The dimensions would be 29 by 29.
To maximize area and minimize perimeter, we make the dimensions as close to equilateral as possible.
Dividing the perimeter by the number of sides, we have
116/4 = 29
This means that both length and width can be 29.
5/68
5 can go into 68 13 times with a remainder of 3
So we add a decimal point and a zero.
Carry the 3 and zero down making 30
5 can go into 30 6 times making the answer 13.6
Answer: cannot be true because cot∅ is less than zero in quadrant 2.
Step-by-step explanation:
Apex trigonometry 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 )
Answer:
-7
Step-by-step explanation:
The line (y-1)=(2/3)(x+1) contains point (a,-3)
=> (-3-1) = (⅔)(a+1)
-4 = (⅔)(a+1(
(a+1)= -4 ÷ ⅔
a + 1 = -4 × 3/2
a+ 1 = -6
a = -6-1
a = -7
