Centering Intervals About a PointIn Exercises 1–6, sketch the interval (a, b) on the x-axis with the point3. a = -7/2, b = -1/2, c = -34. а %3D —7/2, ь%3D -1/2, с %3D—3/25. а %3D 4/9, Ь %3D 4/7, с %3D 1/26. a = 2.7591, b = 3.2391, c = 3Thenaof 8> 0finda < x < b _whenever 0 < |x – c| < 8.1. a = 1, b = 7, c = 52. a = 1, b = 7, c = 2inside.valuesuchthat

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Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.3: The Cartesian Plane And Graphs Of Equations

Problem 18E

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Projectile Motion In Exercises 75 and 76, consider the path of an object projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is x2=v216ys. In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels. A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Write an equation for the parabolic path. (b) How far does the ball travel horizontally before it strikes the ground?
IMPLIED DIFFERENTIATION Two highways intersect at a right angle. An car A, moves along one of the highways, approaching the intersection at 80 km / h, while another car B, moving along the other highway, approaches the intersection a 96 km / h. At what rate is the distance between vehicles varying, at the moment when the cars A and B are, respectively, 5 and 6 kilometers from the intersection?
Slope of a Curve at a PointIn Exercises 7–18, use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.
Regarding a χ2-curve: a. At what point on the horizontal axis does the curve begin?b. Classify its shape as symmetric, left skewed, or right skewed.c. As the number of degrees of freedom increases, a χ2-curve begins to look like another type of curve. What type of curve is that?
Change in Direction A graph of directed distance switches from increasing to decreasing. What happens to velocity?
Vertical tangent linesa. Determine the points where the curve x + y3 - y = 1 has avertical tangent line .b. Does the curve have any horizontal tangent lines? Explain
12. A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find the equation of the curve. Mention step by step with explaination
Distances between points: Find the distance between each pair of points.1. (1, 2, −3) and (4, 7, −3) 2. (−5, 7, 0) and (0, 6, −3) 3. (1, 5, −2) and (3, 9, −1) 4. (4, 6, 2) and (1, 3, −5)
The long run. A chair manufacturer hires its assembly-line labour for $18 an hour and calculates that the rental cost of its machinery is $6 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. The firm is currently using 1 hour of labour for every 3 hours of machine time. (Assume that labour is on the horizontal axis and capital is on the vertical axis). 3. Graphically illustrate your answer by drawing an isoquant, an isocost line for the current combination of labour and capital and an isocost line for the optimal combination of labour and capital. An isocost corresponding to the optimal combination of labour and capital is [a vertical line, a horizontal line, an upward sloping straight line, an upward sloping curve which is not a straight line, a downward sloping straight line, a downward sloping curve which is not a straight line, L-shaped] has slope [ ] at the optimal combination of inputs An isoquant…
A 500 gallon tank is filled with gasoline containing 10 pounds of a seasonal additive. A gasoline mixture containing 0.02 pounds of additive per gallon is added to the tank at the rate of 50 gallons per minute. The gasoline solution in the tank is continuously and thoroughly mixed and drained out at the same rate of 50 gallons per minute. How many points of additive are in the tank 30 minutes into the operation.
An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 30 30°, its height, f left parenthesis x right parenthesis comma f(x), in feet, can be modeled by f left parenthesis x right parenthesis equals negative 0.01 x squared plus 0.6 x plus 5.7 comma f(x)=−0.01x2+0.6x+5.7, where x is the shot's horizontal distance, in feet, from its point of release. Use this model to solve parts (a) through (c) and verify your answers using the graph What is the maximum height of the shot and how far from its point of release does this occur? The maximum height is , which occurs feet from the point of release.
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