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1 year ago

What is the coefficient of the x9y-term in the binomial expansion of (2y + 4x3)4? 4 32 128 512

Mathematics

2 answers:

sasho [114]1 year ago

7 0

Answer:- 512

Explanation:-

We know that $(m+1)^{th},\ (T_{m+1})$ in the binomial expansion $(p+q)^n$ is given by

$T_{m+1}=^nC_m\ p^{n-m}q^m$

Assume that $x^9y$ occurs in the $(m+1)^{th}$ term of the expansion of $(2y+4x^3)^4=(4x^3+2y)^4$

$T_{m+1}=^4C_m\ (4x^3)^{4-m}(2y)^m$

Comparing power of x and y in $x^9y$ we get m=1

Thus term for m=1 $=\ ^4C_1\ (4x^3)^{3}(2y)^1=^4C_1=\frac{4!}{(4-1)!1!}(64x^9)(2y)=4(128x^9y)=512x^9y$

Thus the coefficient of $x^9y$ is 512.

Nesterboy [21]1 year ago

5 0

512 is the coefficient of the x9y-term

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1 year ago

tankabanditka [31]

Answer:

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Step-by-step explanation:

Step 1: Formula of volume of a cylinder is pi*r^2*h

where value of pi is 3.14

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h is the height of the bottle (height is different for both bottles)

After putting the values and estimated radius for both as 3.26, we get the volume of the taller bottle.

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Volume of a cylinder = pi*r^2*h (now put the value of the known volume and height of the smaller cylinder)

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2 years ago

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Answer:

Step-by-step explanation:

To aid in understanding, draw three circles...

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2 years ago

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2 years ago

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