Answer:
SA = 56 sq mi
Step-by-step explanation:
SA = area of base + 1/2(perimeter of base)(slant height)
SA = 16 + 1/2(16)(5)
SA = 16 + 8(5)
SA = 16 + 40
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)
Answer:
b. Right, isosceles
Step-by-step explanation:
right because it has a right angle at the top corner
isosceles because two sides of the triangle are equal to each others
a. The water in the second tank decreases at a faster rate than the water in the first tank. The initial water level in the first tank is greater than the initial water level in the second tank.
Step-by-step explanation:
Step 1:
It is given that the time remaining in first tank is given by the equation y = -10x + 80. We can get the total water in the tank by substituting x = 0 in the equation. The total volume of water in first tank is 80 litres.
Step 2:
The value of y in the equation y = -10x + 80 will be 0 when the tank is fully empty. When y = 0 , 10x = 80, so x = 8. We can conclude that the first tank empties fully in 8 minutes.
In 8 minutes 80 litres of water is emptied from first tank. So the water in the first tank decreases at rate of 80 / 8 = 10 litres per minute
Step 3:
As per the given table for the second tank, 60 litres of water remains when x =0. So the total volume of water in the second tank = 60 litres.
Step 4:
As per the given table for the second tank, the volume becomes 0 in 5 minutes. In 5 minutes 60 litres of water is emptied from second tank. So the water in second tank decreases at rate of 60 / 5 = 12 litres per minute.
Step 5:
The initial volume of water in first tank is higher. The water in second tank decreases at a faster rate than the first tank.
Step 6:
The only correct option is:
a. The water in second tank decreases at a faster rate than the water in the first tank. The initial water level in first tank is greater than the initial water level in the second tank.
