Answer:
b= 11
Step-by-step explanation:
(12x^4 + 17x^3 + 8x - 40) ÷ (x + 2)
<span> =<span><span><span><span><span><span><span>12<span>x^4</span></span>+<span>17<span>x^3</span></span></span>+<span>8x</span></span>−40 / </span><span>x+2</span></span></span></span></span><span> =<span><span><span><span><span>(<span>x+2</span>)</span><span>(<span><span><span><span>12<span>x^3</span></span>−<span>7<span>x^2</span></span></span>+<span>14x</span></span>−20</span>) / </span></span><span>x+2</span></span></span></span></span><span> =<span><span><span><span>12<span>x^3</span></span>−<span>7<span>x^2</span></span></span>+<span>14x</span></span>−<span>20</span></span></span>
You are correct in thinking that the columns of the first matrix must match with the rows of the second matrix.
So for example, we can multiply a 1 x 5 matrix with a 5 x 7 matrix. The two matching '5's are directly what make multiplication possible in this case. For your problem, the first two '3's match and multiplication is possible.
The rows of the first matrix don't need to match with the columns of the second matrix.
a) For this question we set h=59 and solve for t, in order to do so we use the general formula for second-degree equations:
![\begin{gathered} t=\frac{-124\pm\sqrt[]{124^2-4(-16)(-40)}}{2(-16)} \\ t=\frac{-124\pm113.21}{-32} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B-124%5Cpm%5Csqrt%5B%5D%7B124%5E2-4%28-16%29%28-40%29%7D%7D%7B2%28-16%29%7D%20%5C%5C%20t%3D%5Cfrac%7B-124%5Cpm113.21%7D%7B-32%7D%20%5Cend%7Bgathered%7D)
The height of the object will be 59 feet at t=7.41 seconds and t=0.34 seconds.
b) When the object reaches the ground, h=0 therefore:
Solving for t we get:
![\begin{gathered} t=\frac{-124\pm\sqrt[]{124^2-4(-16)(19)}}{2(-16)} \\ t=\frac{-124\pm\sqrt[]{16592}}{-32}=\frac{-124\pm128.81}{-32} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B-124%5Cpm%5Csqrt%5B%5D%7B124%5E2-4%28-16%29%2819%29%7D%7D%7B2%28-16%29%7D%20%5C%5C%20t%3D%5Cfrac%7B-124%5Cpm%5Csqrt%5B%5D%7B16592%7D%7D%7B-32%7D%3D%5Cfrac%7B-124%5Cpm128.81%7D%7B-32%7D%20%5Cend%7Bgathered%7D)
Therefore, since t cannot be negative the solution is t=7.9 seconds.
