A. All cancel to produce the 0 vector.
b. Each one cancels its opposite except the 8:00 vector which is no longer cancelled by 2:00.
c. 2:00 is 1/3 of the way up from 3:00 x-axis to 12:00 y-axis so fie = pi/6
v= (cos pi/6, sin pi/6) = sqrt 3/2, 1/2
hope it helps
The slope of the current line is -2/7. To find the slope of the line perpendicular to it, find the negative reciprocal of the slope. So it would be 7/2. The y intercept or the b would remain the same so the equation would be y=7/2x+8. Hope this helps.
The range is the set of all valid
y
y
values. Use the graph to find the range.
Interval Notation:
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−
∞
,
∞
)
If she goes 75 mph for 2 hours, that's 150 miles altogether. 45 mph for 1 hour is 45 miles, so 150 + 45 is 195 miles.
Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.