sin(<em>θ</em>) + cos(<em>θ</em>) = 1
Divide both sides by √2:
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = 1/√2
We do this because sin(<em>x</em>) = cos(<em>x</em>) = 1/√2 for <em>x</em> = <em>π</em>/4, and this lets us condense the left side using either of the following angle sum identities:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
cos(<em>x</em> - <em>y</em>) = cos(<em>x</em>) cos(<em>y</em>) - sin(<em>x</em>) sin(<em>y</em>)
Depending on which identity you choose, we get either
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = sin(<em>θ</em> + <em>π</em>/4)
or
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = cos(<em>θ</em> - <em>π</em>/4)
Let's stick with the first equation, so that
sin(<em>θ</em> + <em>π</em>/4) = 1/√2
<em>θ</em> + <em>π</em>/4 = <em>π</em>/4 + 2<em>nπ</em> <u>or</u> <em>θ</em> + <em>π</em>/4 = 3<em>π</em>/4 + 2<em>nπ</em>
(where <em>n</em> is any integer)
<em>θ</em> = 2<em>nπ</em> <u>or</u> <em>θ</em> = <em>π</em>/2 + 2<em>nπ</em>
<em />
We get only one solution from the second solution set in the interval 0 < <em>θ</em> < 2<em>π</em> when <em>n</em> = 0, which gives <em>θ</em> = <em>π</em>/2.
Get into ax²+bx+c=0 form
subsitute u=x⁴
x⁸-3x⁴+2=0
(x⁴)²-3(x⁴)+2=0
u²-3u+2=0
factor
(u-2)(u-1)=0
set to zero
u-2=0
u=2
u-1=0
u=1
wait, u=x⁴
2=x⁴
![\sqrt[4]{2}=x](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%7D%3Dx)
1=x⁴
+/-1=x
the subsitution is u=x⁴
and the possible values for x are -1,
, and 1
Given : A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week . and graph
To Find : Maximum profit , breakeven point , profit interval
Solution:
The maximum profit the florist will earn from selling celebration bouquets is $ 675
peak of y from Graph
The florist will break-even after Selling 20 one-dollar decreases.
at breakeven
Break even is the point where the profit p(x) becomes 0
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0 ,20).
after 20 , P(x) is - ve
You got 8 questions wrong.
10% of 50 is 5.
x8 x8
________________
80% of 50 is 40.
84% of 50 is 42.
50-42= 8 questions wrong.
