<img src="https://tex.z-dn.net/?f=27%20%5Ctimes%20%5Cpi%20%3D%20%5Cpi%20%5Ctimes%2027" id="TexFormula1" title="27 \times \pi = \

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Reil [10]

2 years ago

pi \times 27" alt="27 \times \pi = \pi \times 27" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Tju [1.3M]2 years ago

6 0

I'm not sure what the question is here. If an answer is communicative property, go with that. If it is asking for $\pi x 27$ , the answer is about 84.8230016469.

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What is the second term in the binomial expansion of (2r – 3s)12? –73,728r11s 73,728r11s 608,256r10s2 –608,256r10s2?

ZanzabumX [31]

Solution:

A is the correct option.

Explanation:

We have been given that $(2r - 3s)^{12}$

The $r^{th}$ term of a binomial expansion $(a+b)^n$ is given by

$t_r=^{n}C_{r-1}a^{n-r+1}b^{r-1}$

For the given binomial expansion, we have

$a=2r,b=-3s,r=2,n=12$

On plugging this value in the above formula, we have

$t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s$

Therefore, the second term is -73728r^11 s

A is the correct option.

3 0

3 years ago

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A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two air

Lemur [1.5K]

Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

$\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ$

Next, we determine the value of Angle B.

$\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ$

Finally, we find b.

$\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)$

The distance between the small plane and the observation tower is 7.9km.

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