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3 years ago

Factor out coefficient of 3/8d+3/4

Mathematics

1 answer:

Sholpan [36]3 years ago

6 0

The answer is 3(d/8+1/4)

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I) Find the first 4 terms in the expansion of

Katyanochek1 [597]

Answer:

(i) $64+192 x^2+240 x^4+160x^6$

(ii) 1072

Step-by-step explanation:

Part (i)

Using Binomial series formula:

$(2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3$

$=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6$

$=64+192 x^2+240 x^4+160x^6$

Part (ii)

$(1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})$

$=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}$

$(2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)$

$=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...$

There is no need to keep expanding since the remaining will include the variable.

Therefore, the term independent of x = 64 - 1152 + 2160 = 1072

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2 years ago

The graph represents the fees in thousands of dollars, y, depending on the amount invested in millions, x, with one financial in

yanalaym [24]

Answer:

[0.20)

Step-by-step explanation:

I juss know stuff

7 0

3 years ago

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HELP PLZZ!!!!!!!! Look at this equation: 2 H2 + O2 --> 2 H2O. Why isn't there any coefficient in front of oxygen?

HACTEHA [7]

Answer:

D. All of these

Step-by-step explanation:

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3 years ago

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If it takes 13 cup of flour to make 14 of a cake, how many cups of flour are needed to make a whole cake?

kvasek [131]

Answer:

Im guessing you meant it takes 1/3 cups of flour to make 1/4 of a cake not "14"

Step-by-step explanation:

in that case you would do

1/3+1/3+1/3+1/3

or 1/3*4

which would be 4/3

1 1/3

3 0

3 years ago

The total area of a prism can be found by multiplying the perimeter of the base times the height of the prism.

Anna35 [415]

It is false that the total area of a prism can be found by multiplying the perimeter of the base times the height of the prism. If you did that, you'd get the lateral area of that prism, and not the total area. You'd need to add the area of both bases in order to calculate what the total area of a prism is.

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3 years ago