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Scilla [17]
3 years ago
11

9.a )Explain why plane JKL is not an appropriate

Mathematics
1 answer:
VLD [36.1K]3 years ago
6 0

Answer:

I will attach the missing drawing with the answer.

9.b)

Plane JKM

Plane JLM

Plane KLM

Step-by-step explanation:

The drawing for this question is missing. I will attach it with the answer.

9.a) Plane JKL is not an appropriate name for the plane because all of three points lie in the same line.

Through a line pass infinite planes. The plane JKL doesn't define a unique plane. That's why plane JKL isn't an appropriate name for the plane.

9.b) We can name the plane using three points that don't lie in the same line.

Three possible names for the plane are :

Plane JKM

Plane JLM

Plane KLM

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3 years ago
I) Find the first 4 terms in the expansion of
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Answer:

(i)  64+192 x^2+240 x^4+160x^6

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Step-by-step explanation:

<u>Part (i)</u>

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

<u>Part (ii)</u>

<u />(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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Step-by-step explanation:

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