Answer:
[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]
General Formulas and Concepts:
Multivariable Calculus
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]Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle 7z^2 = 8x^2 + 8y^2[/tex]
Step 2: Convert
[Equation] Substitute in Spherical Coordinate Conversions:∴ we have found the given equation in terms of spherical coordinates.
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Topic: Multivariable Calculus
Unit: Triple Integrals Applications
This confuses me, can someone explain it?
there are 500 seventh grade students at heritage middle school. sixty percent of them play a musical instrument. how many seventh grade students play a musical instrument
8-(x+3)=11 solve for x
Which of the following are true of bar graphs?
What is 413,125 rounded to the nearest ten thousand?
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?. .a. y = 2x – 2. b.y = 2x + 2. c.y = x + 2. d. y = x – 2
the equation for a line is y = m x + b
using the first set of coordinates (0,2)
2 = m * 0 + b
b = 2
using the second set of coordinates (4,6)
6 = 4 m + 2
4 m = 4
m = 4 / 4
m = 1
use those numbers into the line equation
y = x +2
Answer is C
Answer:
The equation of line is y = x + 2 .
Option (c) is correct .
Step-by-step explanation:
The equation of line is represented by
[tex](y-y_{1}) = \frac{(y_{2}-y_{1})}{x_{2}-x_{1}} (x-x_{1})[/tex]
As given
Line CD passes through points (0, 2) and (4, 6).
[tex](y-2) = \frac{(6-2)}{4-0}(x-0)[/tex]
[tex](y-2) = \frac{4}{4}(x-0)[/tex]
y -2 = x
y = 2 + x
Therefore the equation of line is y = x + 2 .
Option (c) is correct .
Solve: The quantity 2 x minus 10 divided by 4 = 3x
Using this example, estimate the traffic flow for a roundabout presented below. the graphical model shows the number of cars per hour that are entering or leaving a roundabout. if the portion of the roundabout between a and b has an estimated traffic flow of from 6[e] to 8[a] cars per hour, what is the estimated traffic flow between c and a, and between b and c?
We have three equations that we can use for this problem.
X1 − X3 = 35
X2 − X1 = 50 X3 – X2 = 15 To solve for C and A. We’ll take the first equation and put 23 for X1. X1 − X3 = 35 23 − X3 = 35 −X3 = 35 - 23 −X3 = 12 The estimated traffic flow for C and A is 12 cars per hour. Now, to solve for B and C, we’ll take the second equation and put 23 for X1 as well. X2−X1=50 X2− (23) =50 X2 = 50 + 23 X2 = 73 The estimated traffic flow for B and C is 73 cars per hour.What is the coefficient of the x6y3 term in the expansion of (x + 2y)9?
a)84
b)168
c)336
d)672
The answer is d.) 672
Howard pays $327 for one dozen collector's edition baseball cards. About how much does he pay for each baseball card?
x(7x-3)(x^2+81)=0x (7x-3)(x2+81)=0
What is the sum?
mc003-1.jpg
–20
–4
4
20
the pic is the .jpg
we have that
[tex]8+(-12)[/tex]
eliminate parentesis
[tex]8+(-12)=8-12=-4[/tex]
therefore
the answer is
[tex]-4[/tex]
A and b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by
a.
The probability of the player for final roll is 25%.
Given data:
To find the probability that the final roll is made by player A, we need to consider the possible outcomes of the game. There are two possible scenarios:
Player A rolls a sum of 9 before player B rolls a sum of 6.
Player B rolls a sum of 6 before player A rolls a sum of 9.
Let's calculate the probability for each scenario and determine the probability that the final roll is made by player A.
Scenario 1:
Player A rolls a sum of 9 before player B rolls a sum of 6.
The probability of rolling a sum of 9 with two dice is given by the number of favorable outcomes divided by the total number of possible outcomes.
The number of favorable outcomes for a sum of 9 is 4, as there are four ways to get a sum of 9: (3, 6), (4, 5), (5, 4), and (6, 3).
The total number of possible outcomes when rolling two dice is 36 (6 possible outcomes for each die).
Therefore, the probability of player A rolling a sum of 9 before player B rolls a sum of 6 is 4/36 = 1/9.
Scenario 2:
Player B rolls a sum of 6 before player A rolls a sum of 9.
Similarly, the probability of rolling a sum of 6 with two dice is given by the number of favorable outcomes divided by the total number of possible outcomes.
The number of favorable outcomes for a sum of 6 is 5, as there are five ways to get a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).
Therefore, the probability of player B rolling a sum of 6 before player A rolls a sum of 9 is 5/36.
Now, calculate the probability that the final roll is made by player A by adding the probabilities of both scenarios:
Probability that the final roll is made by player A = Probability of Scenario 1 + Probability of Scenario 2
= 1/9 + 5/36
= 4/36 + 5/36
= 9/36
= 1/4
Hence, the probability that the final roll is made by player A is 1/4 or 25%.
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Write two ways to group and add 4+2+5.
Answer:
We can use the associative property of addition to group the numbers for addition.
Step-by-step explanation:
We are given the following information in the question:
We have to add [tex]4 + 2 + 5[/tex] in two different ways.
Associative property of addition
The associative property states that you can add regardless of how the numbers are grouped. By grouped we mean how we use parenthesis.[tex](a+b)+c = a+(b+c)[/tex]Working:
[tex]4 + 2 + 5[/tex]
[tex](4+2)+5 = 4+(2+5)\\6 + 5 = 4 + 7\\13 =13[/tex]
The associative property allows for different groupings of numbers when adding without affecting the sum, such as (4 + 2) + 5 and 4 + (2 + 5), both resulting in 11.
