Two hot air balloons are traveling along the same path away from a town, beginning from different locations at the same time. Henry's balloon begins 15 miles from the town and is 31 miles from the town after 2 hours. The distance of Tasha's balloon from the town is represented by the function y = 5x + 25. Which balloon was farther from the town at the beginning, and which traveled more quickly?

Q: The assets A of public pension funds (in billions of dollars) can be approximated by the function…

A: x=3 corresponds to 2003.So, 2013 is 3+(2013-2003)= 3+10=13 year

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A: Given  R(x)=400x-0.2x2

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A:

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A:

Q: f(x) = x² + 7x –- 30

A:

Q: The total revenue for Dante's Villas is given as the function R(x)=500x−0.5x2 , where x is the…

A: Given Rx=500x - 0.5x2

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A:

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A:

Q: Differentiate the function, y = 4x² +5 + In (x + 1)

A: Differentiate the given function using the below formulas. ddxxn=nxn-1  ddxC=0        where C is a…

Q: Do f(x) = 2x2 - 1 and h(t) = 2t2 - 1 represent the same function? why or why not

A: The two given functions are

Q: 7) Determine when the function f(x) = 6x - 35x +56x - 20 is positive and when it's negative.

A: The given function is: f(x)=6x3-35x2+56x-20

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A:

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A: The value of China's exports of automobiles and parts (in billions of dollars) is approximately…

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A:

Q: Graph the piecewise function. 2x+3 if x< 0 f (x)%=D if x20

A: The graph is given below

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A:

Q: y = 3Vx – Vx² – 4

A: y = 3x-x2-4we have to find Domain and Range of functionfor Domaindomain of x,  x≥0x2-4 , x2-4≥0…

Q: Two hot air balloons are traveling along the same path away from a town, beginning from different…

A:

Q: Identify the intercepts of the quadratic function from the quadratic below. f (x) = 5 (x +2) (x +…

A: The x-intercepts of a quadratic function is obtained by equating the quadratic to zero.

Q: Differentiate the function.   y = (2x + 4 - 5ex)/4

A: Given function: y=2x+4-5ex4

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A: Note :- Inflexian points of a function can be calculate by putting f"(x) =0 and solve for x.  We get…

Q: Differentiate the function. 2. 8x-1 y = 3 7x +9

A: We can differentiate the function as below

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A:

Q: At what point will f(x) = 2x+1 andf¯1 intersect each other?

A: Topic - functions and inverse function

Q: Checking to see if my answer is correct.

A: Given:

Q: If f(x) = 7x² f'(2) = f''(x) = f''(2) = 8e, find:

A: The given function is fx=7x2-8ex

Q: Graph the function. f(x) --x +3 ifx<2 12x-3 ifx22 %3D -5

A:

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A: Given function f(x) = 4Sec(x)+8.X intercepts of any function are the points where the graph touches…

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A: Given,          The solutions of px=0 are -14 and 11.

Q: When the function f (x) is divided by x + 4, the quotient is 2x2 – 5x – 7 and the remainder is 4.…

A:

Q: Find f(-2), when f(x) = -0.5x + 12

A: Given that f(x) = -0.5x + 12  To find: f(-2)

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A: Given function : f(x) = 0.5x2 -2x -2

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A: The given function is  y = 13x+132

Q: What number of rooms filled produces the maximum revenue?

A: Differentiate the given revenue function and quate it in to zero then solve for x. The. We get the…

Q: State the domain of the function. х-3х+2 а. У- х-4 b. у-4x*+7x?-13х+100 f(x)- V2x-10 С.

A: a. The given function is y=x2-3x+2x-4. It is known that the domain of a function is set of all real…

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately…

A:

Q: Graph the equation f(x) = – 4 by completing a table of values. 4 3 1- -5 -4 -3 -2 -1 2 3 5 -1 -2 -3…

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Q: For the function -a- x3 - 2x?,

A:

Q: Graph the function. 3x-2 if x s 3 2. f(x)= %3D -2x+5 if x >3

A: Given piecewise function, f(x)=3x-2 if x≤3-2x+5 if x&gt;3

Q: Find  f(6). f(x) = 2x3 + 3x -8 f(6) =?

A:

Q: Enter an equation for the line of Symbrietry for the function f(x)=4x2+16X=9

A:

Q: If f (x) = 3x +7, find: f(3) = [ ? ]

A: we have to find f(3)

Q: Describe the end behavior of f (x) = x³ – 4x² + x + 6 -

A:

Q: What is the domain of the function f(x) = 2x – 4?

A: Domain of a function is the possible values of x, which satisfies the function, i.e. we get a value…

Q: At a certain paint factory, the production rate (in gallons per hour) x hours after the factory…

A: Definition used -           Quantity of a substance produced after a hours when the rate of…

Q: Graph the function. -x²+1 for x1 5- 4 2. -4

A:

Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells cans of…

A: Given: P(x)=-0.001x2+3x-1800

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.