A is ball thrown off of a roof has a path that can be modelled by the equation h = -3(t - 2)^2 + 75, where 'h' represents the height of the ball in metres, and 't' represents the time in seconds.   a) determine the maximum height of the ball and when the ball reaches the max height.  b) From what height was the ball initially thrown?  c) When will the ball hit the ground?  d) Sketch the graph.

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: Use the algebraic tests to check for symmetry with respect to both axes and the origin.y = 1/(x2 +…

A: A function is symmetric with respect to the y-axis if f(x)=f(-x). Such a function is also called an…

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

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Q: Find all points having an x-coordinate of 3 whose distance from the point (-2,1)is 13 (a) By using…

A: (a) By using the Pythagorean Theorem (see graph below)   Let (-2,1) denote the coordinates of the…

Q: Use the algebraic tests to check for symmetry with respect to both axes and the origin.x2 − y = 0

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Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

Q: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

Q: The straight-line distance from Earth to Mars at the time the launch is scheduled is 100 million…

A: The straight line distance from earth to mars at the timethe lunch is sheduled is 100 millionmilees…

Q: A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10…

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through the hoop is modeled by the parabola,

Q: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

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Q: an equation is written in the general form f(x)=ax^2+bx+c, what technique/process can one use to…

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Q: Use the side-splitter theorem to solve for x in the triangle below.

A: Given,

Q: Find the real number ( B) such that the line of symmetric equatic x - 3 == ) is parallel to the…

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Q: A parabolic arch has an equation of 3x 2 + y – 300 = 0. a) What is the maximum height of the arch?…

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Q: # 3) Create the equation of the cubic, in standard form, that has x-intercepts of 3, -1, and 2…

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Q: What equation can Pam use to determine x, then distance up the tree trunk from the fork at which she…

A: The length of the wooden platform is BC=10 in. The height of AB=x units. An angle m∠A=52∘

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: the path of a diver is gien by 2y=-x^2+6x+102 where y is the height(in meter) and x is the…

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Q: for the given audratic equation determine, i- which way the parabolla opens ii- the cordinate of…

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Q: 51. Show that the shortest distance from the point (x1, yı) to the straight line Ax + By + C=0 is Ax…

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Q: Find the tangent line to the parabola x2-6y=10 through (3,5) (ILLUSTRATE SOLUTION)

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Q: The temperature at the point (x, y) on a metal plate is x² + y? " Find the direction of greatest…

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Q: If the maximum horizontal range of a particle is R, show that the greatest height attained is R. A…

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Q: A man in a rowboat at P in Fig. 14-3, 5 mi from the nearest point A on a straight shore, wishes to…

A: Assume x be the distance between the shore and the point at which the man lands. So, to reach point…

Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

A:

Q: 22. Find the function for a parabolic arch that has a base length of 24 feet and a height of 36…

A: Equation of parabolic curve is given and in form X^2 = 4aY

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: A man in a rowboat at P.5 miles from the nearest point A on a straight shore. wishes to reach to a…

A: This problem is based on maxima minima function. After getting minima function we got the value of x…

Q: Find the point on the parabola y=x^2 that is closest to the point (6,3) what is the distance between…

A: Given: To find the point on the parabola y=x2 that is closest to the point (6,3) what is the…

Q: An airplane is flying at an airspeed of 600 km/hr in a cross-wind at 50 km/hr that is blowing from…

A: Given: A  = The Airspeed     = the speed of airplane in wind. = 600 km/h  (Black vector) w = The…

Q: Find the point(s) on the parabola x =y closest to the point (0,3)

A:

Q: You have a parabolic bowl in the shape of the equationz=x^2+y^2, from z= 0 to z= 10. If you left the…

A: Let the parabolic bowl is filled till some height, h in..  So, the volume of the water in the bowl…

Q: A jogger runs at a constant speed of one mile every 8 minutes in the direction S40°E for 20 minutes…

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Q: A hawk flying at 16 m/s at an altitude of 170 m accidentally drops its prey. The parabolic…

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Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

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Q: What point on the parabola y = 6 – x is closest to the point (6,6)?

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Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 4? a = b…

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Q: Prove that the equation ax² + 2hxy+by² + 2gx+2 fy+c=0 wi h²2 = ab and bg2 = af?. Also find the…

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Q: Solve for the value of x in the parallelogram below. 13 y + 8 2y + 1

A: The given sides of parallelogram are  13, (y + 8), (2y + 1) and x

Q: The parabolic antenna has an equation of y^2 + 8x = 0. Determine the length of the latus rectum.

A: Here we use the standard form of parabola.

Q: Let's consider points X and Y on the coordinate plane below. y Y (x2, Y2) x (x1,Y1) Write a formula…

A: Consider the given graph. We have to find the formula that can be used to find midpoint of any 2…

Q: 2. Find the point on the parabola x+y? 0 that is the closest to the point (0, -3).

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Q: Suppose that the elevation on a hill is given by flx, y) = 200 – 4,² – 5. From the site at (4, 2),…

A: Given query is to find the direction of the rain's run off.

Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here