Answer:
![$ \frac{\sqrt{3} - 1}{2\sqrt{2}} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B%5Csqrt%7B3%7D%20-%201%7D%7B2%5Csqrt%7B2%7D%7D%20%24)
![$ \frac{-(\sqrt{3} + 1)}{2\sqrt{2}} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B-%28%5Csqrt%7B3%7D%20%2B%201%29%7D%7B2%5Csqrt%7B2%7D%7D%20%24)
![$ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $](https://tex.z-dn.net/?f=%24%20-%20%5Cfrac%7B%5Csqrt%7B3%7D%20-%201%7D%7B%5Csqrt%7B3%7D%20%2B%201%7D%20%24)
Step-by-step explanation:
Given ![$ \frac{11 \pi}{12} = \frac{3 \pi}{4} + \frac{\pi}{6} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B11%20%5Cpi%7D%7B12%7D%20%3D%20%5Cfrac%7B3%20%5Cpi%7D%7B4%7D%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%24)
(A) ![$ sin(\frac{11\pi}{12}) = sin (\frac{3 \pi}{4} + \frac{\pi}{6}) $](https://tex.z-dn.net/?f=%24%20sin%28%5Cfrac%7B11%5Cpi%7D%7B12%7D%29%20%3D%20sin%20%28%5Cfrac%7B3%20%5Cpi%7D%7B4%7D%20%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%24)
We know that Sin(A + B) = SinA cosB + cosAsinB
Substituting in the above formula we get:
![$ sin (\frac{3\pi}{4} + \frac{\pi}{6}) = \frac{1}{\sqrt{2}} . \frac{\sqrt{3}}{2} + \frac{-1}{\sqrt{2}}. \frac{1}{2} $](https://tex.z-dn.net/?f=%24%20sin%20%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20.%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D.%20%5Cfrac%7B1%7D%7B2%7D%20%24)
![$ \implies \frac{1}{\sqrt{2}} (\frac{\sqrt{3} - 1}{2}) = \frac{\sqrt{3} - 1}{2\sqrt{2}}](https://tex.z-dn.net/?f=%24%20%5Cimplies%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20%28%5Cfrac%7B%5Csqrt%7B3%7D%20-%201%7D%7B2%7D%29%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%20-%201%7D%7B2%5Csqrt%7B2%7D%7D)
(B) Cos(A + B) = CosAcosB - SinASinB
![$ cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}}) $](https://tex.z-dn.net/?f=%24%20cos%28%5Cfrac%7B11%5Cpi%7D%7B12%7D%29%20%3D%20cos%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%7D%29%20%24)
![$ \implies \frac{-1}{\sqrt{2}}. \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} . \frac{1}{2} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D.%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20.%20%5Cfrac%7B1%7D%7B2%7D%20%24)
![$ \implies cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}) $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20cos%28%5Cfrac%7B11%5Cpi%7D%7B12%7D%29%20%3D%20cos%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%24)
![$ = \frac{-(\sqrt{3} + 1)}{2\sqrt{2}}](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B-%28%5Csqrt%7B3%7D%20%2B%201%29%7D%7B2%5Csqrt%7B2%7D%7D)
(C) Tan(A + B) = ![$ \frac{Sin(A +B)}{Cos(A + B)} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7BSin%28A%20%2BB%29%7D%7BCos%28A%20%2B%20B%29%7D%20%24)
From the above obtained values this can be calculated and the value is
.
Answer:P(t) = 10t - 400
Step-by-step explanation:
Selling price of each ticket = $10
Cost of setting up the dance= $400
Profit = Revenue - cost
Revenue = price × quantity
Revenue that will maximize profit = 10t
where t= quantity of tickets that maximises profits
Cost = $400
Profit(t) = Revenue - cost
P(t)= 10t - 40
hmu if you need sumin els
Answer:
-5.5
4.5
Step-by-step explanation:
Given:
The numbers to order from least to greatest is given as:
![-5.5, 4.5, 22/7,\sqrt4,-\sqrt{20}](https://tex.z-dn.net/?f=-5.5%2C%204.5%2C%2022%2F7%2C%5Csqrt4%2C-%5Csqrt%7B20%7D)
In order to compare these numbers, we have to convert them in same form.
Let us simplify each number in decimal form.
![-5.5 = -5.5\\\\4.5=4.5\\\\\frac{22}{7}=3.14\\\\\sqrt4=2\\\\-\sqrt{20}=-\sqrt{5\times 2^2}=-2\sqrt5=-4.47](https://tex.z-dn.net/?f=-5.5%20%3D%20-5.5%5C%5C%5C%5C4.5%3D4.5%5C%5C%5C%5C%5Cfrac%7B22%7D%7B7%7D%3D3.14%5C%5C%5C%5C%5Csqrt4%3D2%5C%5C%5C%5C-%5Csqrt%7B20%7D%3D-%5Csqrt%7B5%5Ctimes%202%5E2%7D%3D-2%5Csqrt5%3D-4.47)
So, the least number is one which has the largest value with a negative sign.
Here, -5.5 is the least number.
The next smallest number is -4.47. So, ![-\sqrt{20}](https://tex.z-dn.net/?f=-%5Csqrt%7B20%7D)
The next smallest number is 2. So, ![\sqrt4](https://tex.z-dn.net/?f=%5Csqrt4)
The next smallest number is 3.14. So, ![\frac{22}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7B7%7D)
The greatest number is 4.5.
Therefore, the order from the least to greatest is:
-5.5 <
<
<
< 4.5
Answer:
No , (x-5) is not a factor
Step-by-step explanation:
x⁴ - 3x³ – 9x² - 4x = (x³ + 2x² + x + 1) (x - 5) <u>+ 5</u>