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2 years ago

15

What is the coefficient of x7 in the expansion of (1 + x)11?

1 answer:

eduard2 years ago

4 0

You can choose to expand the equation to find the coefficient of x7 but that would take a lot of time. Here is a useful tactic that can help;

11C(something)(1)(x)⁷ ----> This gives the coefficient of x⁷
11C7(1)⁴(x)⁷ ----> You know that pascal's triangle is equal on both sides
11C7×1⁴ = coefficient of x⁷ (just ignore x⁷)
330x1⁴=330

This means that the coefficient of x⁷ is 330. You can double check by expanding the equation. If you do not understand what I did there, you can ask me how I got to the solution.

Hope I helped :)

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Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the lett

Jobisdone [24]

Answer:

(a) 720 ways

(b) 120 ways

(c) 24 ways

Step-by-step explanation:

Given

$Word = DANCER$

$n =6$ --- number of letters

Solving (a): Number of arrangements.

We have:

$n =6$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =6!$

This gives:

$Total =6*5*4*3*2*1$

$Total =720$

Solving (b): DA as a unit

DA as a unit implies that, we have:

[DA] N C E R

So, we have:

$n = 5$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =5!$

This gives:

$Total =5*4*3*2*1$

$Total =120$

Solving (c): NCE as a unit

NCE as a unit implies that, we have:

D A [NCE] R

So, we have:

$n = 4$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =4!$

This gives:

$Total =4*3*2*1$

$Total =24$

8 0

2 years ago

6. (5 points) What is 3loga + logb − logc written as a single logarithm?

Jobisdone [24]

Answer: $log(\frac{a^3b}{c})$

Step-by-step explanation:

You need to use the following Properties of Logarithms:

$1)m*log(a)=log(a)^m\\\\2)log(a)+log(b)=log(ab)\\\\3)log(a)-log(b)=log(\frac{a}{b})$

Given the following expression:

$3log(a) + log(b) - log(c)$

You can follow these steps in order to write it as a single logarightm:

- Apply the first property shown above:

$=log(a)^3 + log(b) - log(c)$

- Apply the second property:

$=log(a^3b)- log(c)$

- Finally, apply the third property:

$=log(\frac{a^3b}{c})$

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3 years ago

Solve the equation for t. (t-7)^2+18=9

Anika [276]

Answer:

t = 7 + 3i

Step-by-step explanation:

(t-7)^2 + 18 = 9

(t-7)^2 = 9 - 18

(t-7)^2 = -9

(t-7) = sqrt(-9) = |3| sqrt(-1)

t = 7 + 3i

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2 years ago

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kvasek [131]

Answer:

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Step-by-step explanation:

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elixir [45]

Answer:

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Step-by-step explanation:

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