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:
The medical doctor prescribed 0.35 ml of insulin per day.
Step-by-step explanation:
To find out how many millimiters of insulin was prescribed we need to find out how many units we have to took. The doctor prescribed two does of 15 units and 20 units, so the total of units for the day is the sum of the two in this cas 15 + 20 = 35 units. Now we can use a proportion rule, if we have 100 units for 1 ml in 35 units we will have an x amount of ml:
x = 35/100 = 0.35 ml
The medical doctor prescribed 0.35 ml of insulin per day.
To the right: 0.51
to the left: -0.51
<span>Rigid motion does not change the shape of an object. if you move an object to another place, you can think of it as a new object (a copy) at the new position and it will be congruent to the object at the original position. or, if two objects are congruent, you can move one object so it lies on top of the other, showing they are congruent.</span>
