Concept explainers
EXERCISE
River flow The cross sectional area
where,
a Find a formula that gives
b Use the formula you found in part a to find the flow rate of the river that has a width of
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Forming a pen We want to form a rectangle pen of area 100 square feet. One side of the pen is to be formed by an existing buliding and the other three sides by a fence see Figure 2.106. Let W be the length, in feet, of the sides of the rectangle perpendicular to the buliding, and let L be the length, in feet, of the other side. Figure 2.106 a.Find a formula for the total amount of fence needed in terms of W and L b. Express, as an equation involving W and L, the requirement that the area be 100 square feet. c.Solve the equation you found in part b for L. d.Use your answers to parts a and c to find a formula for F, the total amount, in feet, of fence needed, as a function of W alone. e.Make a graph of F versus W. f.Determine the dimension of the rectangle that requires a minimum amount of fence.arrow_forwardKinetic Energy The kinetic energy E of an object can be calculated by the formula E=12mv2, where m is the mass and v is the velocity. Solve for m.arrow_forwardSpeed of a Skidding Car Police use the formula s=30fd To estimate the speed s (in mi/h) at which a car is traveling if it skids d feet after the brakes are applied suddenly. The number f is the coefficient of friction of the road, which is a measured of the “slipperiness” of the road. The table gives some typical estimates for f . If a car skids 65 ft. on wet concrete, how fast was is moving when the brakes were applied? If a car is traveling at 50 mi/h, how far will it skid on wet tar?arrow_forward
- Falling-Body Problems Suppose an object t dropped from a height h0 above the ground. Then its height after t seconds is given by h=16t2+h0 , where h ¡s measured in feet. Use this information Lo solve the problem. If a ball is dropped from 288 ft above the ground, how bug does it take to reach ground level?arrow_forwardSound Location Two microphones, 2 miles apart, record an explosion. Microphone A receives the sound 6 seconds before microphone B. Where did the explosion occur? (Assume sound travels at 1100 feet per second.)arrow_forwardBlood Flow As blood moves through a vein or an artery, its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases see the figure. The formula that gives v as the function of r is called the law of laminar flow. For an artery with radius 0.5 cm, the relationship between v in cm/s and r in cm is given by the function v(r)=18,500(0.25r2)0r0.5 a Find v(0.1)andv(0.4). b What do your answers to part a tell you about the flow of blood in this artery? c Make a table of values of v(r)forr=0,0.1,0.2,0.3,0.4,0.5. d Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm.arrow_forward
- Engine Displacement The displacement for an automobile engine is the total volume displaced by the cylinders in one cycle of the engine. It is calculated in terms ofthe stroke S and the bore B. The stroke is the total distance travled by the piston from the top of the cylinder to the bottom of the cylinder. The bore is the diameter of the cylinder. If the bore and the stroke are given in inches, then the displacement D is in cubic inches. The displacement is given by the formula D=nSB/2 2, where n is the number cylinders. a. Subarus 2.5L H4 model 2000 engine has 4 cylinders with a bore of 3.92 inches and a stroke of 3.11 inches. What is the displacement for this engine? b. A 6-cylinder engine with a stroke of 3.01 inches is to be built so that the total displacement is 175 cubic inches. What is the proper bore for this engine.arrow_forwardEnlarging a Field A farmer has a rectangular cow pasture with width 100 ft. and length 180 ft. An increase the number of requires the farmer to increase the area of her pasture. She has two options: Option 1: Increase the length of the field. 0ption 2: Increase the width at the field. It costs $10 per foot to install new fence. Moving the old fence costs $6 per linear foot of fence to be moved. (a) For each option, find a formula for A, the area gained, in terms of the cost C. (b) Complete the table for the area gained in terms of the cost for each option. (c) If the farmer has $1200 for this project, which option gives her the greatest gain in area for her money? What if she had $2000 for the project?arrow_forwardRelativistic Length A rocket ship travelling near the speed of light appears to a stationary observer to shorten with speed. A rocket ship with a length of 200 meters will appear to a stationary observer to have a length of 2001-r2 meters, where r is the ratio of the velocity of the ship to the speed of light. What is the apparent length of the rocket ship if it is travelling at a speed that is 99% of the speed of light?arrow_forward
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