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3 years ago

Use the Binomial Theorem Which of the following is equivalent to the expression (m + 3)4

Mathematics

1 answer:

kondor19780726 [428]3 years ago

3 0

Answer:

Step-by-step explanation:

(x+a)^n=nc0x^n+nc1x^{n-1}a+nc2x^{n-2}a^2+...+ncna^n

(x+3)^4=4c0m^4+4c1m^3(3)+4c2m^2(3)^2+4c3m(3)^3+4c4(3)^4

4c0=1

4c1=4/1=4

4c2=(4×3}/(2×1)=6

4c3=(4×3×2)/(3×2×1)=4

4c4=(4×3×2×1)/(4×3×2×1)=1

(m+3)^4=m^4+4m³(3)+6m²(3)²+4m(3)³+3^4

=m^4+12m³+54m²+108m+81

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3 years ago

Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are

Ganezh [65]

Answer:

The values of $a$ and $b$ are $33$ and $\frac{20\sqrt{3}}{3}$ , respectively.

Step-by-step explanation:

The statement is equivalent to the following mathematic expression:

$\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}$ (1)

By definition of the perfect square trinomial:

$25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}$

$33 + 20\sqrt{2} = a + b\cdot \sqrt{6}$

And by direct comparison we have the following system:

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By (3), we solve for $b$ :

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The values of $a$ and $b$ are $33$ and $\frac{20\sqrt{3}}{3}$ , respectively.

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3 years ago

Once upon a time, there was a former whose family raised pigs and chickens. One morning, the farmer's wife looked into the barny

Fed [463]

Using a system of equations, it is found that:

There are 8 chickens in the yard.

There are 16 pigs in the yard.

-----------------------------------------

This question is solved using a system of equations. I am going to say that:

x is the number of chickens.

y is the number of pigs.

-----------------------------------------

A chicken has 1 head, as do a pig.
There are 24 heads.

Thus:

$x + y = 24 \rightarrow y = 24 - x$

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A chicken has 2 feet.
A pig has 4 feet.
In total, there are 80 feet.

Thus:

$2x + 4y = 80$

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Number of chicken:

Since $y = 24 - x$

$2x + 4y = 80$

$2x + 4(24 - x) = 80$

$2x + 96 - 4x = 80$

$2x = 16$

$x = \frac{16}{2}$

$x = 8$

There are 8 chickens in the yard.

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Number of pigs:

$y = 24 - x = 24 - 8 = 16$

There are 16 pigs in the yard.

A similar problem is given at brainly.com/question/24104709

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Use the Binomial Theorem Which of the following is equivalent to the expression (m + 3)4​

Use the Binomial Theorem Which of the following is equivalent to the expression (m + 3)4