Answer:
the horizontal distance of the pumpkins from the launch site when their heights are the same
Step-by-step explanation:
Hi I think your answer should be 6.28 yards
Answer:
The first set of consecutive even integers equals (8 , 6)
The second set is ( - 8 and - 6) which also works.
Step-by-step explanation:
Equation
(x)^2 + (x + 2)^2 = (x)(x + 2) + 52 Remove the brackets on both sides
Solution
x^2 + x^2 + 4x + 4 = x^2 + 2x + 52 Collect the like terms on the left
2x^2+ 4x+ 4 = x^2 + 2x + 52 Subtract right side from left
2x^2 - x^2 + 4x - 2x + 4 - 52 = 0 Collect the like terms
x^2 + 2x - 48 = 0 Factor
(x + 8)(x - 6) = 0
Answer
Try the one you know works.
x - 6 = 0
x = 6
Therefore the two integers are 6 and 8
6^2 + 8^2 = 100
6*8 + 52 = 100
So 6 and 8 is one set of consecutive even numbers that works.
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What about the other set.
x + 8 = 0
x = - 8
x and x + 2
- 8 and -8 + 2 = - 8, - 6
(- 8 )^2 + (- 6)^2 = 100
(-8)(-6) + 52 = 100
Both sets of consecutive numbers work.
Answer:
n times 5
Step-by-step explanation:
A matrix Anxn of this way is called an upper triangular matrix. It can be proved that the determinant of this kind of matrix is
In this case, it would be 5+5+...+5 (n times) = n times 5
We are going to develop each determinant by the first column taking as pivot points the elements of the diagonal
![det\left[\begin{array}{cccc}5&a_{12}&a_{13}...&a_{1n}\\0&5&a_{23}...&a_{2n}\\...&...&...&...\\0&0&0&5\end{array}\right] =5+det\left[\begin{array}{ccc}5&a_{23}...&a_{2n}\\0&5&a_{3n}\\...&...&...\\0&0&5\end{array}\right]=5+5+...+det\left[\begin{array}{cc}5&a_{n-1,n}\\0&5\end{array}\right]=5+5+...+5+5\;(n\;times)](https://tex.z-dn.net/?f=det%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D5%26a_%7B12%7D%26a_%7B13%7D...%26a_%7B1n%7D%5C%5C0%265%26a_%7B23%7D...%26a_%7B2n%7D%5C%5C...%26...%26...%26...%5C%5C0%260%260%265%5Cend%7Barray%7D%5Cright%5D%20%3D5%2Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26a_%7B23%7D...%26a_%7B2n%7D%5C%5C0%265%26a_%7B3n%7D%5C%5C...%26...%26...%5C%5C0%260%265%5Cend%7Barray%7D%5Cright%5D%3D5%2B5%2B...%2Bdet%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26a_%7Bn-1%2Cn%7D%5C%5C0%265%5Cend%7Barray%7D%5Cright%5D%3D5%2B5%2B...%2B5%2B5%5C%3B%28n%5C%3Btimes%29)
