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2 years ago

Plsss answer it's very urgent

Mathematics

2 answers:

Jet001 [13]2 years ago

8 0

Answer:nopare\

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Step-by-step explanation:

gavmur [86]2 years ago

3 0

Fxgxdjvgddhjvxxdfkmk

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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

A scientist is studying a certain strain of bacteria that grows at an exponential rate, doubling each cell every 5 minutes. Imag

riadik2000 [5.3K]

Not sure if the question is complete, but if the cell doubles every five minutes, you must first double the one, then simply square the answer every five minutes.

3 0

3 years ago

Evaluate f(4)<br> f(x) = 3x + 4

RSB [31]

The answer is definitely 7xf

7 0

2 years ago

The average of three different positive integers is 8. What is the largest integer that could be one of them?

galina1969 [7]

Answer:22

Step-by-step explanation: the smallest the other two can be is 1 so you have to multiply 8 with 3, that equals 24, then you have to subtract 2 (1+1) and that gives you 22.

4 0

2 years ago

What is equivalent to this formula: y=3(x+5)(x-2)

nadezda [96]

Answer:

y = 3*(x^2) + 9x -30

Step-by-step explanation:

y=3(x+5)(x-2)

y = (3*x + 3*5) * (x - 2)

y = (3*x + 15) * (x - 2)

y = 3*x*x + 3*x*(-2) + 15*x + 15*(-2)

y = 3*(x^2) - 6x + 15x - 30

y = 3*(x^2) + 9x -30

5 0

2 years ago

Plsss answer it's very urgent ​

Plsss answer it's very urgent