Answer:
The solutions are linearly independent because the Wronskian is not equal to 0 for all x.
The value of the Wronskian is
Step-by-step explanation:
We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.
Thus replacing the functions of the exercise we get:
Working with the determinant we get
Thus we have found that the Wronskian is not 0, so the solutions are linearly independent.
The first triangle has a perimeter of 4+6+10 = 20.
The 2nd longest side is 6/20 = 3/10 of the perimeter. In the larger triangle, the 2nd longest side will have length (3/10)*60 = 18.
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These side lengths mean the "triangle" is a line segment. That is, it has zero area.
Answer:
Acute angle = 30°
Obtuse angle = 150°
Step-by-step explanation:
Method 1:
Let x represent the measurement of the obtuse angle
Obtuse angle = x
Acute angle = ⅕ of x = x/5
Thus:
x + x/5 = 180° (angels on a straight line)
Solve for x
(5x + x)/5 = 180
Multiply both sides by 5
5x + x = 180 × 5
6x = 900
x = 900/6
x = 150
Obtuse angle = 150°
Acute angle = x/5 = 150/5 = 30°
Method 2:
Since acute angle = ⅕ of the obtuse angle, therefore,
Obtuse angle = 5*acute angle
Let acute angle = x
Obtuse angle = 5x
Equation:
5x + x = 180° (angles on a straight line)
Solve for x
6x = 180
x = 180/6
x = 30
Acute angle = x = 30°
Obtuse angle = 5x = 5*30 = 150°
Answer:
There is money left over. They have 48.98 dollars left.
Step-by-step explanation:
Men costumes in total cost $102.68 and women costumes in total cost $248.34. There budget it $400 so we add both the men and women costumes together which is $351.02 which means that they do have left over money. To find the left over money, we have to subtract $400 from $351.02 which is equal to $48.98.