Answer:
It will take 50 years to decay from 512 grams to 121.5 grams.
Step-by-step explanation:
The decay formula :

where
N= amount of substance after t time
N₀= initial of substance
t= time.
A substance decays at a rate 25% every 10 years.
So, remaining amount of the substance is = (100%-25%)= 75%
, t= 10



Taking ln both sides



Now , N₀= 512 grams, N= 121.5 grams, t=?




Taking ln both sides




⇒t=50 years
It will take 50 years to decay from 512 grams to 121.5 grams.
Answer:
The distance is:
Step-by-step explanation:
We re-write the equation of the line in the format:
Notice we divided the fraction of y by 2/2, and the fraction of z by 3/3.
In that equation, the director vector of the line is built with the denominators of the equation of the line, thus:
Then the parametric equations of the line along that vector and passing through the point (-2, 3, -4) are:
We plug them into the equation of the plane to get the intersection of that line and the plane, since that intersection is the image on the plane of the point (-2, 3, -4) parallel to the given line:
Then we solve that equation for t, to get:
Then plugging that value of t into the parametric equations of the line we get the coordinates of the intersection:
Then to find the distance we just use the distance formula:
So we get:
Answer: 1:3
Step-by-step explanation: for every pear she uses 3 apples