Questions on Algebra: Conic sections - ellipse, parabola, hyperbola answered by real tutors!

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Question 1194579: The sketch shows the graph of a function f, which is a straight line defined by y = mx +k such that the point
V lies on the line, and the graph of a function g, which is a parabola with vertex R.
The straight line and parabola intersect at P and Q. The points S and T lie on the parabola and straight line,
respectively, between P and Q. The line ST is parallel to the y-axis.
Find the equation of the parabola
P.S I can email the graph.
Click here to see answer by Alan3354(69443)

Question 1194611: A printing shop makes bumper stickers for cars. Whether
orders 𝑥 stickers (in thousands), where 𝑥 ≤ 10 so the price for each
decal is “0.15 −
𝑥
100
" Suns. Find an expression for Revenue as a function
of the number of decals sold, and their respective domain. What kind of function is it
income function? Also, find the revenue when 3,000 stickers are sold.
Click here to see answer by ikleyn(52795)

Question 1194610:
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Question 1194609:
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Question 1194626: Consider the function 𝑓(𝑥) = (x^2+4)√9−𝑥^2/𝑥^3−1, determine functions 𝑔, ℎ and 𝑖, such that 𝑓(𝑥) = 𝑔(𝑥)ℎ(𝑥)𝑖(𝑥)
And find the domain of 𝑓 using the equation
𝐷𝑜𝑚(𝑓) = 𝐷𝑜𝑚(𝑔) ∩ 𝐷𝑜𝑚(ℎ) ∩ 𝐷𝑜𝑚(𝑖)
Click here to see answer by greenestamps(13200)

Question 1194638: A satellite follows an elliptical orbit around the earth such that the center of the earth is one of the foci. The farthest point that the satellite will be from the earth’s surface is 2500 miles and the closest will be 1000 miles. Use 4000 miles as the radius of the earth and find the equation of the orbit of the satellite.
Answering this question would mean a lot to me. Thank you in advance!
Click here to see answer by ikleyn(52795)

Question 1194678: What is the equation that represents an ellipse with foci at (3, 2) and ( - 9, 2) that passes through the point ( - 3, 10)? Show all steps and provide the answer (the ellipse's equation).

Click here to see answer by ikleyn(52795)

Question 1194738: Write the equation of the hyperbola with a center at (4, -1), transverse axis is parallel to the y-axis, distance between the foci is 10, one endpoint of the conjugate axis is at (6, -1).
Answering this question would mean a lot to me, thanks!!
Click here to see answer by MathLover1(20850)

Question 1194749: Find the equation of the hyperbola with vertices at (-1, -1) and (3, -1) and an equation of asymptote (x−1)/2 = (y+1)/3
I'm still struggling to answer this kind of problem. Your answer would help me a lot. Thank you in advance!
Click here to see answer by MathLover1(20850)

Question 1194765: Find the equation of the hyperbola with vertices at (-1, -1) and (3, -1) and an equation of asymptote (𝑥−1)/2=(𝑦+1)/3
Click here to see answer by MathLover1(20850)

Question 1194818: Given the functions 𝑓(𝑥) = √25 − 𝑥 , 𝑔(𝑥) = 𝑥^2+ 9 , ℎ(𝑥) = √𝑥 − 5
a) Obtain the domains of each given function.
b) Calculate the domain and rule of ℎ ∘ 𝑔 .
c) Calculate the domain of 𝑔 ∘ 𝑓 .
Click here to see answer by MathLover1(20850)

Question 1194815: Let 𝑓 = {(3, 8), (2, 5), (4, −5), (9, 3 )} and 𝑔 = {(9, 2), (−5, 3), (5, 9 ), (8; 10), (1; 9)}. Determine the
compositions (𝑓 ∘ 𝑔) and (𝑔 ∘ 𝑓) if they exist.
1) (𝑓 ∘ 𝑔)
2) (𝑔 ∘ 𝑓)
Click here to see answer by math_tutor2020(3817)

