Answer:
multiply the left side of the constant vector by the inverse matrix
Step-by-step explanation:
The matrix equation ...
AX = B
is solved by left-multiplying by the inverse of A:
A⁻¹AX = A⁻¹B
IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix
X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix
![\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-4%261%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%267%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B11%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%261%5C%5C3%264%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%267%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%265%5Cend%7Barray%7D%5Cright%5D)
<span>So we want to know how much clay did Joseph add after he built the cone. So the formula for the volume of the cone is V=(1/3)*pi*r^2*h where r is the radius and h is height. We know h1=12cm and r1=6cm, r2=6cm and h2=18 cm. So to get the amount of added clay Va we simply subtract the volume of the clay of the first cone V1 from the volume of the second cone V2: Vd=V2-V1=(1/3)*pi*(r1^2)*h1 - (1/3)+pi*(r2^2)*h2. Va=678.24 cm^3-452.39 cm^3= 266.08 cm^3.</span>
Okay so we just need to find out the pattern...
in this case the pattern is adding..
we did
1 + 4 = 5
2 + 5 = 12
we figure this one out by adding 2 and 5 twice so it look like this
2 + 5 + 5 = 12
now moving on to our next one
3 + 6 = 21
so we added 3 and added 6, three times so look
3 + 6 + 6 + 6 = 21
so now
8 + 11 = 96 because we added 8 and added 11, eight times look..
8 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 = 96
so our answer to 8 + 11 is 96!
hope this helps:)
and don't forget 2
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