Answer:
The correct answer is option 4
(The value of the expression is 7)
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<span>4.98 ft/s
Let's determine the distance between the man and the woman for the moment that she's been walking 15 minutes. For this you can create a right triangle where one leg is 500 ft long (the east west difference between their locations) and the other leg is (distance man walked for 20 minutes + distance woman walked for 15 minutes). So
Distance man walked = 20 min * 60 s/min * 2 ft/s = 2400 ft.
Distance woman walked = 15 min * 60 s/min * 3 ft/s = 2700 ft.
So the north south different in the man and woman's location is 2400+2700 = 5100 ft and will be increasing by 5 ft/sec.
Creating a function of time (in seconds) for the distance the two people are apart is
f(t) = sqrt(500^2 + (5100 + 5t)^2)
where
t = number of seconds from the 15 minutes the woman has been walking.
For rate of change, you want the first derivative of the function. So let's calculate it.
f(t) = sqrt(500^2 + (5100 + 5t)^2)
f(t) = sqrt((5100 + 5t)^2 + 250000)
f'(t) = d/dt[ sqrt((5100 + 5t)^2 + 250000) ]
f'(t) = 0.5((5t + 5100)^2 + 250000)^(-0.5) * d/dt[ (5t + 5100)^2 + 250000 ]
f'(t) = d/dt[ (5t + 5100)^2 ] / (2 * sqrt((5t + 5100)^2 + 250000))
f'(t) = 2(5t + 5100) * d/dt[ 5x + 5100 ]/(2 * sqrt((5t + 5100)^2 + 250000))
f'(t) = 5(5t + 5100/sqrt((5t + 5100)^2 + 250000)
f'(t) = (25t + 25500)/sqrt((5t + 5100)^2 + 250000)
Now calculate f'(t) for t = 0. So
f'(t) = (25t + 25500)/sqrt((5t + 5100)^2 + 250000)
f'(0) = (25*0 + 25500)/sqrt((5*0 + 5100)^2 + 250000)
f'(0) = 25500/sqrt((5100)^2 + 250000)
f'(0) = 25500/sqrt(26010000 + 250000)
f'(0) = 25500/sqrt(26260000)
f'(0) = 25500/5124.45119
f'(0) = 4.976142626 ft/sec
So the man and woman are moving away from each other at the rate of 4.98 ft/s.</span>
Could you do 31 add 31 which would also be 31 multiplyed by 2
hope this helps
R=(0,2), T=(4,2)
vector:
v=(4-0,2-2)=(4,0)
v/2=(2,0)
(0,2)+v/2=(2,2)
so (2,2) is the midpoint
<h3>
Answer: d. Contingency table</h3>
Explanation:
It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.
We can have the responses along the rows and the party affiliation along the columns, or vice versa.
See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).