The first one and the last one
Answer:
18π ft^2
Step-by-step explanation:
The area of the circle is
pi *r^2
pi * 12^2
144pi
The part that is shaded is 45 degrees
An entire circle is 360 degrees
The fraction that is shaded is 45/360 = 1/8
Multiply the area by the fraction that is shaded
1/8 * 144 pi
18 pi
Equation of a circle in standard form:
(x-h)²+(y-k)²=r²
r=radius
(h,k) is the center.
In this case:
(h,k) =(0,0) (h=0,k=0 )
r=4
Therefore:
(x-0)²+(y-0)²=4²
x²+y²=16
Answer: x²+y²=16
Answer:
first graph is negative
second is undefined
third is zero
fourth is positive
Step-by-step explanation:
If you plug it all in a calculator it will show
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)
