800+75h=a. 800 is what she started with so you have to add that on to the 75 acorns per hour she gets, since you don't know how many hours the variable remains h and a is going to represent the total number at the end
Answer:
x= 3
y=2
Step-by-step explanation:
-3x + 9y = 9 ----------- equation 1
3x + 2y = 13--------------- equation 2
In Matrix Form
![\left[\begin{array}{cc}-3&9\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}9\\13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-3%269%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C13%5Cend%7Barray%7D%5Cright%5D)
Let A = ![\left[\begin{array}{cc}-3&9\\3&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-3%269%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D)
X = ![\left[\begin{array}{c}x\\y\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D)
and B = ![\left[\begin{array}{c}9\\13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C13%5Cend%7Barray%7D%5Cright%5D)
Then Mathematically AX= B
or X= A⁻¹ B
Where A⁻¹ = Adjacent A/ mod of A
Adjacent A = ![\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-9%5C%5C-3%26-3%5Cend%7Barray%7D%5Cright%5D)
Mod Of A= -6 - (27) = -33 which is not equal to zero
so Putting These values in the given formula
X= 1/-33
Now Multiplying Rows and Columns
= -1/33 ![\left[\begin{array}{cc}2*9+- 9*13\\-3*9 +- 3*13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%2A9%2B-%209%2A13%5C%5C-3%2A9%20%2B-%203%2A13%5Cend%7Barray%7D%5Cright%5D)
Solving the Matrix we get
= -1/33 ![\left[\begin{array}{cc}18-117\\-27-39\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D18-117%5C%5C-27-39%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= -1/33 ![\left[\begin{array}{cc}-99\\-66\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-99%5C%5C-66%5Cend%7Barray%7D%5Cright%5D)
From Here we find x= 99/33 or 3
and y = 66/33= 2
Answer:
2√6 m
Step-by-step explanation:
The formula for the vol. of a cone is V = (1/3)(area of base)(height).
Here, V = 20π m³ = (1/3)(area of the base)(10 m)
We need to solve for (area of the base).
Multiplying both sides of this equation by (3/10) results in:
(3/10)(20 π m³) = (area of the base)
This simplifies to 6π m² = (area of the base)
We still must find the diameter of the base. Let's find the radius of the base first: The formula for the area of a circle is A = πr². Here we have 6π m² = πr², which tells us that r² = 6 m². Since d = 2r, and r = d/2, r² = d²/4. Then the equation 6 m² = r² becomes:
6 m² = d²/4.
Solve this for d. Multiplying both sides by 4, we get:
24 m² = d²2, and d = √(24 m²) = 2√6 m
The cone diameter is 2√6 m.
