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2 years ago

13

I really need help with this and I looked up how to this with a lots of websites and I looked up youtube so if u know how to do

this please help???

1 answer:

nikitadnepr [17]2 years ago

6 0

If you are trying to solve for X the answer is -9

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

2 years ago

Alvin is 13 years older than Elga the sum of their age is 55 what is elgas age

Makovka662 [10]

Answer:

Elga is 42 years old

Step-by-step explanation:

55-13=42

5 0

2 years ago

Find the inverse of the following function

KatRina [158]

f-¹(x)= $\frac{2-7x}{x+2}$

Answer:

Solution given:

f(x)= $\frac{-2x+2}{x+7}$

Let f(x)=y

y= $\frac{-2x+2}{x+7}$

Interchanging role of x and y

x= $\frac{-2y+2}{y+7}$

doing crisscrossed multiplication

x(y+7)=-2y+2

now solve it:

xy+7x=-2y+2

keep like terms in one side

xy+2y=2-7x

take common

y(x+2)=2-7x

make a value of y

y= $\frac{2-7x}{x+2}$

So,

f-¹(x)= $\frac{2-7x}{x+2}$

3 0

1 year ago

Read 2 more answers

Given the recursive formula:<br> a1=3<br> An=2(an-1+1)<br> Find a2 a3 a4

fenix001 [56]

Answer:

$a_2 = 8$

$a_3 = 18$

$a_4 = 38$

Step-by-step explanation:

We are given the following recursive formula:

$a_n = 2(a_{n-1}+1)$

And consider $a_1 = 3$

a2

$a_2 = 2(a_1 + 1) = 2(3 + 1) = 8$

a3

$a_3 = 2(a_2 + 1) = 2(8 + 1) = 18$

a4

$a_4 = 2(a_3 + 1) = 2(18 + 1) = 38$

6 0

2 years ago

Can anybody please help me with question 1 please...I would really appreciate it so much

In-s [12.5K]

Answer:

The total time the water balloon is in the air is 8 seconds. The balloon reaches the maximum height of 25 fee after 3 seconds. The water balloon has a height of 24 feet at 2 seconds and a half.

Step-by-step explanation:

5 0

1 year ago

Read 2 more answers