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1. An endpoint of the minor axis is at (– 1, – 10), a vertex is at (– 14, 2), ...

t (4, 2). Find the equation of the ellipse in standard form.

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certain objects. So in this case, I derived a log spiral equation in polar coordinates to model an spiral galaxy. I plan on finding the area as well as volume of the galaxy using the function which I have derived. So is there any way, I could integrate these spiral functions to find area?

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y: When income is $1000, the expenditure on consumer goods is $800. Whenever income increases by 100, the expenditure on consumer goods increases by 80.
(a) find the slope of the consumption function
(b) find the equation of the consumption function
(c) find the consumption when income is $7000
Question 8 options:
i)
(a) m = 4/5
(b) c(I) = (4/5) I + 80
(c) 5680
ii)
(a) m = 4/5
(b) c(I) = (4/5) I + 880
(c) 5660
iii)
(a) m = -4/5
(b) c(I) = -(4/5) I + 800
(c) 600
iv)
(a) m = 4/5
(b) c(I) = (4/5) I + 7000
(c) 7600
v)
(a) m = 4/5
(b) c(I) = (4/5) I + 0
(c) 5600

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4.At a price of $1.04 per roll, the supply of toilet paper in a large town is 25,000 rolls, and ...

mand is 18,200 rolls. When the demand increases to 26,200 rolls, the supply is 20,000 and the price is $1.24 per roll. Let x be the quantity in thousands of rolls. The table below gives the price-supply and price-demand equations.
Price Equations for Toilet Paper
Type Equation
Price-Supply P = -0.04x + 2.04
Price-Demand P = 0.025x + 1.495
QUESTION 1
Find the supply at a price of $2 per roll.
1000 rolls
10,000 rolls
1 roll
5000 rolls
QUESTION 2
Find the demand at a price of $2 per roll.
20.2 rolls
202 rolls
20,200 rolls
500 rolls
QUESTION 3
Use the substitution method to find the equilibrium quantity. Round x to the nearest tenth first and then convert to thousands. Include the units in your answer.
QUESTION 4
What is the equilibrium price? Write the answer in dollars and cents, rounding to the nearest cent.

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le above gives values of the functions and their first derivatives as selected values of x. The function h is given by the equation h(x) = f(g(x))-6
b) find the rate of change of h for the interval 1>x>3. Graph in picture

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ble above gives values of the functions and their first derivatives as selected values of x. The function h is given by the equation h(x) = f(g(x))-6
a) find h’(3)
b) find the rate of change of h for the interval 1>x>3.
Graph in picture

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terms of a and b.
(ii) Explain why a ≠ -3/4b '
(
b) A cylinder has a length equal to 3 times its diameter. Find the total area of the
cylinder as a function of its radius.

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countered (unidirectional flow or parallel flow). The planer walls and the fluids are initially at rest. Lower plate moves to left and upper plate to right. Let the fluids be an oil, where kinematic viscosity (ν) = 2.17 x 10-4m2/s and the distance between both plate (h) is 10 mm. U0 = 0.4 m/s I need to find the governing equation, boundary conditions, initial conditions and to derive velocity distribution in steady state.
Also, Use FTCS explicit method to calculate the velocity distribution as a function of time by implementing these governing equation in Matlab

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e form. (3.-5) (9.-13). I’ve found the slope I believe, it’s -4/3. I don’t know what to do now

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rts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each graph with its equation. Use the following
equations to assist with this assignment.
• The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time it t, and 0 h is the initial height is
2
0 ht t h ( ) 16 =− + .
• The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity
in feet per second is 2
0 0 ht t vt h ( ) 16 =− + + .
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
Task 1
First, conduct some research to help you with later portions of this portfolio
assessment.
• Find a local building and estimate its height. How tall do you think the
building is?
• Use the Internet to find some initial velocities for different types of fireworks.
What are some of the initial velocities that you found?
Task 2
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below.
a. How long will it take the tool to fall to the ground? (Hint: use the first
equation that you were given above, 2
0 ht t h ( ) 16 =− + . For the building’s
height, use the height of the building that you estimated in Task 1.)
b. Draw a graph that represents the path of this tool falling to the
ground. Be sure to label your axes with a title and a scale. Your graph
should show the height of the tool, h, after t seconds have passed.
Label this line “Tool”.

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11.1. Suppose that X0 =100. (a) Find (by hand) the next four terms of the difference equation ...

d by Xn+1 = 2.5Xn + 3n. In other words, find X1, X2, X3 and X4. (Note: Show all of your work. You may enter this difference equation and initial value in your calculator to confirm that you did the calculations correctly.)

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44t, where t is the time in seconds. Find the average rate of change in the height of the firework from when it reaches the maximum height until when it reaches the ground.

