Multiplying both sides by cos x and dividing both sides by tan x results in
<span>cos x = (sin x)/(tan x), and sticking in the numbers gives </span>
<span>cos x = 0.99/7.07 = 0.14.</span>
Sin 2x - sin x=0
Using the trigonometric identity: sin 2x=2 sinx cosx
2 sinx cosx - sinx =0
Common factor sinx
sinx ( 2 cosx -1)=0
Two options:
1) sinx=0
on the interval [0,2π), the sinx=0 for x=0 and x=<span>π=3.1416→x=3.14
2) 2 cosx - 1=0
Solving for cosx
2 cosx-1+1=0+1
2 cosx = 1
Dividing by 2 both sides of the equation:
(2 cosx)/2=1/2
cosx=1/2
cosx is positive in first and fourth quadrant:
First quadrant cosx=1/2→x=cos^(-1) (1/2)→x=</span><span>π/3=3.1416/3→x=1.05
Fourth quadrant: x=</span>2π-π/3=(6π-π)/3→x=5<span>π/3=5(3.1416)/3→x=5.24
Answer: Solutions: x=0, 1.05, 3.14, and 5.24</span>
so we have those critical values, which gives us the intervals of (-∞, 0] , [0, 6] and [6, +∞).
where is it increasing or decreasing? well, that's just a matter of checking a value on each region for the the first derivative, namely the first derivative test.
we can check for f(-1) = 12(-1)² - 72(-1), is a positive value, increasing.
and check f(1) = 12(1)² - 72(1), is a negative value, decreasing.
and check f(7) = 12(7)² - 72(7), positive, so increasing.
check the picture below, and you can see there which are the minima or maxima.
Answer:
The negative solution
-2
Step-by-step explanation:
Let the number be
Then 5 times the number is 5x.
14 less than the square of the number is
So our equation becomes
This implies that
We factor to get:
Answer:
60cm
Step-by-step explanation:
Length of 1 side = 5cm [ A cube has 12 edges]
Length of 12 sides = 5*12
= 60cm
