Water runs into a vase with a fillable height of 35 cm at a constant rate. The vase is fullafter 5 seconds and the water is turned off. Use this information and the shape of the vaseshown to answer the questions if d is the depth of the water in cm at time t in seconds (seepicture below).a) Explain why d is a function of t.b) Determine the domain and range of the function.c) Sketch a possible graph of the function, based on the shape of the vase. Make sure that youraxes are labeled correctly.depth dat anytime t35 cm

Given information:Water runs into vase of height 35 centimetres at a constant rate.The vase is full…

Answered: Water runs into a vase with a fillable…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Countries in the northern hemisphere, including the Philippines, experience summer solstice (longest day) every June 21 with an average time of daylight of 15.7 hours while the winter solstice (shortest day) occurs every December 22 with an average time of daylight of 8.3 hours. The average daylight time varies sinusoidally to the number of days every year. Sketch the graph that models the situation. b. a. Determine the equation of the function that relates the number of days of the year to the average daylight time. DDL 1.
2) A 50 foot diameter Ferris wheel is constantly turning at four revolutions per hour. The bottom of the Ferris wheel is 10 feet of the ground. Graph the height of the Farris wheel as a function of time, f(t), if the starting time is when the Farris wheel is at the highest point. Be sure to state the angular frequency, period, amplitude, and midline of the function. Angular Frequency: Period: Amplitude: Midline: 2a)Write a possible formula for the cosine function f(t) represented by the information and graph from question 5.
Outside temperature over the course of a day can be modeled as a sinusoids function. Suppose the temperature is 50 degrees at midnight and the high temperature for the day will be 60 degrees and low will be 40 degree ax Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.
2. As shown in Figure 2, a camera is mounted at a point 3000 ft from the base of a rocket launching pad. The rocket rises vertically when launched, and the camera's elevation angle is continually adjusted to follow the bottom of the rocket. (a) Express the height x as a function of the elevation angle 0. (b) Find the domain of the function in part (a). Rocket 3000 ft Camera Figure 2
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
A Ferris wheel has a radius of 35 feet. The bottom of the Ferris wheel sits 0.7 feet above the ground. You board the Ferris wheel at the 6 o'clock position and rotate counter-clockwise. a. Write a function f that determines your height above the ground (in feet) in terms of the number of radians you have swept out from the 6 o'clock position, a. f(a) = tan(35) Preview b. Write a function g, that determines your height above the ground (in feet) in terms of the number of feet you have traveled since you started rotating, s. g(s) : Preview
The water from an outdoor fountain follows a path that is shaped like a parabola. The arch created by the water is 32 inches wide and 27 inches high. If the arch were 32 inches wide but 44 inches high, how could you modify your function W to model the new arch? Explain or show your reasoning.

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