# 472 on a string instrument the length of a string

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472. On a string instrument, the length of a string varies inversely with the frequency of its vibrations. If an 11-inch string on a violin has a frequency of 360 cycles per second, what frequency does a 12-inch string have? Answer: 330 vibrations 7.6 Solve Rational Inequalities Solve Rational Inequalities In the following exercises, solve each rational inequality and write the solution in interval notation. 473. 3 0 4 x x 474. 5 1 2 x x Answer: 1 , 2, 2   475. 3 2 2 4 x x 476. 2 1 0 4 12 x x Answer: ( 2,6) 477. 2 1 4 1 2 x x 478. 4 3 2 1 x x Answer: ( , 10) ( 1,2)     Solve an Inequality with Rational Functions In the following exercises, solve each rational function inequality and write the solution in interval notation 479. Given the function   5 , , 2 x R x x find the values of x that make the function greater than or equal to 0. 480. Given the function   1 , , 3 x R x x find the values of x that make the function less than or equal to 0. Answer: ( 3, 1]
OpenStax 7.6 Solve Rational Inequalities This file is copyright 2017, Rice University. All Rights Reserved. 481. The function ( ) 150 100000 C x x represents the cost to produce , x number of items. Find (a) the average cost function , ( ) c x (b) how many items should be produced so that the average cost is less than \$160? 482. Tillman is starting his own business by selling tacos at the beach. Accounting for the cost of his food truck and ingredients for the tacos, the function ( ) 2 6000 C x x represents the cost for Tillman to produce , x tacos. Find (a) the average cost function , ( ) c x for Tillman’s Tacos (b) how many tacos should Tillman produce so that the average cost is less than \$4? Answer: (a) 2 6000 ( ) x c x x (b) Tillman must make more than 3,000 tacos to keep the average cost below \$4 per taco. Chapter Practice Test In the following exercises, simplify. 483. 2 2 4 12 a b ab 484. 2 6 18 9 x x Answer: 6 3 x In the following exercises, perform the indicated operation and simplify. 485. 2 2 4 5 6 2 12 x x x x x 486. 2 3 2 2 3 2 1 1 y y y y y y Answer: 2 1 y y 487. 2 2 2 2 6 20 5 11 7 81 81 x x x x x x 488. 2 3 5 3 3 3 4 a a a a a Answer: 4 a a
OpenStax 7.6 Solve Rational Inequalities This file is copyright 2017, Rice University. All Rights Reserved. 489. 2 2 2 2 2 8 1 7 1 1 1 n n n n n n 490. 2 2 10 16 7 2 3 1 8 3 3 8 x x x x x x Answer: 2 x 491. 1 1 1 1 m n n m In the following exercises, solve each equation. 492. 1 3 5 4 8 x Answer: 8 x   493. 2 1 1 1 5 5 25 z z z 494. 2 2 3 3 16 16 2 8 4 8 8 2 64 z z z z z z z Answer: There is no solution. In the following exercises, solve each rational inequality and write the solution in interval notation. 495. 6 2 6 x x 496. 2 3 1 6 x x Answer: ( , 9) (6, )   497. 2 1 12 5 2 x x In the following exercises, find R x given   2 4 3 10 x f x x x and   2 5 . 2 8 x g x x x
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