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on of the parabola in vertex form ‘passes through (13,8) and has a vertex of (3,2)’”and “Write an equation of the parabola in intercept form ‘x-intercepts of 12 and -6; passes through (14,4)

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Use your result in (a) to solve the system:
■(x&+2y&+z&=1@x&y&+2z&=2@x&+y&+2z&=3)
Question#2 (5) (modified from #13 p. 102 in your book)
Solve the matrix equation for X
X[■(1&1&1@1&2&0)]=[■(1&1&1@3&4&2)]
Question#3 (5) (modified from #9 p. 102 in your book) Let
[■(a&0&b&2@0&a&3&6@0&a&b&c+2)] be the augmented matrix of a linear system.
Find for what values of a,b,c the system has:
(i) a unique solution
(ii) a one-parameter solution
(iii) a two-parameter solution
iv) no solution
Question#4 (7) Write the matrix A=[■(-1&1&-1@1&1&-1@1&-1&2)] as a product of elementary matrices
Question#5 (3) Find the determinant by any method:
|■(0&-1&0&0&1@1&1&1&3&1@1&2&3&1&2@1&-1&0&3&1@1&-1&1&0&1)|
Question#6 (3-2)Given thissystem:
■(x_1&+2x_2&+x_3&=1@x_1&-〖3x〗_2&+0x_3&=2@x_1&+0x_2&+2x_3&=3)
a) Use Cramer’s method to solve for x_1 only
b) Solve for the other variables by any method.

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seen an equation of a circle this is moved in both the x and y direction be converted to a polar equation.
For example, I know that the equation of a circle x^(2)+(y-2)^(2)=4 is r=4sin(theta) when converted to polar. Same thing for a translation with the x variable. However, I have never seen, nor do I know how to do, a conversion of a circle with both translations. For example, converting this equation of a circle to a polar equation: (x+3)^(2)+(y-4)^(2)=4. I have no idea how to do such a thing and cannot find any examples of such.
Hope you can shed some light on this, Thanks.

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19.Find an equation of the line passing through the pair of points. Write the equation in the form Ax + ...

By = C. (7,8), (6,-5)

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20.There are so many formulas we use in our stats course. I had a tutor explain a problem to me ...

ad the computer software we use explain a different way on how to calculate the answer. I have to find the regression equation. I believe that the equation is y=ax+b, or intercept + slope. Please correct me if I am wrong
My final answer was y= 57.598+0.607

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l unemployment rate dropped to about 4%.
Find the average decline/year in unemployment rate from 2010 to 2018.
Let x be the year since 2010 and y be the unemployment rate. Write an equation for unemployment rate versus year.
Use your equation to estimate the unemployment rate in 2020.

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ed in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, a (measured in billions of miles), that the planet is from the Sun.
A) Use Uranus’s time of 84 and mean distance of 1.784 billion miles, find the equation relating T and a.
B) Use the result from part a. to determine the time required for Pluto to orbit the Sun if its mean distance is 3.67 billion miles.

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ed in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, a (measured in billions of miles), that the planet is from the Sun.
A) Use Uranus’s time of 84 and mean distance of 1.784 billion miles, find the equation relating T and a.
B) Use the result from part A. to determine the time required for Pluto to orbit the Sun if its mean distance is 3.67 billion miles.

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t (-7,-1). Find the equation of the line.

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ned online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 130 and a y-intercept of negative 363. Complete parts (a) and (b) below.
a. What is the equation of the regression line? Select the correct choice below and fill in the answer boxes to complete your choice.

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26.hello sir I have a doubt in 3D geometry. day after tomorrow is my math board exam please help. the ...

uestion is how to find equation of a plan passing through A point (1,1,1) and containinig the line r=(-3i+j+5k)+α(3i-j-5k) . Please help me

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27.Must know how to use TI 84 Plus CE calculator and be able to teach that skill without wasting time, ...

or give some complimentary/bonus time while you figure it out, or figure out how to do particular things between sessions instead of during the session
Current topics: understand slope and y-intercept and be able to apply it to equations written using different letters instead of m and b or instead of y and x; parallel, perpendicular line equations; calculate slope/gradient of graphs/sides of shapes/equations; calculate midpoint; calculate distance between two points on a graph; find the equation of a line given a graph or given 2 points; learn the meanings of symbols such as R for real numbers, Z for integers' calculate area of a triangle on a graph
The student is in Kazakhstan and speaks Russian and Kazakh fluently, but is intermediate in English. Please speak with her in English as much as possible, but knowing Russian or Kazakh would be a good bonus that would make you preferable to other tutors all else being about the same, though familiarity with TI calculators or the ability to figure them out is also very important.

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28.2. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value ...

s of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
5. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
9. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
22. What is the greatest value of c for which the roots of the equation x^2 + 4x + c = 0 are real?
24. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
7, 24 and 25
A._________________ (smaller value)
B._________________ (larger value)

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29. 1. What is the greatest value of c for which the roots of the equation x^2 + 4x + ...

2. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
A._______________________ (Smaller Value)
B. _______________________ (Larger Value)
3. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
4. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
5. If 8 ounces of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
6. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value of x?

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that models profit earned is D = n(54 – n) – 10n. I need to find the vertex of this equation, and what does the vertex tell me about this situation.. For what x-values is the function increasing? Decreasing? What does this mean in terms of daily profit for Water World? Rewrite the function in vertex form. . Solve the equation 0 = n(54 – n) – 10n for n. Describe your solution method. How are the solutions from part (e) related to the graph of this function? Are the solutions real or complex? How do you know? What do the solutions from part (e) tell you about this situation?

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31.13) Ten people from a local youth group went to Ozark Outdoors Resort to go on a one-day raft trip. ...

The
fees for the trip included a guide's fee as well as charge of $35 per person. The total cost for the
group was $425. a) Write an equation in slope-intercept form to find the total cost C for p people. b) How much would it cost for

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics