Cos( 6 x ) = 1/2
6 x = 60° ⇒ x 1 = 10°
6 x = 300° ⇒ x 2 = 50°
6 x = 420° ⇒ x 3 = 70°
6 x = 660° ⇒ x 4 = 110°
x 5 = 130°, x 6 = 170°, x 7 = 190° , x 8 = 230°, x 9 = 250°,
x 10 = 290°, x 11 = 310°, x 12 = 350°
Answer: there are 12 solutions on the interval ( 0 , 2π ).
Answer:
f(x) and g(x) have the same x-intercepts (is <em>not true</em>)
Step-by-step explanation:
g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)
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<em>Comment on the question/answer</em>
f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)
Step-by-step explanation:
c/(c - 5) = 4/(c - 4)
By Cross-multiplying,
We have c(c - 4) = 4(c - 5).
=> c² - 4c = 4c - 20
=> c² - 8c + 20 = 0
Since the discriminant is negative,
there are no real solutions for c.
However, there exist complex solutions for c.
Using the Quadratic Formula,
c = [8 ± √(-16)]/2
=> c = 4 ± √(-4)
=> c = 4 ± 4i or c = 4(1 ± i).
C
6x^2-13X-5=0
(3X+1)(2X-5)
3x-1=0
X=1/3. 2x-5=0. X= 5/2
The answer would be D, 2 cm represents 12 cm. 2/12=1/6