Question 1194819: Determine analytically, if the function 𝑓, whose correspondence rule is 𝑓(𝑥) = 𝑥^3
is
injective
Click here to see answer by MathLover1(20850)

Question 1194819: Determine analytically, if the function 𝑓, whose correspondence rule is 𝑓(𝑥) = 𝑥^3
is
injective
Click here to see answer by ikleyn(52795)

Question 1194816: Let 𝑓(𝑥) = 2(4𝑥 + 1) + 3(𝑥 − 2) − 1. Determine:
1) 𝑓(3) + 𝑓(2)
2) 𝑓^-1(6) − 𝑓^-1(−5)
3) 𝑓^-1(17) + 𝑓(17)
Click here to see answer by josgarithmetic(39618)

Question 1194831: A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 308 people over the age of 55, 77 dream in black and white, and among 315 people under the age of 25, 15 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.

Click here to see answer by ikleyn(52795)

Question 1194817: Given the functions
𝑓(𝑥) = 2𝑥 − 1 , 𝑥 ∈ ]1; 10[ ,
𝑔(𝑥) = 3𝑥 + 1 , 𝑥 ∈ ]−1; two[ .
Calculate the domain
and the correspondence rule of
a) 𝑓 ∘ 𝑔
b) 𝑔 ∘ f
Click here to see answer by Edwin McCravy(20056)

Question 1194857: Determine the correspondence rule of (𝑓 ∘ 𝑔) and (𝑔 ∘ 𝑓), where 𝑓(𝑥) = 6𝑥^2 and 𝑔(𝑥) = 14𝑥 + 4, are the results equal?
Click here to see answer by MathLover1(20850)

Question 1194862: Let 𝑓 be the function with correspondence rule 𝑓(𝑥) = (𝑥 − 1) ^3+ 2, determine the inverse function 𝑓^−1
and its domain.
Click here to see answer by MathLover1(20850)

Question 1194862: Let 𝑓 be the function with correspondence rule 𝑓(𝑥) = (𝑥 − 1) ^3+ 2, determine the inverse function 𝑓^−1
and its domain.
Click here to see answer by MathTherapy(10552)

Question 1194862: Let 𝑓 be the function with correspondence rule 𝑓(𝑥) = (𝑥 − 1) ^3+ 2, determine the inverse function 𝑓^−1
and its domain.
Click here to see answer by greenestamps(13200)

Question 1194863: Let 𝑓 be the function with correspondence rule 𝑓(𝑥) =−3−2𝑥/𝑥+3, determine the inverse function 𝑓^−1 and its domain.
Click here to see answer by greenestamps(13200)

Question 1194864: Let 𝑓 be the function with correspondence rule 𝑓(𝑥) = 3𝑥^2 + 5𝑥 − 3 with 𝑥 ∈ [0; +∞[, determine the inverse function 𝑓^−1 and its domain.
Click here to see answer by shlomitg(8)

Question 1195008: Using the properties of logarithms, simplify the expression ln 𝑦 such that there is no
contain products, quotients or powers.
𝑦=√(3𝑥−4)(3−2𝑥)/4𝑥^2 − 1
Click here to see answer by greenestamps(13200)

Question 1195031: Using the properties of logarithms, simplify the expression ln 𝑦 such that there is no contain products, quotients or powers.
𝑦 = √(3𝑥 − 4)(3 −2𝑥) / √4𝑥^2 − 1

Click here to see answer by greenestamps(13200)

Question 1195032: Using the properties of logarithms, simplify the expression ln 𝑦 such that there is no
contain products, quotients or powers.
𝑦 = √(3𝑥 − 4)(3 −2𝑥) / √(4𝑥² − 1)
Click here to see answer by greenestamps(13200)

Question 1195058: Determine the domain, range, equation of the horizontal asymptote and construct the graph of the following exponential function: f(x) =6^3-x - 4
Click here to see answer by MathLover1(20850)

Question 1195068: I need help with this please: What is the equation of the parabola with a vertex at(-4,5), that opens up, and is congruent to the quadratic function y=-1/4x2?
Click here to see answer by josgarithmetic(39618)

