Explanation Given: The velocity is v 0 = 32 ft/s . Initial height is s 0 = 128 ft . Procedure used: Factoring general trinomials by grouping : In a trinomial of the form a x 2 + b x + c , a ≠ 1 , split up the x -term into two terms using the method described below. “Step 1: Find the product a c . Step 2: Find two numbers whose product is a c and whose sums is b . Step 3: Replace the middle term bx with two x -terms having these numbers as coefficients. That is, a x 2 + b x + c = a x 2 + m x + n x + c . Step 4: Complete the factorization by grouping”. Calculation: Obtain the expression − 16 t 2 + v 0 t + s 0 for the height as follows. Substitute v 0 = 32 and s 0 = 128 in − 16 t 2 + v 0 t + s 0 . − 16 t 2 + v 0 t + s 0 = − 16 t 2 + 32 t + 128 Thus, the expression − 16 t 2 + v 0 t + s 0 for the height is − 16 t 2 + 32 t + 128 . Factor the expression − 16 t 2 + 32 t + 128 as follows. Rewrite the expression as, − 16 t 2 + 32 t + 128 = − 16 ( t 2 − 2 t − 8 ) (1) Consider the expression t 2 − 2 t − 8 . It is observed that, the coefficients are a = 1 , b = − 2 and c = − 8 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 1 ( − 8 ) = − 8 Thus, the value of a c is –8. Step 2: Find the two number, e and f, whose product is a c = − 8 and whose sum is b = − 2 . Obtain the list of integer factors of –8 such that product is –8 and sum is –2 as shown below in Table 1. Integers whose product is –8 1 , − 8 − 1 , 8 − 4 , 2 4 , − 2 Sum –7 7 –2 2 Table 1 From Table 1, it is observed that the numbers whose product is –8 and sum is –2 are − 4 and 2

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.2, Problem 71E

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The expression −16t2+v0t+s0 for the height and write it in the factored form.

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Chapter 6.2, Problem 70E

Chapter 6.2, Problem 72E

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Chapter 6 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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The expression − 16 t 2 + v 0 t + s 0 for the height and write it in the factored form.

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The expression −16t2+v0t+s0 for the height and write it in the factored form.

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Chapter 6 Solutions