The problem statement gives the correct answers for parts (a) and (b). The total number of roots of the characteristic polynomial is the dimension of the matrix: 6. The eigenvalues are the zeros of the characteristic polynomial, 3 (multiplicity 2), 6 (multiplicity 3), and -1.
(c) The matrix is not invertible when one or more eigenvalues is zero. None of yours are zero, so the matrix is invertible.
<span>Try simplifying the number to start. For example, if the population of the town is 100 people and the population growth is 2%, then there will 102 people in the town next year (Y=1). Continue adding 2% to the population for each of 10 years to get the answer for the 10th year. Growth would be considered 100% of current population plus 2% additional for a total of 102% - convert 102% to to a factor and you will have your formula Y=15,200*1.02;18,529</span>
Answer:
The height of the triangle is 5.2 inches
Step-by-step explanation:
we know that
An <u>equiangular triangle</u> is a triangle where all three interior angles are equal in measure
Remember that an equilateral triangle has three equal sides and three equal interior angles
so
An equiangular triangle Is the same that an equilateral triangle. The measure of its interior angles is equal to 60 degrees
Let
h ----> the height of triangle
b ---> the length side of the triangle
Applying Pythagoras Theorem

we have

substitute





see the attached figure to better understand the problem
Well, since it only asking about the product, you don't have to multiply the result
The product would be :
3 x 2 = 6
3x 20 = 3 x 2 x 10 = 60
3 x 200 = 3 x 2 x 10 x 10 = 600
hope this helps
The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.