Q.43 Use the Binomial Theorem to find... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q.43 (page 837)

Use the Binomial Theorem to find the numerical value of
(1.001)⁵ correct to five decimal places.

Short Answer

Expert verified

The numerical value of

(1.001)⁵ correct to five decimal places is $1.00501$

Step by step solution

Step1. Given information

Here(1.001)⁵ is given.

We need to find out the numerical value of (1.001)⁵ correct to five decimal places .

Step 2. Description of expanding (1.001)5

we can rewrite the given expression as (1+10^-3)⁵

now we can apply Binomial Theorem.

$L e t x a n d a b e r e a l n u m b e r s . F o r a n y p o s i t i v e i n t e g e r n, w e h a v e {(x + a)}^{n} = (\begin{matrix} n \\ 0 \end{matrix}) x^{n} + (\begin{matrix} n \\ 1 \end{matrix}) a x^{n - 1} + (\begin{matrix} n \\ 2 \end{matrix}) a^{2} x^{n - 2} + . . . . . . . + (\begin{matrix} n \\ j \end{matrix}) a^{j} x^{n - j} + . . . . . + (\begin{matrix} n \\ n \end{matrix}) a^{n} {(1 + 10^{- 3})}^{5} = (\begin{matrix} 5 \\ 0 \end{matrix}) {{(10^{- 3})}^{0} (1)}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {{(10^{- 3})}^{1} (1)}^{4} + (\begin{matrix} 5 \\ 2 \end{matrix}) {{(10^{- 3})}^{2} (1)}^{3} + (\begin{matrix} 5 \\ 3 \end{matrix}) {{(10^{- 3})}^{3} (1)}^{2} + (\begin{matrix} 5 \\ 4 \end{matrix}) {{(10^{- 3})}^{4} (1)}^{1} + (\begin{matrix} 5 \\ 5 \end{matrix}) {{(10^{- 3})}^{5} (1)}^{0} = (\begin{matrix} 5 \\ 0 \end{matrix}) + (\begin{matrix} 5 \\ 1 \end{matrix}) (10^{- 3}) + (\begin{matrix} 5 \\ 2 \end{matrix}) {(10^{- 3})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(10^{- 3})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(10^{- 3})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(10^{- 3})}^{5}$

Step3. Finding the numerical value of(1.001)5

The expanded form of (1.001)⁵is

{(1 + 10^{- 3})}^{5} = (\begin{matrix} 5 \\ 0 \end{matrix}) + (\begin{matrix} 5 \\ 1 \end{matrix}) (10

^-3)+52(10-3)2+53(10-3)3+54(10-3)4+55(10-3)5numericalvalueof(1+10-3)5=50+51(10^-3)+52(10-3)2+53(10-3)3+54(10-3)4+55(10-3)5=1+5!4!1!脳10-3+5!3!2!脳10-6+5!2!3!脳10-9+5!1!4!脳10-12+1脳10-15=1+5脳4!1脳4!脳10-3+5脳4脳3!1脳2脳3!脳10-6+5脳4脳3!1脳2脳3!脳10-9+5脳4!1脳4!脳10-12+10-15=1+5脳10-3+10脳10-6+10脳10-9+5脳10-12+10-15(1+10-3)5=1+0.005+0.00001+10-8+5脳10-12+10-15Numericalvaluescorrecttothe5decimalplacesis1.00501..

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91影视

Use the Binomial Theorem to find the numerical value of
(1.001)⁵ correct to five decimal places.

Short Answer

Step by step solution

Step1. Given information

Step 2. Description of expanding (1.001)5

Step3. Finding the numerical value of(1.001)5

One App. One Place for Learning.

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91影视

Use the Binomial Theorem to find the numerical value of(1.001)5 correct to five decimal places.

Short Answer

Step by step solution

Step1. Given information

Step 2. Description of expanding (1.001)5

Step3. Finding the numerical value of(1.001)5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Statistics

Mechanics Maths

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the Binomial Theorem to find the numerical value of
(1.001)⁵ correct to five decimal places.