Performing laplace transform of the equation.
sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)
Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)
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Answer:
m - 7 = -13 + m
Step-by-step explanation:
Answer: total number of teaspoons of spices in the dish =3.25 teaspoons
Step-by-step explanation:
Step 1
Listing the spices and their quantities , we have
Salt = 1/2 teaspoon
Orégano =1 1/4 teaspoon =5/4 teaspoons
Basil = 3/4 teaspoon
Pepper= in half as much pepper as salt -- This means that the quantity of pepper should be 50% more in quantity than salt
Therefore quantity of pepper = 50% x 1/2 = 0.5 x 0.5= 0.25
0.25 + 1/2 = 0.25 + 0.5 = 0.75 = 3/4 teaspoon of pepper.
Step 2
Adding the amount of spices we have
1/2 + 5/4+ 3/4+ 3/4 = 2+ 5+3+ 3/4 = 13/4 = 3 1/4 teaspoons of spices = 3.25 teaspoons of spices .
There are 3 boxes, each box has 93 tangerines.

There are 279 tangerines. They will be divided equally among 9 classrooms.

Each classroom will get 31 tangerines.