26. The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second. (a) Find the speed of the bicycle in feet per second and miles per hour. (b) Use your result from part (a) to write a function for the distance d (in miles) a cyclist travels in terms of the number n of revolutions of the pedal sprocket. (c) Write a function for the distance d (in miles) a cyclist travels in terms of timet (in seconds). Compare this function with the function from part (b). 14 in.

Q: In a laboratory setting, the heart rate of a patient was carefully monitored. Below is the graph of…

A: Solution:At t=0, heart rate is 110, Maximum is 160 and minimum is 60.This sinusoidal function will…

Q: My velocity along a straight line is shown in the image attached. Help sketch the graph of my…

A: Step 1:Step 2:-

Q: 2. An observer views a space shuttle from a distance 2 miles from the launch pad. (a) Sketch a…

A: Use trigonometric identity of tan(theta) to solve the question. Tan(theta)=Perpendicular/Base

Q: This problem illustrates a typical approach for creating a model. Use lower case letters. We want to…

A:

Q: Two hot-air balloons are moored to level ground below, each at a different location. An observer at…

A:

Q: 11. Martha Stewart is designing a box for her cat to sleep in. It has 4 sides and a bottom but no…

A: We will use the basic knowledge of the application of differentiation and the surface area and…

Q: Find an equation of the following function: The depth of the water in Cape Cod at low tide is 2…

A:

Q: Based on the view from above, write an equation describing Han's vertical position v, in feet,…

A: In this question, the concept of a trigonometric function is applied. Trigonometric Function The…

Q: 9. A windmill has a radius of 8m and rotates once every 20 metres off the ground (i.e. the vertical…

A:

Q: Hampton is a small town on a straight stretch of coastline running north and south. A lighthouse is…

A: The figure is shown below and we can use trigonometry ratios to find the distance from Hampton to…

Q: へ6, - -1 も Problem 4. The area of the house shape is 30 square feet. Find a formula for the height…

A:

Q: The function gives the distances (in feet) traveled in time t (in seconds) by a particle. Find the…

A:

Q: Find an equation to model the vertical motion of the tip of a second hand on a clock, if the second…

A:

Q: 2) A 50 foot diameter Ferris wheel is constantly turning at four revolutions per hour. The bottom of…

A: Amplitude, A:The diameter of the wheel,d = 50 ftThe radius of the wheel is,r = d2 = 25 ftAmplitude…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.