A bee with velocity vector r ′ ( t ) starts out at the origin at t = 0 and flies around for T seconds. Where is the bee located at time T if ∫ T 0 r ′ ( u ) d u = 0 ? What does the quantity ∫ T 0 ∥ r ′ ( u ) ∥ d u represent?

At time T the bee will be at (0,0).

The quantity represents the integral of function with the time interval of (0,T).

Step-by-step explanation:

Given :

As we already know that

Thus we can say that

Now,          

So at time T the bee will be at (0,0).

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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