Question 1195082: An object moves according to the
2
equation: y= 3sin [ - t + 2 ]
4
, where T is measured in seconds. What is the period, how many cycles are completed in 4 seconds, and what is the difference from the object to the origin when t=0?
Click here to see answer by ikleyn(52795)

Question 1195187: Determine the domain of y= f(x) = cos^-1(3x + 2) and solve the equation y = 𝜋/4
Click here to see answer by math_tutor2020(3817)

Question 1195241: Please explain all the steps to all my questions:
1. The Sum of a number and three times another number is 18. Find the numbers if their product is maximum.
2. A rectangular lot is bordered on one side by a string and on the other three sides by 600m of fencing. Find the dimensions of the lot if the area is a maximum.
3. Eights meters of fencing are available to enclose a rectangular play area.
A. What is the maximum area than can be enclosed?
B. What dimensions produce the maximum area?
Click here to see answer by ikleyn(52795)

Question 1195243: Please explain all the steps to my questions
1. The Sum of a number and three times another number is 18. Find the numbers if their product is maximum.
Click here to see answer by josgarithmetic(39618)

Question 1195250: Eight meters of fencing are available to enclose a rectangular play area.
A. What is the maximum area that can be enclosed?
B. What dimensions produce the maximum area?
Click here to see answer by Alan3354(69443)

Question 1194562: A hyperbolic mirror has the property that a light ray directed at a focus will be reflected to the other focus. The focus of a hyperbolic mirror has coordinates (-10,0). Find the vertex of the mirror if the mounting point of the mirror is located at (10,10). Round your answer to the nearest hundredth.

Click here to see answer by MathLover1(20850)

Question 256816: A hyperbolic mirror (used in some telescopes) has property that a light ray directed at a focus will be reflected to the other focus. The focus of a hyperbolic mirror can be represented on a rectangular coordinate system by coordinates (24,0). Find the vertex of the mirror if the Mount at the the top edge of the mirror has coordinates (24,24). Sketch the focus, vertex, and part of the hyperbola to represent the mirror. Can you explain this?
Click here to see answer by ikleyn(52795)

Question 1195252: The greenback begins 2022 with a slight decrease of 0.56% against the Peruvian sol despite the political and economic crisis in our country, likewise the dollar closed 2021 close to its maximum of 18 years ago due to the effects of the coronavirus health crisis, which led to greater demand for dollars by investors. Complete information can be found at the following link: https://es.investing.com/currencies/usd-pen-historical-data Assuming that the relationship between the price of the dollar “y=f(x)” in soles and the days elapsed “x” gives rise to a linear function: f(x)=ax+b develop the following questions:
b) Write the linear function f(x) that describes "y=f(x)" in terms of "x". To do this, use the linear adjustment method of least squares, use only 10 data (10 consecutive days) and work only with the first 2 columns, consider x=1 the date 06/20/22.
c) Knowing the linear function f(x) obtained in the previous item, what would be the price of the dollar on July 11?
d) What would be the percentage change in the price of the dollar on 08/04/22 compared to 07/20/22?
Click here to see answer by nycmathdad(2)

Question 1195789: 1. Sketch the graph of y=3e^2x ,x=0, x=2 and x-axis. Shade the region bounded by
the curves. Find the volume of the solid that is formed by revolving the
region shaded about the y-axis.
2. Sketch the graph of y=e^x , y=e and y-axis. Shade the region bounded by
the curves. Find the volume of the solid that is formed by revolving the
region shaded about the y-axis.
3. Sketch the graph of y=x^2 + 4 ,x=3, x=0 and y=x. Shade the region bounded by
the curves. Find the volume of the solid that is formed by revolving the
region shaded about the y-axis.

Click here to see answer by ikleyn(52795)

Question 1196473: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the base and a height of 24 m at the center. If the vertex of the parabola is at the top of the arch, what maximum height should the rectangular object have?
Click here to see answer by greenestamps(13200)

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