A heat-seeking particle is located at the point P on a flat metal plate whose temperature at a point x , y is T x , y . Find parametric equations for the trajectory of the particle if it moves continuously in the direction of maximum temperature increase. T x , y = 5 − 4 x 2 − y 2 ; P 1 , 4
A heat-seeking particle is located at the point P on a flat metal plate whose temperature at a point x , y is T x , y . Find parametric equations for the trajectory of the particle if it moves continuously in the direction of maximum temperature increase. T x , y = 5 − 4 x 2 − y 2 ; P 1 , 4
A heat-seeking particle is located at the point
P
on a flat metal plate whose temperature at a point
x
,
y
is
T
x
,
y
.
Find parametric equations for the trajectory of the particle if it moves continuously in the direction of maximum temperature increase.
Find a pair of parametric equations for y=
3(2-5)² +2. Show all your work for full credit.
A watermelon is launched by a catapult with an initial velocity of 89 feet per second and an angle of 61∘ to the horizontal. If the watermelon is launched with an initial height of 9 feet, thus the parametric equations for the watermelon's motion is x(t)=(89cos61∘)t, y(t)=−16t2+(89sin61∘)t+9.
After how many seconds does the watermelon reach its maximum height? (Round your answer to the nearest tenth if necessary.)
Two objects E and F are traveling by the following parametrically defined functions
x = 2t - 4 x = 2ty = t - 1 y = t + 1
a. If the paths of the objects E and F intersect at (6,4), at what time do they intersect if the parameter t stands for time?
b. Write an equation d(t) that represents the distance between the two objects E and F at any point in time. Graph d(t).
c. What do you notice about the graph of d(t)? What does this tell us about the objects E and F?
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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