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.
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(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}.
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(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.
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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.
Answer:
31 is a positive number, while -169, -369, and -569 is negative.
Step-by-step explanation:
Negative numbers, are numbers less then 0 and include a negative sign that looks like this "-".
Positive numbers are numbers above 0 and don't include a negative sign.
-169, -369, and -569 is negative because they have a negative symbol and the number is below 0, while 31 is positive because it's above 0 and doesn't include a negative sign.
For this case we must algebraically rewrite the given expression. So:
x: It is the variable that represents an unknown number
"double a number" is represented as: 
"6 less than double a number" is represented as: 
So, the final expression is: 
If we want to rewrite the expression in an equivalent way, we take common factor 2:

Asnwer:

Equivalent expression: 
A new born beluga weighs 6 times as much as a newborn muskox.