Verify the identity.cos 3x = cos3 x - 3 sin2 x cos x

What will be an ideal response?

cos 3x = cos (2x + x) = cos 2x cos x - sin 2x sin x = = = cos³ x - 3 sin² x cos x.

Mathematics

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Decide whether the statement is true or false.For no real number y, |y| < 0 and y3 > 0.

A. True B. False

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Mathematics

Solve by graphing. Label the axes and show where the solution is located on the graph.The value, v, in hundreds of dollars, of Juan's computer is approximated by where t is the number of years since he first bought the computer.(a) Sketch the graph the equation.(b) Find the missing coordinate for the ordered pair solution (4, ? ).(c) Interpret the point from part (b).(d) Find and interpret the y-intercept.(e) What does the x-intercept represent in this problem?

A. (a)

(b) (4, 600); (c) The value of Juan's computer
is $600 after 4 years of ownership.; (d) The
y-intercept, (0, 1200) indicates that the value
of Juan's computer was $1200 when he first
bought it.; (e) The x-intercept, (8, 0)
indicates that after 8 years, Juan's computer
will be worthless ($0).
B. (a)

(b) (4, 1800); (c) The value of Juan's computer
is $1800 after 4 years of ownership.; (d) The
y-intercept, (0, 1200) indicates that the value
of Juan's computer was $1200 when he first
bought it.; (e) The x-intercept, (8, 0)
indicates that after 8 years, Juan's computer
will be worthless ($0).
C. (a)

(b) (4, 1800); (c) The value of Juan's computer
is $1800 after 4 years of ownership.; (d) The
y-intercept, (0, 1200) indicates that the value
of Juan's computer was $1200 when he first
bought it.; (e) The x-intercept, (12, 0)
indicates that after 12 years, Juan's computer
will be worthless ($0).
D. (a)

(b) (4, 600); (c) The value of Juan's computer
is $600 after 4 years of ownership.; (d) The
y-intercept, (0, 1200) indicates that the value
of Juan's computer was $1200 when he first
bought it.; (e) The x-intercept, (12, 0)
indicates that after 12 years, Juan's computer
will be worthless ($0).