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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Answer:
see below for drawings and description
Step-by-step explanation:
For geometry problems involving translation, rotation, and reflection—transformations that change location, but not size ("rigid" transformations)—it might be helpful for you to trace the image onto tracing paper or clear plastic so that you can manipulate it in the desired way. Eventually, you'll be able to do this mentally, without the aid of a physical object to play with.
For the images attached here, I copied the triangle onto a piece of clear plastic so I could move it to the desired positions. The result was photographed for your pleasure.
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a. Translation means the image is moved without changing its orientation or dimensions. You are asked to copy the triangle so that the upper left vertex is moved to what is now point E. See the first attachment.
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b. Reflection means the points are copied to the same distance on the other side of the point or line of reflection. Just as an object held to a mirror has its reflection also at the mirror, any points on the line of reflection do not move. Reflection flips the image over. See the second attachment.
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c. Rotation about point D means point D stays where it is. The angle of rotation is the same as the angle at D, so the line DE gets rotated until it aligns with the line DF. The rest of the triangle maintains its shape. See the third attachment.
