Note that
108° = 90° + 18°
so
sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)
Then
sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1
by the Pythagorean identity.
Answer:
A.) Max at x = 6 and Min at x = -6
Step-by-step explanation:
We say that f(x) has a relative (or local) maximum at x=c if f(x)≤f(c) f ( x ) ≤ f ( c ) for every x in some open interval around x=c . We say that f(x) has an absolute (or global) minimum at x=c if f(x)≥f(c) f ( x ) ≥ f ( c ) for every x in the domain we are working on.
Answer: Choice D) ![y = \pm \sqrt{x+5}](https://tex.z-dn.net/?f=y%20%3D%20%5Cpm%20%5Csqrt%7Bx%2B5%7D)
The steps to finding the inverse will have us swap x and y. Afterward, we solve for y
![y = x^2 - 5 \\\\x = y^2 - 5 \\\\x+5 = y^2 \\\\y^2 = x+5 \\\\y = \pm \sqrt{x+5} \\\\](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%205%20%5C%5C%5C%5Cx%20%3D%20y%5E2%20-%205%20%5C%5C%5C%5Cx%2B5%20%3D%20y%5E2%20%5C%5C%5C%5Cy%5E2%20%3D%20x%2B5%20%5C%5C%5C%5Cy%20%3D%20%5Cpm%20%5Csqrt%7Bx%2B5%7D%20%5C%5C%5C%5C)
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Extra info:
The inverse relation is not a function because of the plus minus. For instance, plugging x = 4 into
leads to y = -3 and y = 3 simultaneously. You would have to apply a domain restriction on
to make it a one-to-one function, to make the inverse a function. One possible domain restriction is
which would lead to the inverse function ![y = \sqrt{x+5}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7Bx%2B5%7D)
![\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BThe%20simplification%20of%20n%7D%5E2%2B3n%2B2n%5Ctext%7B%20is%3A%7D%20%5C%5C%20i%29n%5E2%2B5n%20%5C%5C%20By%5Ctext%7B%20collecting%20common%20term%2C%20this%20can%20be%20written%20in%20form%20of%3A%7D%20%5C%5C%20ii%29%5Ctext%7B%20n%28n%2B5%29%7D%20%5Cend%7Bgathered%7D)
Thus, options A and D hold, from the simplifications above.
Let's consider the validity of the remaining options provided.
![\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BFor%20option%20B%29%7D%20%5C%5C%20%5Ctext%7Bsubstitute%20for%20n%3D1%20into%20the%20expression%20n%7D%5E2%2B3n%2B2n%2C%5Ctext%7B%20we%20have%7D%20%5C%5C%201%5E2%2B3%281%29%2B2%281%29%3D1%2B3%2B2%3D6%20%5C%5C%20%5Ctext%7Bsubstitute%20for%20n%3D1%20into%20the%20expression%206n%2C%20we%20have%7D%20%5C%5C%206%281%29%3D6%20%5C%5C%20%5Ctext%7BThus%2C%20the%20expression%20n%7D%5E2%2B3n%2B2n%5Ctext%7B%20is%20equivalent%20to%206n%2C%20for%20n%3D1%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BFor%20option%20C%29%7D%20%5C%5C%20%5Ctext%7BThe%20expression%20n%7D%5E2%2B3n%2B2n%5Ctext%7B%20does%20not%20simplify%20to%207n%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BFor%20option%20E%29%7D%20%5C%5C%20%5Ctext%7Bsubstitute%20for%20n%3D4%20into%20the%20expression%20n%7D%5E2%2B3n%2B2n%2C%5Ctext%7B%20we%20have%3A%7D%20%5C%5C%204%5E2%2B3%284%29%2B2%284%29%3D16%2B12%2B8%3D36%20%5C%5C%20%5Ctext%7Bsubstitute%20for%20n%3D6%20into%20the%20expression%206n%2C%20we%20have%3A%7D%20%5C%5C%206%284%29%3D24%20%5C%5C%20%5Ctext%7BThus%2C%20the%20two%282%29%20expressions%20are%20not%20equivalent%20to%20each%20other%2C%20for%20n%3D4%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BFor%20option%20F%29%7D%20%5C%5C%20%5Ctext%7Bsubstitute%20for%20n%3D3%20into%20the%20expression%20n%7D%5E2%2B3n%2B2n%2C%5Ctext%7B%20we%20have%3A%7D%20%5C%5C%203%5E2%2B3%283%29%2B2%283%29%3D9%2B9%2B6%3D24%20%5C%5C%20%5Ctext%7Bsubstitute%20for%20n%3D3%20into%20the%20expression%206n%2C%20we%20have%3A%7D%20%5C%5C%206%283%29%3D18%20%5C%5C%20%5Ctext%7BThus%2C%20the%20two%282%29%20expressions%20are%20not%20equivalent%20to%20each%20other%2C%20for%20n%3D3%7D%20%5Cend%7Bgathered%7D)
Hence, the correct options that apply are options A, D, E and F
The correct answer is answered letter send out via email fruing the a syncranus hour is number c