Find exact solutions of for

Step-by-step explanation:

cos(2x+√3)+cos 2x=0

2 cos (2x+√3+2x)/2 cos (2x+√3-2x)/2=0

or cos(2x+√3/2) cos √3/2=0

or cos (2x+√3/2)=0=cos (2n+1)π/2

or 2x+√3/2=(2n+1)π/2

or x=(2n+1)π/4+√3/4

x=π/4+√3/4=(π+√3)/4,(3π+√3)/4,(5π+√3)4,(7π+√3)/4,(9π+√3)/4,(11π+√3)/4,(13π+√3)/4,(15π+√3)/4

(4π=4×3.14=12.56 nearly)

or

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!