Which expression is equivalent to 8/9 divided by 3/4
2 answers:
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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.
11 bottles are needed to fill a 16 liter jug
<em><u>Solution:</u></em>
Given that, there is a 16 liter jug
There are liters of bottle
<em><u>Let us first convert the mixed fraction to improper fraction</u></em>
Multiply the whole number part by the fraction's denominator.
Add that to the numerator.
Then write the result on top of the denominator.
Thus the bottle is of 1.5 liter
We have to find the number of 1.5 liter bottles needed to fill 16 liter jug
Divide 16 by 1.5 to get result
Thus 11 bottles are needed to fill a 16 liter jug