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.
<span>14 = GCF of M and 210
M = possible values
GCF = Greatest common denominator
Now, let’s start decomposing
=> 210 | 2
=> 105 | 2
=> 35 | 5
=> 7 | 7
=> 1
Thus, 2 x 3 x 5 x 7 = 210
Now let’s find the factors of 14
=> 14 | 2
=> 7 | 7
=> 1
Thus, 2 x 7 = 14
Notice that’s there’s no 14 in 210 shown factors, but the only GCF found is 7.
Thus, the value of M that we’re looking for is infinite. All numbers that has
the GCF of 7 are applicable.</span>
Given:
Given the inequalities:4
Required: Identify the inequality in which x = 8 is a solution.
Explanation:
Substitute 8 for x in each inequality and check whether it satisfies the inequality.
Consider 4x + 3 > 0.
So, x = 8 satisfies the inequality 4x + 3 > 0.
Consider 9x - 5 < 100.
So, x = 8 satisfies the inequality 9x - 5 < 100.
Consider x + 4 ≤ 10.
So, x = 8 not satisfies the inequality.
Consider 72 ÷ x ≥ 4.
So, x = 8 satisfies the inequality.
Final Answer: The inequality in which x = 8 is not a solution is x + 4 ≤ 10.
Answer:
9
Step-by-step explanation:
