Answer:
<em>Both castles will have the same height at 3.33 minutes</em>
Step-by-step explanation:
This problem will be solved with linear modeling, that is, expressing both people's sand castle's height as a function of time.
Justin built a sandcastle 180 cm tall, and its height is losing at 8 cm/min by the effect of wind. Thus, the height of Justin's sandcastle is:
Where t is the time expressed in minutes.
Taylor's sandcastle is initially 160 cm tall. The wind blows away sand at 8 cm/min but she adds sand at 6 cm/min, thus the real loss of sand is 8 cm/min - 6 cm/min= 2 cm/min. Thus, the height of Taylor's sandcastle is:
To find when both castles have the same height, we set:
Simplifying:
6t=20
Solving:
t=20/6=3.33\ minutes
Both castles will have the same height at 3.33 minutes
Answer:
x = 30/π, in general case x=30/π +2πn
Step-by-step explanation:
30 cos(30x) + 14 = -16
30 cos(30x) = -16 - 14
30 cos(30x) = -30
cos(30x)= - 1
30x = π
x = 30/π, in general case x=30/π +2πn
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