Randy rented a rectangular storage shed with the volume of 357 ft does it sheds height is 8 and 1/2 ft and the width of is 6 ft
1 answer:
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Answer:
The set of natural numbers can be denoted as: {} (null set) because no natural number will satisfy the given equation.
Step-by-step explanation:
Given equation:
To find the set of natural numbers that satisfies the above equation.
Solution:
In order to find the set of solutions for the equation, we will solve it for
We have:
Subtracting both sides by 8.
∴
Thus, we get only one solution for that satisfies the given equation but it is not a natural number. -3 is an integer.
Set of natural numbers {1,2,3,4,5,6........}
Thus, we can say the set of natural numbers that satisfies the equation is a null set {}.
Answer:
Step-by-step explanation:
y′′ + 4y′ − 21y = 0
The auxiliary equation is given by
m² + 4m - 21 = 0
We solve this using the quadratic formula. So
So, the solution of the equation is
where m₁ = 3 and m₂ = -7.
So,
Also,
Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,
Substituting A into (1) above, we have
Substituting B into A, we have
Substituting A and B into y, we have
So the solution to the differential equation is