Answer:
BC ≈ 19.4 cm
Step-by-step explanation:
using the cosine ratio in the right triangle
cos71° = 
= 
= 
( multiply both sides by BC )
BC × cos71° = 6.3 ( divide both sides by cos71° )
BC = 
≈ 19.4 cm ( to 3 sig. figs )
Answer:
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Step-by-step explanation:
Answer:
Joe's y = 4x + 20 ($20 initial value and a rate of $4 per hr)
slope/rate is $4 per hour and the initial fee/y interceot is 20
Callie's y = 14x (no initial fee and a flat rate if $14 per hr)
slope/rate is $14 per hour and the initial fee/y intercept is 0
Substitute in 3 for x to see who's price is better for 3 hours
y = 4(3) +20 or y = 14(3)
y = $32 y = $42
Callie's has the better deal for 3 hours. Only for 1 hour Joe has the better deal. At 2 hours, both are the same price, and 3 hours plus, Callie will always be cheaper.
Place the dock at (0, 0) in the xy-plane. At 5:00 P.M. boat A is at (0, 0). It's position after 5:00 P.M. is given by (0, -20t) where t is in hours. At 6:00 P.M. boat B is at (0, 0). That's 1 hour after boat A left the point (0, 0) so 1 h x 15 Km/h=15 Km which means at 5:00 P.M. boat B was 15 Km west of the dock at (0, 0) which means it was at (-15, 0) at 5:00 P.M. Boat B's position after 5:00 P.M. is therefore (-15+15t, 0). Use the distance formula to find the distance between the two boats.
<span>d=√((x2-x1)²+(y2-y1)²) </span>
<span>=√((-15+15t-0)²+(0+20t)²) </span>
<span>=√(225-450t+225t²+400t²) </span>
<span>=√(225-450t+625t²) </span>
<span>Find the derivative </span>
<span>d'= (1/2)(225-450t+625t²)^(-1/2)(-450+1250t) </span>
<span>Set equal to zero and you get </span>
<span>-450+1250t=0 </span>
<span>t=450/1250 </span>
<span>=0.36 h=22 minutes </span>
