1. The equation x² + y² = 1 describes a circle of radius 1. Solving for y, we get y = √√1 – x².(a) Explain why y√1- x² gives only the top half of the circle.=(b) Thinking about area, what should[√1 - x² da equal?-1

The equation x2+y2=1 describes a circle of radius 1

Answered: 1. The equation x² + y² = 1 describes a…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter13: Conic Sections

Section13.1: Circles

Problem 48PS

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When the Radius Increases a. A rope is wrapped tightly around a wheel with radius of 2 feet. If the radius of the wheel is increased by 1 foot to a radius 3 feet, by how much must the rope be lengthened to fit around the wheel? b. Consider a rope wrapped around the Earths equator. We noted in Exercise 17 that the radius of the Earth is about 4000 miles. That is 21,120,000 feet. Suppose now that rope is to be suspended exactly 1 foot above the equator. By how much must the rope be lengthened to accomplish this? The Size of the Earth The radius of the Earth is approximately 4000 miles. a. How far is it around the equator? Hint: You are looking for the circumference of a circle b. What is the volume of the Earth? Hint: The volume of a sphere of radius r is given by 43r3. b. What is the surface area of the Earth? Hint: The surface area of a sphere of radius r is given by 4r2.
By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0
The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.
Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?
Of two gears that mesh, the one that has the greater number of teeth is called the gear, and the one that has the fewer teeth is called the pinion (Figure 218). For each of the problems, set up a proportion, and determine the unknown value, x. Round the answers to 1 decimal place where necessary.
Compute the following problems. Express the answers to the nearer whole number. Use C=3.1416DN12 or DN12 for customary units and C=3.1416DN1000 or DN1000 for metric units. What is the surface speed of a 16-inch diameter surface grinder wheel running at1194 rpm?
Solve the following exercises based on Principles 11-14, although an exercise may require the application of two or more of any of the principles. Round the answers to 3 decimal places where necessary unless otherwise stated. a. If radius x = 7.500" and y = 4.500", find PM. b. If radius x = 8.000" and y = 4.800", find PM.

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1. The equation x² + y² = 1 describes a circle of radius 1. Solving for y, we get y = √1-x². (a) Explain why y = √1- x² gives only the top half of the circle. L (b) Thinking about area, what should √1-x² dx equal?