Hello :
f(x) = sin²(x) +cos(x)
the dirivate is : f'(x) = 2sin(x) cos(x) -sin(x) because :
( sin²(x) )' = 2sin(x) cos(x) and (cos(x))' = - sin(x)
f'(x) = 0 : sin(x) (2cos(x) - 1) = 0
sin(x) = 0 : x = k <span>π k in Z
</span>2cos(x) - 1 =0 : 2cos(x) =1
cos(x) = 1/2 = cos( π /3)
x = π /3 +2k π or x = - π /3 +2k π
in intervall : <span> <span>[0
, 2π] :
k=0 : x= 0 f(0) = 1 ( </span></span>minimum<span>)
</span>k=1 : x = π f(π) = -1 (<span>minimum)
x= </span> π /3 f ( π /3 ) = 1.25 ( <span>maximum)</span>
For this case we define the following variable:
- <em>x: number of stamps
</em>
We now write the equation that models the problem:
From here, we clear the value of x.
We have then:
Answer:
The number of stamps he has is:
If the track is 10km long, and X travels at 40 km/h, it will take 1 hour to do 4 laps. this means that car X will do one lap in 15 minutes. Y travels at 30 km/h, which means it will do 3 laps in 1 hour, meaning that car X will do 1 lap in 20 minutes.
X- 15, 30, 45, 60
Y-20, 40, 60
Therefore, after an hour, they will pass again.
The pic is blurry, but looks like 18x²-21x-15
(3x-5)(6x+3) is the factored form.
3 and 6 are the factors of 18
-5, 3 or -3, 5 are the factors of -15
I line them up like this
3 -5
6 3
then I multiple them diagonally: 3*3=9, -5*6=-30, the sum of 9 and -30 is exactly -21, the coefficient for x. (If the sum doesn't make -21, I'd switch -5 and 3, or change to -3 and 5 to try again.)
so the factored form is (3x-5)(6x+3)
Vanilla, Chocolate, Mint. Convert them all to percents, it's the easiest.
