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3 years ago

Coefficient of y^15x^2 in expansion of (y^3+x)^7

Mathematics

2 answers:

Hitman42 [59]3 years ago

7 0

The coefficient of y∧15×∧2 in expansion of (y∧3+x)∧7 is (15×2)+(3×7)= 51

Bess [88]3 years ago

4 0

Hello,

$(x+y^{3})^7 =
$
$x^7+7x^{6}y^{3}+21x^{5}y^{6}+35x^{4}y^{9}+35x^{3}y^{12}+21x^{2}y^{15}+7xy^{18}+y^{21}\\
$

Coefficient=21=2P7=7*6/2!

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

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3 years ago

Which of the following three-dimensional figures is formed when an equilateral triangle is rotated around the x-axis of the coor

VMariaS [17]

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3 years ago

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P=s1+s2+s3 solve for s3

tresset_1 [31]

P=s1+s2+s3

Move +s1 to the other side. Sign changes from +s1 to -s1

P-s1=s1-s1+s2+s3

p-s1=s2+s3

Move s2 to the other side. Sign changes from s2 to -s2

p-s1-s2=s2-s2+s3

p-s1-s2=s3

Answer: p-s1-s2=s3

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2 years ago

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grin007 [14]

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3 years ago

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According to a bridal magazine, the average cost of a wedding reception for an American wedding is $8213. Assume that the averag

amm1812

Answer:

Point estimate of the corresponding population mean = $8,213

Step-by-step explanation:

Given:

Average cost of a wedding reception (x) = $8,213

Total number of sample (n) = 450

Standard deviation = $2185

Find:

Point estimate of the corresponding population mean

Computation:

Average cost of a wedding reception (x) = Point estimate of the corresponding population mean

Point estimate of the corresponding population mean = $8,213

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3 years ago