Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Answer:
Step-by-step explanation: <u>Speed</u> is distance an object travelled per unit time.
It is represented by letter v and can assume various units.
1) 

v = 18 miles per hour
Her average speed is 18 mph.
2) Rearraging formula for distance:
d = v.t
d = 70 * 4
d = 280 miles
You would travel 280 miles.
3) 

v = 52.5 mph
My average speed is 52.5 mph.
4) Rearranging formula to determine time:


t = 2.34 hours
It will take 2 hours and half to arrive in Leeds. So, we will be expected to arrive at 12:04.
5) The unit change but the way of calculating time is the same.

t = 500 s
or t = 8.34 minutes
It will take, for an athlete to run 2000m, 8.34 minutes.
6) a) All units must match, so for a speed in mph:
45 minutes is 0.75 hours. Total time is 8.75 hours.

v = 560 mph
The average speed is 560 mph.
b) 

t = 6.67 hours
Sam will take 6.67 hours to covered the distance.
At the start, the tank contains
(0.25 lb/gal) * (100 gal) = 25 lb
of sugar. Let
be the amount of sugar in the tank at time
. Then
.
Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

Separate variables, integrate, and solve for <em>S</em>.







Use the initial value to solve for <em>C</em> :


The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

has passed. At this time, we want the tank to contain
(0.5 lb/gal) * (5 gal) = 2.5 lb
of sugar, so we pick <em>P</em> such that

B: (0, a)
C should have the same y value as B
D: (a,0)
C should have the same x value as D
So point C is (a,a)
Since point A is on the origin, its point is (0,0)
You use the slope formula and plug in point A and C:



m = 1
So the value that belongs in the green box is 1
Answer:
B
Step-by-step explanation: