Answer: x=2π/3 and x=4π/3
Step-by-step explanation:
The equation we have is . All we have to do is get cosine alone to find the 2 values of x.
Now that we have our cosine left, we can use our unit circle to figure out when does cosx=-1/2. Cosine is the x value of the coordinate.
x=2π/3
x=4π/3
Answer:
V = 1/6 cubic units
Step-by-step explanation:
Applying the concept of integrals for volume calculation:
(1)
V = volume of the solid bounded by x = a and x = b
S(x) = cross section area of the solid, perpendicular to the x axis
From the figure we have that S is the area of a triangle that has base Z and height Y
Area of the triangle = (2)
Calculation of y(x) and z(x)
We apply the equation of the point-slope line (plane xy):
Slope = (3)
Equation of the line = (4)
Replacing the points (1,0) and (0,1) in (3):
Replacing the point (1,0) and m = -1 in (4):
y(x) = -x + 1 (Line A-B) (5)
We apply the equation of the point-slope line (plane xz):
Slope = (6)
Equation of the line = (7)
Replacing the points (1,0) and (0,1) in (6):
Replacing the point (1,0) and m = -1 in (7):
z(x) = -x + 1 (Line A-C) (8)
Replacing (5) and (8) in (2)
(9)
Replacing (9) in (1) and knowing that a = 0 and b = 1:
evaluated from x=0 to x=1
