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Phantasy [73]
4 years ago
9

Which of the following tables represents a function?

Mathematics
1 answer:
SVEN [57.7K]4 years ago
3 0

Answer:

B

Step-by-step explanation:

The others have an x val with 2 y vals

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7. By using binomial expansion show that the value of (1.01)^12 exceed the value of (1.02)^6 by 0.0007 correct to four decimal p
BlackZzzverrR [31]

Binomial expansion is used to factor expressions that can be expressed as the power of the sum of two numbers.

The proof that (1.01)^12 exceeds (1.02)^6 by 0.0007 is\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }

The expressions are given as:

\mathbf{(1.01)^{12}\ and\ (1.02)^6}

A binomial expression is represented as:

\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}

Express 1.01 as 1 + 0.01

So, we have:

\mathbf{(1.01)^{12} = (1 + 0.01)^{12}}

Apply the above formula

\mathbf{(1.01)^{12} = ^{12}C_0 \times 1^{12 - 0} \times 0.01^0 + .........  .......... +  ^{12}C_{12} \times 1^{12 - 12} \times 0.01^{12} }}

\mathbf{(1.01)^{12} = 1 \times 1 \times 1 + .........  .......... +  1 \times 1 \times 10^{-24} }}

\mathbf{(1.01)^{12} = 1  + .........  .......... +  10^{-24} }}

This gives

\mathbf{(1.01)^{12} = 1.1268\ (approximated)}

Similarly,

Express 1.02 as 1 + 0.02

So, we have:

\mathbf{(1.02)^6 = (1 + 0.02)^6}

Apply \mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}

\mathbf{(1.02)^6 = ^6C_0 \times 1^{6 - 0} \times 0.02^0 +  ^6C_1 \times 1^{6 - 1} \times 0.02^1 +.............. + ^6C_6 \times 1^{6 - 6} \times 0.02^6 }\mathbf{(1.02)^6 = 1 \times 1 \times 1 +  6 \times 1 \times 0.02 +.............. + 1 \times 1 \times 6.4 \times 10^{-11} }

\mathbf{(1.02)^6 = 1 +  0.12 +.............. + 6.4 \times 10^{-11} }

This gives

\mathbf{(1.02)^6 = 1.1261\ (approximated) }

Calculate the difference as follows:

\mathbf{(1.01)^{12} - (1.02)^6 \approx 1.1268 - 1.1261 }

\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }

The above equation means that:

(1.01)^12 exceed the value of (1.02)^6 by 0.0007

Read more about binomial expansions at:

brainly.com/question/9554282

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If x2 − 8xy + 12y2 = 8 and x − 6y = 3, then x − 2y =
otez555 [7]
I hope this helps you

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