Since the first car travels 55 miles per hour and starts an hour early, by 4:00 it is 55 miles away from the other car. Therefore, the equation is 55+a(some value)+b(another value)=380. If a car travels 55 miles per hour, that means that we add 55 for each hour and 55*x (if x is the number of hours) is the distance traveled. We have accounted for the first hour, so this is similar to saying that they start 55 miles away at 4:00 and go from there. For the other car, since it travels 75 miles per hour, its distance in hours is 75*x (the amount of time spent should be the same if we start at 4:00). Therefore, since they travel away from each other, our total distance is 55+55x+75x=380. Subtracting 55 from both sides (and combining like terms), we get 130x=325. Next, we divide both sides by 130 to get 2.5 hours, or 2 hours and 30 minutes
Answer:
4.9361
Step-by-step explanation:
Rieman sum = ∫∫
ΔA
ΔA = ΔxΔy
Δx =
=
= pi/2 = Δy
ΔA = pi/2 * pi/2 =
Evaluating at the four corners
=
= 2
∫∫
ΔA = 2 *
=
= 4.9361
<h3>
Answer:</h3>
600 m
<h3>
Step-by-step explanation:</h3>
The slope between 1 minute and 2 minutes is ...
... (800 -500)/(2 -1) = 300 . . . . . . m/min
Thus in 20 seconds, 1/3 minute, Jason will fall ...
... (1/3 min)·(300 m/min) = 100 m
This distance is in addition to the 500 m he has already fallen in the first minute.
In 1 min 20 sec, Jason falls 500 m + 100 m = 600 m.
_____
<em>Comment on the graph</em>
We don't expect Jason's rate of fall to change dramatically at the 2-minute mark. We suspect the last point should be (2 2/3, 1000).
We will evaluate Martin's work step by step:
Step 1:
f (x) = sinA,
where
A = arctan x
and
x = tanA
step 1 it's OK
Step 2:
tanA = opp / adj = x / 1
step 2 it's OK
Step 3:
hypotenuse = square root of 1 ^ 2-x ^ 2 = square root of 1-x ^ 2
step 3 it's NOT OK
The correct form in this case is:
hypotenuse = square root of 1 ^ 2 + x ^ 2 = square root of 1 + x ^ 2
Answer:
Martin did make his first mistake in Step 3.