Find all solutions to the equation cos x cox(3x)+sin x sin(3x)=0 on the interval [0,2pi]

Step-by-step explanation:

cos x cos (3x)+sinx sin (3x)=0

cos (x-3x)=0

cos(-2x)=0

cos 2x=0=cos (2n+1)π/2

where n=0,1,2,3∞∞∞∞

2x=(2n+1)π/2

x=(2n+1)π/4

put n=0,1,2,3

x=π/4,3π/4,5π/4,7π/4

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950