Explanation:In mathematics, especially when dealing with arithmetic operations like addition, we have the flexibility to group numbers in different ways due to the associative property of addition. This property tells us that the way in which numbers are grouped does not affect the sum. Here's how you can group and add the numbers 4, 2, and 5 in two different ways:
Way #1: Group (4 + 2) + 5 = 6 + 5 = 11Way #2: Group 4 + (2 + 5) = 4 + 7 = 11Both methods give us the same result, which is 11, demonstrating the associative property in action.
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There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. a least-squares fit of some data collected by a biologist gives the model = 25.2 + 3.3x, where x is the number of chirps per minute and is the estimated temperature in degrees fahrenheit. what is the predicted increase in temperature for an increase of 5 chirps per minute?
For an increase of 5 chirps per minute, the predicted increase in temperature is approximately 41.7 degrees Fahrenheit.
What is the predicted increase in temperature for an increase of 5 chirps per minute?In the given linear relationship model, the equation is:
T = 25.2 + 3.3x
Where:
T represents the estimated temperature in degrees Fahrenheit.
x represents the number of chirps per minute.
To find the predicted increase in temperature for an increase of 5 chirps per minute, you can simply plug in the value of x as 5 into the equation:
T = 25.2 + 3.3(5)
Now, calculate the result:
T = 25.2 + 16.5
T = 41.7
So, for an increase of 5 chirps per minute, the predicted increase in temperature is approximately 41.7 degrees Fahrenheit.
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karen sells clothes. after studing her constraints, she knows that she will make $10 profit on each jacket, j, she sells and $6 profit on each shirt, s, she sells. which equation or inequaltiy should she use to show her maximum profit , P?
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A camera televising the opening kickoff of a football game is positioned 5 yards from the east edge of the field and in line with the goal line. The player with the football runs down the east edge of the field (just in bounds) for a touchdown. When he is 10 yards from the goal line, the camera is turning 0.4 rad/sec. How fast is the player running.
I know that the professor wants a diagram with a formula, then you take the derivative of that and plug in your information to find the answer, however, i can not figure out the diagram.
12 yellow balls and 9 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow? a) 0.8333 b) 0.4500 c) 0.5714 d) 0.4762 e) 0.2593 f) None of the abov
A student solved the equation 6s – 10 = 2 + 3s + s and got s = –4. His work shown below is his check for this problem. Which statement best applies to the work shown? A. His check does not work, thus s = –4. B. The work in his check is all correct, thus s = –34. C. The work in his check is all correct, thus s = –4. D. His check does not work, thus
The student's check does not work, thus s = -4. Therefore, the correct statement is A.
Let's evaluate the student's check for the equation 6s - 10 = 2 + 3s + s when s = -4.
Substitute s = -4 into the equation:
6(-4) - 10 = 2 + 3(-4) + (-4)
-24 - 10 = 2 - 12 - 4
-34 = -14
Since [tex]\(-34 \neq -14\)[/tex], the result obtained by the student's check is incorrect.
Therefore, the statement that best applies to the work shown is:
A. His check does not work, thus s = -4.
85 x 63 whoever gets it gets braiest
The table shows the height in feet of several student in mrs. Patel. Class
Answer:
Is there a table that i can help with.
Step-by-step explanation:
True or false. The equation csc^2x-1=cot^2x is an identity.
Answer: true
Step-by-step explanation:
a pe x
Type the integer that makes the following subtraction sentence true:
– 0 = 8
what is the correct math operation to determine the price per ounce (unit price) for the 6-pack of 12-ounce cans priced at $1.69.
you subscribe to m different magazines. your friend subscribes to 2 fewer than you
Jamar is factoring 90x-15. Find his mistake and correct it
Answer: 15(6x - 1)
Step-by-step explanation: Jamar had a great start, by figuring out the factors of both 90 and 15; of which he picked 15.
What he got wrong was failing to do same to the value 15 exactly what he did to 90x.
To put it right, here is how to go about it:
90x - 15
Factor of both 90 and 15 is 15
Therefore:
15 (6x - 1)
This is correct. You can as well expand the result to check.
The correct factorization will be: 15(6x - 1)
Given,
90x-15
Here,
Jamar had a great start, by figuring out the factors of both 90 and 15; of which he picked 15.
What he got wrong was failing to do same to the value 15 exactly what he did to 90x.
To make it correct:
90x - 15
Factor of both 90 and 15 is 15
Therefore:
15 (6x - 1)
Hence the correct factorization is achieved .
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Find the value of sec θ for the point (7,6)
Use the chain rule to find dz/dt. z = xy9 − x2y, x = t2 + 1, y = t2 − 1
The value of dz/dt using the chain rule is [tex]2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
According to chain rule:
[tex]\frac{dz}{dt} = \frac{\delta z}{\delta x} \frac{dx}{dt} + \frac{\delta z}{\delta y} \frac{dy}{dt}[/tex]
Given the following expressions
z = xy⁹ − x²y,
x = t² + 1
y = t² − 1
Get the differentials in the equation
[tex]\delta z/\delta x = y^9-2xy\\dzx/dt = 2t\\\delta z/\delta y =9xy^8-x^2\\dy/dt = 2t[/tex]
Substitute the differentials into the formula
[tex]\frac{dz}{dt} = (y^9-2xy)(2t)+(9xy^8-x^2)(2t)\\\frac{dz}{dt} = 2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
Hence the value of dz/dt using the chain rule is [tex]2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
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what is the prime factorization of 720
Francois baked just enough cookiesto fill all the orders at his bakery. While the cookies were cooling, a kitchen assistant knocked over a cooling rack and spilled 12 percent of the cookies onto the floor. Francois had to bake 36 more cookies to replace them.
How many cookies were ordered in total? And please explain.