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Tutors Answer Your Questions about Quadratic-relations-and-conic-sections (FREE)
Question 1206901: The sides of a nuclear power plant cooling tower form a hyperbola. The diameter of the bottom of the tower is 288 feet. The smallest diameter of the tower is 143 feet which is 393.5 feet above the ground. The tower is 581 feet tall.
Find the width of the tower at a height of 38 feet.
Click here to see answer by CPhill(1959)   |
Question 1199700: The equation of hyper bola is ((X)^2/9)-((Y)^2/16)=1
And it's asymptotes are y=4x/3 and y=-4x/3
Here, h(x) represents the portion of the hyperbola in the first quadrant. Based on this:
a. Write an expression for h(x) in terms of x .
b. Use the expression from part a. to justify why h(x) lies below the line y=4x/3 .
Click here to see answer by textot(100) |
Question 1198216: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 72 feet across at its opening and 6 feet deep at its center, where should the receiver be placed? (Hint: Draw a cross section of the dish on a graph and place the vertex at (0, -6) so that the opening of the dish lies on the x-axis).
Find the equation of the parabola.
How far above the vertex should the receiver be placed?
Click here to see answer by onyulee(41) |
Question 1190079: Please help me solve this problem.
The dome of a whispering gallery has the form of a semi-ellipse so that the two person standing at the foci will be able to hear each other. This is because sound waves from one focus, when they reach the semi-elliptical ceiling, bounce off to the other focus. If one such whispering gallery has a focus of 3m away from the end of the semi-ellipse, and the foci are 14m away from each other, how high is the dome at the center?
Click here to see answer by CPhill(1959) |
Question 1186192: Mrs. Flores recently subscribed in a tv cable plan at GSAT Company. The
receiving dish of the GSAT Cable is in the shape of a paraboloid of revolution.
Find the location of the receiver which is placed at the focus if the dish is 12
feet across and 3 feet deep. Also write the standard form equation of the ellipse.
Click here to see answer by CPhill(1959) |
Question 1186192: Mrs. Flores recently subscribed in a tv cable plan at GSAT Company. The
receiving dish of the GSAT Cable is in the shape of a paraboloid of revolution.
Find the location of the receiver which is placed at the focus if the dish is 12
feet across and 3 feet deep. Also write the standard form equation of the ellipse.
Click here to see answer by ikleyn(52795)  |
Question 1185983: When a fighter jet travels faster than sound, it generates a sonic boom shock wave in the shape of a cone. If the plane is flying at a constant altitude, this cone intersects the ground in the shape of one branch of a hyperbola. Suppose a jet is flying north at level altitude and at a speed of 500 m/s (which is super sonic speed). In this model, let the position of the jet be the origin. The vertex of the sonic boom hyperbola is on the ground 15km behind the jet, and the hyperbola has an eccentricity of 1.5. Use a scale of 1 unit = 1 km
A.) Find the coordinates of the focus and the equations of the asymptotes. Round all answers to the nearest hundredth.
B.) Write an equation for the sonic boom hyperbola in standard form.
C.) A person on the ground will hear the sonic boom when the hyperbola passes over him. Suppose the jet is located at the origin at time t=0. The jet and the sonic boom line are moving due north at 500 m/s, and John is standing at (7, 10). Calculate the time, in seconds, until John will hear the sonic boom. Round your answer to the nearest tenth of a second
Click here to see answer by CPhill(1959) |
Question 1185983: When a fighter jet travels faster than sound, it generates a sonic boom shock wave in the shape of a cone. If the plane is flying at a constant altitude, this cone intersects the ground in the shape of one branch of a hyperbola. Suppose a jet is flying north at level altitude and at a speed of 500 m/s (which is super sonic speed). In this model, let the position of the jet be the origin. The vertex of the sonic boom hyperbola is on the ground 15km behind the jet, and the hyperbola has an eccentricity of 1.5. Use a scale of 1 unit = 1 km
A.) Find the coordinates of the focus and the equations of the asymptotes. Round all answers to the nearest hundredth.
B.) Write an equation for the sonic boom hyperbola in standard form.
C.) A person on the ground will hear the sonic boom when the hyperbola passes over him. Suppose the jet is located at the origin at time t=0. The jet and the sonic boom line are moving due north at 500 m/s, and John is standing at (7, 10). Calculate the time, in seconds, until John will hear the sonic boom. Round your answer to the nearest tenth of a second
Click here to see answer by ikleyn(52795) |
Question 1185825: A large cooling tower in the shape of a hyperboloid is used to remove the heat from a nuclear power plant. The shortest width of the cooling tower is 56 meters. From this part, the length to the top of the cooling tower is 65 meters. The diameter of the top of the cooling tower is 60 meters. What is the equation of the hyperbola that represents the sides of the cooling tower? Set the middle of the shortest width as the origin.
Click here to see answer by CPhill(1959) |
Question 1185775: Yohan and Jesx want to test the acoustics of a whispering gallery. Yohan is
standing at one of the focus of the gallery, 5 feet away from the nearest wall. Jesx is standing at the other focus and is 9 feet away from Yohan.
a. What is the highest point of the ceiling from the ground?
b. How high is the ceiling from the point where Yohan and Jesx stand?
Click here to see answer by CPhill(1959) |
Question 1209671: Square ABCD has side length 6. An ellipse $\mathcal{E}$ is circumscribed about the square and there is a point $P$ on the ellipse such that $PC = PD = 8$. What is the area of ellipse $\mathcal{E}$? (You may assume the sides of the square are parallel to the axes of the ellipse.)
Click here to see answer by CPhill(1959) |
Question 1209672: An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis $24,$ and minor axis $13.$ The distance between the vertices of the hyperbola is $5$. Let $P$ be one of the points of intersection of the ellipse and hyperbola. What is $PA \cdot PB$?
Click here to see answer by CPhill(1959) |
Question 1184287: The line joining A(bCosx, bSinx) and B(aCosy, aSiny), where a and b have different values is produced to the point M(x, y) so that AM:MB = b:a then find the value of uCos((x+y/2)) + vSin((x+y)/2)) and uCos(x+y) + vSin(x+y)?
Click here to see answer by CPhill(1959) |
Question 1175757: Your group has been commissioned to design a new roller coaster for an amusement park. The roller coaster should be more spectacular than all existing roller coasters, and in particular it should include a vertical loop. In order to stay on the track through the loop, the cars must travel at a speed given (in miles per hour) by
v = 90r where r is the radius of the loop in feet.
1.a) The location of the amusement park is somewhere in Bukidnon and you are planning to have a total height of 160 feet. Find the speed of the car that it must reach on the roller coaster. (Write your answer in exact value form using the concept of simplifying radicals.) 2 points
Note: Because the vertical loops used in roller coasters are not perfect circles, the total height of the loop is about 2.5 times its radius.
Click here to see answer by CPhill(1959) |
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