Answered: Given the equation y = 2cos3(x − 30 °)…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section1.1: Graphs Of Equations

Problem 9ECP

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A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/s at an angle of 30°. The height of the water can be approximated by h (x)--0.026x²+0.562x+3, where h (x) is the height of the water in meters at a point x meters horizontally from the firefighter to the building. Part 1 of 3 (a) Determine the horizontal distance from the firefighter at which the maximum height of the water occurs. The water reaches a maximum height when the horizontal distance from the firefighter to the building is approximately 10.8 m. Round to I decimal place. Part: 1/3 Part 2 of 3 (b) What is the maximum height of the water? The maximum height of the water is 1 m. Round to I decimal place. X
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A Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point, express the person's height above the ground as a function of time, assuming the center of the Ferris wheel is at ground level. Answer: The Ferris wheel has a diameter of 40 meters, which means the radius (r) is half of the diameter, i.e., (r = 20) meters. The Ferris wheel completes one full revolution every 2 minutes. The period (T) of the Ferris wheel is the time it takes to complete one full revolution. In this case, T = 2 minutes. The angular frequency (w) can be calculated using the formula (w = 2/?). Substituting the given value for (T): w = 2/? = ? radians per minute. Now, the height (h) of the person above the ground as a function of time (t) can be expressed using a sine function. The general form of a sine function is h(t) = A sin(wt+ϕ)+C where: - A is the amplitude (half the range of the…
4. A penny is dropped from the top of the tallest radio tower in the U.S., the KVLY-TV tower in North Dakota (629 meters). Neglecting wind resistance, the position function of the object in meters can be described by the equation: s(t)= -4.91 +629 a) What is the average speed of the penny from t = 0s to t= 2s? b) At what time does the object hit the ground (s = 0)? Note: time is in seconds = ? c) Determine the velocity as function of time: v(t)= dt d) How fast is the object traveling (meters/second) when it hits the ground? Next, multiply your answer by 2.2369363 to convert to mph, round to nearest integer.
Suppose you are climbing a hill whose shape is given by the equation z = 2,000 - 0.005x2 - 0.01y?, where x, y, and z are measured in meters, and you are standing at a point with coordinates (160, 160, 1616). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? O ascend O descend At what rate (in vertical meters per horizontal meter)? vertical meters per horizontal meter
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Two objects moving along x-axis are starting at the same time. Their positions are measured in centimeters at time t in seconds. If the equation of motion of objects 1 and 2 are s, =212- 3t and s,=3t – 12 respectively, determine the distance between the objects at the instant when they have the same velocity.

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Given the equation y = 2cos3(x − 30 °) + 1 has a maximum when x = 30°. Explain how to find other values of x when the same maximum value occurs