Help!!!! I have worked on this for hours.

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

7 0

3 years ago

A spinner has 8 options and a bag

Anni [7]

Answer:

1/18

Step-by-step explanation:

Spinner: 1 out of 8

Even number: 4 out of 9

1/8x4/9=4/72 = 2/36 = 1/18

3 0

4 years ago

Get brainiest if right?

aev [14]

Answer:

30 mph

Step-by-step explanation:

train stopped after 520 miles

780 miles to go

stopped at 20 hours

stopped for 4 hours

34 hours used up...

26 hours left

780 miles to go

780 miles/26 hrs = 30 m/hr

5 0

3 years ago

Find the area of this circle.

dmitriy555 [2]

Answer:

201.06

Step-by-step explanation:

You can plug in the 8 from the circle into the equation to find the area.

7 0

2 years ago

You and your friends Jose and Sarah all live on the same street. You know that Jose lives five blocks from away from you. Jose s

Mila [183]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Sarah, Jose and you live in the same street:

Distance between you and Jose = 5 blocks

Distance between Jose and Sarah = 2 blocks

Distance (b) between you and Sarah:

Since it isn't stated whether Sarah lives closer to you than Jose or vice versa ;

Then;

Distance b between you and Sarah will be :

(Distance between you and Jose ± distance between Jose and Sarah)

b = (5 ± 2)

b = (5 + 2) or (5 - 2)

b = 7 blocks or 3 blocks

4 0

3 years ago