The answer is No, they are not proportional. This is because 8/42 is not equal to 20/105.
I believe 10c-4d would be your answer
Answer:
-3
1 + 4 sqrt( 241 )
1 - 4 sqrt( 241 )
Step-by-step explanation:
We need minus lambda on the entries down the diagonal. I'm going to use m instead of the letter for lambda.
[-43-m 0 80]
[40 -3-m 80]
[24 0 45-m]
Now let's find the determinant
(-43-m)[(-3-m)(45-m)-0(80)]
-0[40(45-m)-80(24)]
+80[40(0)-(-3-m)(24)]
Let's simplify:
(-43-m)[(-3-m)(45-m)]
-0
+80[-(-3-m)(24)]
Continuing:
(-43-m)[(-3-m)(45-m)]
+80[-(-3-m)(24)]
I'm going to factor (-3-m) from both terms:
(-3-m)[(-43-m)(45-m)-80(24)]
Multiply the pair of binomials in the brackets and the other pair of numbers;
(-3-m)[-1935-2m+m^2-1920]
Simplify and reorder expression in brackets:
(-3-m)[m^2-2m-3855]
Set equal to 0 to find the eigenvalues
-3-m=0 gives us m=-3 as one eigenvalue
The other is a quadratic and looks scary because of the big numbers.
I guess I will use quadratic formula and a calculator.
(2 +/- sqrt( (-2)^2 - 4(1)(-3855) )/(2×1)
(2 +/- sqrt( 15424 )/(2)
(2 +/- sqrt( 64 )sqrt( 241 )/(2)
(2 +/- 8 sqrt( 241 )/(2)
1 +/- 4 sqrt( 241 )
Smaller!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(a)10 modules per floor
(b)Two different rectangular prism
Step-by-step explanation:
<u>Part A</u>
Number of modules=130
Number of stories=13
Since all of the modules were divided evenly among the number of stories:
Number of module per floor =130÷13=10 modules per floor
There would be 10 modules on each floor.
<u>Part B</u>
Next, we determine how many different rectangular prisms could be made from the number 10 derived above.
Step 1: List the factors of 10
Factors of 10 are: 1,2,5 and 10
Step 2:
Form a product of three terms which equals 10 using the factors derived above. We have two possible combinations:
Therefore, two different rectangular prisms could be made from the number of modules on each floor.
