which sequence of transformation would yied a triangle similar to the original triangle but not congruent

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

Make arguments. Sue said that 200+20+23 is the same as 200+30+3. Is she correct? Explain.

Leya [2.2K]

No she is not correct if she said 200+20+23 was the same as 200+40+3 she would have been correct.

4 0

3 years ago

A flush is five cards of the same suit. Find the probability of pulling 5 cards from a deck and getting a flush.

ValentinkaMS [17]

Answer:

0.00198079

Step-by-step explanation:

6 0

3 years ago

Which ordered pair is a solution to the equation? 3x-4y=13

ASHA 777 [7]

The correct answer is B
When you put the values of x and y in the equation

3(3) - 4(-1) = 13

9 + 4 =13

13=13 (correct answer)

When you try putting the rest of the values in the equation the answer doesn’t match ,hence ,the correct answer is B.I hope I get the brainliest answer!

7 0

3 years ago

What is the mean, median, mode of the data set

Inga [223]

Answer:

Step-by-step explanation:

mean: 24.444444444444

median: 25

mode: 25 appeared 2 times

7 0

3 years ago

which sequence of transformation would yied a triangle similar to the original triangle but not congruent​

which sequence of transformation would yied a triangle similar to the original triangle but not congruent