Answer: x = pi/6 and x = pi/3.
Step-by-step explanation:
We have the function:
y = x + 2*cos(x)
It will have a horizontal tangent at the point where it's derivate is equal to zero.
Then first let's differentiate y.
y' = dy/dx = 1 - 2*sin(x).
Then we must find the value of x between 0 and 2*pi (or 0° and 360°)
y'(x) = 1 - 2*sin(x) = 0.
Let's solve that:
2*sin(x) = 1
sin(x) = 1/2.
We know that:
sin(30°) = 1/2.
and
Sin(120°) = 1/2
Then let's convert 30° into radians.
We know that:
pi = 180°.
Then:
pi/180° = 1.
30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6
120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.
Then the two values of x are: pi/6 and pi/3.
Answer:
y=-7
Step-by-step explanation:
first, you want variables on one side, numbers on the other side of the equation.
4y+4=2y-10
*plus ten on both side to get rid of -10*
4y+14=2y
*minus 4y on each side to get rid of 4y*
14=-2y
*divide by -2 on each side to get the value of just one y itself*
y=-7
There is no one answer (ordered pair) to this equation and the answer is found by graphing or trying out different values for each variable. Anyway, here are some solutions; (1,0), (4,1), (0,-1/3).
Answer:
Because the dashed triangle is smaller than the original it's a reduction. The scale factor is 1/3 because if we look at the altitudes of the triangle, the original is 6 and the dilated is 2 and 2 / 6 = 1 / 3.
Answer:
$192
Step-by-step explanation:
2400/48=50
50x3.84=192
