Answer:
(a) t = ±2
(b) t ∈ {0, 1}
(c) In navigation terms: east by north. The slope is about 0.42 at that point.
Step-by-step explanation:
(a) dy/dx = 0 when dy/dt = 0
dy/dt = 3t^2 -12 = 0 = 3(t -2)(t +2)
The slope is zero at t = ±2.
__
(b) dy/dx = (dy/dt)/(dx/dt) = <em>undefined</em> when dx/dt = 0
dx/dt = 6t^2 -6t = 6(t)(t -1) = 0
The slope is undefined for t ∈ {0, 1}.
__
(c) At t=3, dy/dx = (dy/dt)/(dx/dt) = 3(3-2)(3+2)/(6(3)(3-1)) = 15/36 = 5/12
The general direction of movement is away from the origin along a line with a slope of 5/12, about 22.6° CCW from the +x direction.
_____
The first attachment shows the derivative and its zeros and asymptotes. It also shows some of the detail of the parametric curve near the origin.
The second attachment shows the parametric curve over the domain for which it is defined, along with the point where t=3.
The maximum height of the projectile is the maximum point that can be gotten from the projectile equation
The projectile reaches the maximum height after 5 seconds
The function is given as:
Differentiate the function with respect to t
Set to 0
So, we have:
Collect like terms
Solve for t
Hence, the projectile reaches the maximum after 5 seconds
Read more about maximum values at:
brainly.com/question/6636648
Answer:
=> Amelia's answer is incorrect
Step-by-step explanation:
Dot plots are used for continuous, quantitative, univariate data. They can be also used for finding outliers, compare distributions, locate the central tendency of your data, etc…
Answer:
3750
Step-by-step explanation:
each number is being multiplied by five
6*5=30
30*5=150
150*5=750
750*5= 3750