dfrac{ -5}{3}\\[/tex]
f(7)= -5/3 = -1.67
Learn more about function here:
https://brainly.com/question/2253924
#SPJ2
find the values of x between 0 and 2pi where the tangent line to the graph of y=sinxcosx is horizontal.
what is the measures in degrees and radians of the angle representing 7-8th of a circle
Expand the fraction 72/125 .so that it has a denominator of 1000.
EASY 5 POINTS!!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?
formula for volume of a sphere is V=4/3 x pi x R63
if diameter = 16 than radius = 16/2 = 8
so the equation would be 4/3 x pi x 8^3
Simplify (7x+42)/(x^2+13x+42)
The simplified expression is given by:
[tex]\dfrac{7}{x+7}[/tex]
Step-by-step explanation:We are asked to simplify the expression which is given in terms of variable x as:
[tex]=\dfrac{7x+42}{x^2+13x+42}[/tex]
The given expression is a rational expression as it is a polynomial expression in the denominator as well as in the numerator.
Now we know that:
[tex]7x+42=7(x+6)[/tex]
and
[tex]x^2+13x+42=x^2+7x+6x+42\\\\\\i.e.\\\\\\x^2+13x+42=x(x+7)+6(x+7)\\\\\\i.e.\\\\\\x^2+13x+42=(x+7)(x+6)[/tex]
Hence, we get:
[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{(x+6)(x+7)}\\\\\\i.e.\\\\\\\dfrac{7x+42}{x^2+13x+42}=\dfrac{7}{x+7}[/tex]
Hence, the simplified expression is:
[tex]\dfrac{7}{x+7}[/tex]
what value in place of the question mark makes the polynomial below a perfect square trinomial? 9x2+?x+49
the missing number should be the square root of the last number times 2 for a perfect trinomial
so square root of 49 = 7
7*2 =14
so the missing number should be 14
Which of the following is not an appropriate method of proving triangles congruent a) AAA b)SSS c) AAS D) SAS
Answer:
a) AAA.
Step-by-step explanation:
Triangles which are of the same shape and size are called congruent triangles. Triangles of same shape are similar triangles.
Two triangles can be proved congruent by SSS ,SAS AAS ,ASA ,HL postulates.
Two triangles can be proved similar by AAA method.
All congruent triangles are similar but all similar triangles are not congruent.
Hence option a) AAA is not an appropriate method of proving triangles congruent.
Which of theses numbers is the smallest 0.02, 0.24, 0.11, 0, 2
A bicycle store costs $2,400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?
Simplify: 20 sin(2x) cos(2x)
To simplify 20 sin(2x) cos(2x), apply the double-angle trigonometric identities for sine and cosine.
The given expression: 20 sin(2x) cos(2x) can be simplified using the double-angle trigonometric identity for sine and cosine.
Apply the identities sin(2x) = 2sin(x)cos(x) and cos(2x) = cos²(x) - sin²(x).Substitute these identities into the expression and simplify to get the final result.A pea seller had some peas. He sold 40% of his stock and still had 420 peas. Originally, he had how many peas?
100-40= 60%
60% = 0.60
420/0.60 = 700
he had 700 peas
100 - 99 + 98 - 97 + 96 ect formula
20 friends and 12 invations are left how many has she mailed
20-12 8
She has mailed 8 invitations.
Car cost $40000 it depreciates 12% each year. What is the cars value in 5yrs
Find m2, if m6 = 57° and m7 = 23°.
Final answer:
To find m2, subtract m6 from 180 degrees.
Explanation:
To find m2 in this problem, we can use the fact that angles in a triangle sum up to 180 degrees. We know that m6 = 57° and m7 = 23°.
First, we can find m1 by subtracting m7 from 180 degrees: m1 = 180° - 23° = 157°.
Next, we can find m2 by subtracting m6 from 180 degrees: m2 = 180° - 57° = 123°. Therefore, m2 is equal to 123 degrees.
How many times do you need to divide by ten to get from 5947.7 to 5.9477 ?
A new cruise ship line just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean Paradise.
The Caribbean Paradise has 29 more than the Pacific Paradise. The Mediterranean Paradise has 30 fewer deluxe staterooms than twice the number of deluxe staterooms on the Pacific Paradise. Find the number of deluxe staterooms for each of the ships if the total of deluxe staterooms for the total of the three ships is 719.
To find the number of deluxe staterooms for each of the three ships, we can set up and solve an equation based on the given information.
Explanation:Let's represent the number of deluxe staterooms on the Pacific Paradise ship as x.
The number of deluxe staterooms on the Caribbean Paradise is 29 more than the Pacific Paradise, so it can be represented as x + 29.
The number of deluxe staterooms on the Mediterranean Paradise is 30 fewer than twice the number of deluxe staterooms on the Pacific Paradise, so it can be represented as 2x - 30.
We can form an equation with the sum of the deluxe staterooms on all three ships: x + (x + 29) + (2x - 30) = 719.
Simplifying the equation gives us 4x - 1 = 719.
By adding 1 to both sides and dividing by 4, we can find the value of x which represents the number of deluxe staterooms on the Pacific Paradise ship.
Finally, we can substitute the value of x into the expressions for the other two ships to find their number of deluxe staterooms.
Learn more about Finding the number of deluxe staterooms on three cruise ships here:https://brainly.com/question/305669
#SPJ2
The distance between points
An indoor staircase has a 6 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 44 degrees and there are 15 feet of horizontal space total for each of the landings combined, answer the following questions showing each step of your work: a) What is the landing space per step (in inches, rounded to the nearest tenth of an inch)?
Professor whata guy surveyed a random sample of 420 statistics students. one of the questions was, "will you take another mathematics class?" the results showed that 252 of the students said yes. what is the sample proportion, p, of students who saud they would take another math class?
The sample proportion, p, of students who said they would take another math class, p = 0.6 or 60%.
To determine the sample proportion, p, you can use the following formula:
p = x/nwhere:
x is the number of students who said yes (successes).n is the total number of students surveyed.From the question,
x = 252n = 420Substituting these values into the formula gives:
p = 252 / 420 = 0.6
Therefore, the sample proportion of students who said they would take another math class is 0.6 or 60%.
Find the exact value of cos 105°.
A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Another way to state the transformation is D. R0, 360°
Calculations and Parameters
Given that the rotation is:
(x,y) --------> (x,y)
This shows that it goes back to its original position and there is a full rotation occurred.
Based on its full rotation to 360°, it can be noted that option D is another way to state the transformation as other given rotations would give different translations.
Read more about transformations here:
https://brainly.com/question/1961977
#SPJ6
Answer: I can confirm it’s D Ro, 360°
Step-by-step explanation:
For football tryouts at a local school, 12 coaches and 42 players will split into groups. Each group have the same number of coaches and players. What is the greatest number of groups that can be formed? How many coaches and players will be in each of these groups?
Many practical applications require calculations of area. some of these calculations are straightforward, but others are more difficult, and it turns out that the idea of the definite integral can help us with the more difficult cases. let’s start with some familiar shapes. what is the area of a rectangle of length l and width w? express your answer in terms of l and w.
The area of a rectangle with length l and width w is given by the product l * w.
what is the area of a rectangle of length l and width w?The area of a rectangle is calculated by multiplying its length (l) by its width (w).
Therefore, the area (A) of a rectangle can be expressed as:
A = l * w
So, the area of a rectangle with length l and width w is given by the product l * w.
Read on area on https://brainly.com/question/25292087
#SPJ3
The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8