Binomial Expansion

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Question 70

An engineering model for the structural density $\rho\,$ of a composite material, relative to a depth $x$ , is given by the binomial expansion of $3 + kx)^6$ in ascending powers of $x$ . The expansion is written in the form:

\rho = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \dots

where $c_0, c_1, c_2,\,$ and $c_3\,$ are constants.

a.

Find the value of $c_0$ .

[2]

b.

Given that:

$c1=2740c3\displaystyle c_1 = \frac{27}{40} c_3$
$0\,$

Find:

(i) the value of $k$

(ii) the value of $c_2$

[7]

Binomial Expansion

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Question 70

An engineering model for the structural density $\rho\,$ of a composite material, relative to a depth $x$ , is given by the binomial expansion of $3 + kx)^6$ in ascending powers of $x$ . The expansion is written in the form:

\rho = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \dots

where $c_0, c_1, c_2,\,$ and $c_3\,$ are constants.

a.

Find the value of $c_0$ .

[2]

b.

Given that:

$c1=2740c3\displaystyle c_1 = \frac{27}{40} c_3$
$0\,$

Find:

(i) the value of $k$

(ii) the value of $c_2$

[7]

Binomial Expansion

Question 70

Binomial Expansion Questions

Binomial Expansion

Question 70

Binomial Expansion Questions