Name Period. Algebra 2 Agenda. Week 3.4 Objective Summary Grade

Transcription

1 Name Period Algebra Agenda Week 3.4 Objective Summary Grade Monday January 3, 07 Tuesday January 4, 07 Wednesday January 5, 07 Thursday January 6, 07 Friday January 7, 07 Solving Equations with Radicals Day Practice Solving Equations with Radicals Day Practice Applications Practice Review Complete review Test Relax First Things First Average

2 Monday Tuesday Wednesday Thursday Friday

3 Algebra : Unit 5 Solving Equations Involving Radicals Practice Solving Equations Involving Radicals Pages Name Date Period Solve each equation. Be sure to check for extraneous solutions.. y 0. - x m x x x = x 7 7

4 Algebra : Unit 5 Solving Equations Involving Radicals 8. A. Solve x 6 using the table and graph below. y x y y x B. Solve x 6 algebraically.

5 Algebra : Unit 5 Solving Square and Cube Root Equations Day Practice Solving Square and Cube Root Equations Day pp Name Date Period Solve each equation. Be sure to check for extraneous solutions.. 4 3x p p 3. m- 6 3m x 7 x 3 5. c - 7 c x 5 3x 7. n n 8. 4 x 4 3 x 6

6 Algebra : Unit 5 Solving Square and Cube Root Equations Day 9. x - 64 x- 4 ` 0. x x 5 y x

7 Algebra : Unit 5 Applications Involving Radicals Practice Applications Involving Radicals Pages Name Date Period. Pilots use the function D( A) 3.56 A to approximate the distance, D, in kilometers to the horizon from an altitude, A, in meters. If the distance to the horizon is 390 km, find the altitude of the plane to the nearest meter.. The time t in seconds required for an object to fall from a certain height can be modeled by the h function t, where h is the initial height of the object in feet. To the nearest tenth of a second, 4 how much longer will it take for a piece of an iceberg to fall to the ocean from a height of 40 ft. than from a height of 00 ft? 3. For a spinning amusement park ride, the velocity v in meter per second of a car moving around a curve with a radius r meters is given by v ar, where a is the car s acceleration in m/s. A. For safety reasons, a ride has a maximum acceleration of 39. m/s. If the cars on the ride have a velocity of 4 m/s, what is the smallest radius that any curve on the ride may have? B. What is the acceleration of a car moving at 8 m/s around a curve with a radius of.5 m? 4. The amount of current in amperes I that an appliance uses can be calculated using the formula P I R, where P is the power in watts and R is the resistance in ohms. How much current does an appliance use if P=0 watts and R = 3 ohms? Round your answer to the nearest tenth. 5. Helena drops a ball from 5 feet above a lake. The formula t 5 h describes the time t in 4 seconds that the ball is h feet above the water. How many feet above the water will the ball be after second?

8 Algebra : Unit 5 Applications Involving Radicals 6. The speed, s(d), in miles per hour of a tsunami can be modeled by the function s( d) 3.86 d, where d is the average depth in feet of the water over which the tsunami travels. A. Determine the speed of a tsunami over water with a depth of 500 feet. B. How deep would the water be if the tsunami was calculated to be travelling 75 mph? 7. The formula v 4909gR approximates the velocity in miles per hour necessary to escape the gravity of a planet with acceleration due to gravity, g, in ft/s and radius, R, in miles. On Earth, which has a radius of 3960 mi, the acceleration due to gravity is 3 ft/s. On the Moon, which has a radius of 080 mi, the acceleration due to gravity is about that on Earth. How much faster 6 would a vehicle need to be traveling to escape Earth's gravity than to escape the Moon's gravity? 8. The formula s 30fd can be used to estimate the speed, s, in miles per hour that a car is traveling when it goes into a skid, where f is the coefficient of friction and d is the length of the skid marks in feet. Ashley skids to a stop on a street with a speed limit of 5 mi/h to avoid a dog that runs into the street about 0 ft ahead of her. Ashley claims to have been going less than 5 mi/h. The coefficient of friction is 0.7. A. If Ashley were driving the speed limit, by what distance would she have missed the dog? B. If Ashley were driving less than 0 mi/h, by what distance would she have missed the dog? 9. A tree casts a shadow 5 feet long. The distance from the top of the tree to the end of the shadow is 7 feet. How tall is the tree?

9 Algebra Review: Exponents and Square Root Functions Name Date Period Simplify Completely. Assume all expressions are defined.. 3a b c a b c 5. x 3x The area of the rectangle is rectangle? (A=lw) a b. If the length of the rectangle is 0ab, what is the width of the 3x 4. Solve for x Simplify, do not leave any negative exponents d e f

10 Add or subtract the radicals as indicated. (Leave in simplest radical form) Find the Inverse of each of the following. 9. y x 3 Solve each of the following equations x 4. The graph of f( x) x is shown below. y x Graph g(x) above and identify the domain and range of the graph of g( x) x 3 7. Domain: Range:

11 . The formula s 30d is used to estimate speed, s, in miles per hour given the distance, d, that a car takes to stop. Often, this distance is left on the road by skid marks. If a vehicle is moving at a speed of 30 miles per hour, and the driver applies the brakes and begins to skid, how long should the skid marks, s, be? 3. Two data sets are given. a) What is the equation for f(x)? b) What is the equation for g(x)? c) How are f(x) and g(x) related? For #4-7, solve the radical equation. Be sure to check for extraneous solutions. 4. x x x ( x ) x 5

12 8. What is the solution to x 4 x, graphed below? y x Write each expression in indicated form and simplify. Radical Form Simplified Exponential Form Simplified 3 4 (6 ab) (4 xy) 6 3 (8 x ) c. Simplify the following: m n