Radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time
t (in weeks), then dQ dt = −rQ, where r > 0 is the decay rate.
A) If 500 mg of a mystery substance decays to 83.01 mg in 5 weeks, determine the decay rate r.
B) Find an expression for the amount of this substance present at any time t.
C) Find the time required for the substance to decay to one-half its original amount.
A) If 500 mg of a mystery substance decays to 83.01 mg in 5 weeks, determine the decay rate r.
B) Find an expression for the amount of this substance present at any time t.
C) Find the time required for the substance to decay to one-half its original amount.
1 answer:
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Given:
Point (7,12) is rotated 1260° counterclockwise about the origin.
To find:
The x-coordinate of the point after this rotation.
Solution:
If a point is rotated 360 degrees then its coordinates remains unchanged.
If a point is rotated 180 counterclockwise about the origin degrees, then
We know that,
After rotation the coordinates of points remains same, i.e., (7,12). So, after that (7,12) is rotated 180° counterclockwise about the origin.
The point (7,12) becomes (-7,-12) after rotation of 1260° counterclockwise about the origin.
Therefore, the x-coordinate of the required point is -7.