For the point P(−19,18) and Q(−14,23), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ.
A certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the rat
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(a) Differentiate each of the components to get r'(t). The rule is
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
The empirical rule you're referring to is the 68-95-99.7 rule, which asserts that for a normal (bell-shaped) distribution, approximately 68% of the distribution lies within 1 standard deviation of the mean; 95% lies within 2 standard deviations of the mean; and 99.7% lies within 3 standard deviations of the mean.
Let be the random variable denoting vehicle speeds along this highway. We want to find
. To use the rule, we need to rephrase this probability in terms of the mean and standard deviation.
Notice that , and
. In other words, 61 and 79 both lie exactly 3 standard deviations away from the mean, so
.