Answer:
0.1 milligrams
Step-by-step explanation:
We have been given that the number of milligrams, m, varies directly with the weight of the dog, w.
We know that two directly proportional quantities are in form
, where y is directly proportional with x and k is constant of proportionality.
Upon substituting our given variables in inversely proportion, we will get:
![m=kw](https://tex.z-dn.net/?f=m%3Dkw)
We have been given that veterinarian knows that a 50-pound dog gets 0.5 milligram of a certain medicine.
Let us find constant of proportionality using our given information.
![0.5=k(50)](https://tex.z-dn.net/?f=0.5%3Dk%2850%29)
![\frac{0.5}{50}=\frac{50k}{50}](https://tex.z-dn.net/?f=%5Cfrac%7B0.5%7D%7B50%7D%3D%5Cfrac%7B50k%7D%7B50%7D)
![k=0.01](https://tex.z-dn.net/?f=k%3D0.01)
So our required equation would be
.
Now, we will substitute
in our equation to solve for medicine needed for a 10-pound dog.
![m=0.01(10)](https://tex.z-dn.net/?f=m%3D0.01%2810%29)
![m=0.1](https://tex.z-dn.net/?f=m%3D0.1)
Therefore, the vet will give 0.1 milligrams of medicine to give a 10-pound dog.