Answer:
x = 6
Step-by-step explanation:
x = 3 sin(90) / sin (30)
x = 3(1)/(1/2)
x = 3 ÷ 
x = 6
By definition, the slope of a curve is the rate of change of the independent and dependent variables. When graphed in a Cartesian plane, the slope between any two point on the curve is equal to Δy/Δx. However, we should not that only a linear function has a constant slope. For this problem, the equation is quadratic. Hence, you must specify the point where we should get the slope.
In calculus, the slope is the first derivative of the equation:
<span>y=3x</span>²<span>-8
dy/dx = slope = 6x - 0
Thus, the slope at any point of the curve is 6x. For instance, you want to find the slope of the curve at point (1,1), then the slope is equal to 6(1) = 6 units.</span>
Answer:
The solution of the system of equations is, (1,-1,2)
Step-by-step explanation:
Given system equation;
x + 5y - 3z = -10
-5x + 6y – 5z = -21
-x + 8y - 8z = -25
Matrix form is written as;
![\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%265%26-3%5C%5C-5%266%26-5%5C%5C-1%268%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C6%26-5%5C%5C8%26-8%5Cend%7Barray%7D%5Cright%5D%20-5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%5D%20-3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%28-8%29%20-5%2835%29-3%28-34%29%3D%20-8%20-%20175%2B%20102%20%3D%20-81)
Cofactor;
![First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\](https://tex.z-dn.net/?f=First%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%206%26-5%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%20-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5B-8%20%20%5C%20%5C%20-35%20%5C%20%5C%20-34%5D%5C%5C%5C%5C%5C%5C%5C%20Second%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%205%26-3%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%201%26-3%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C1%265%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5B16%5C%20%5C%20-11%20%5C%20%5C%20-13%5D%5C%5C%5C%5C%5C%5C)
![Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]](https://tex.z-dn.net/?f=Third%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%205%26-3%5C%5C%5C%206%26-5%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%201%26-3%5C%5C-5%26-5%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C1%265%5C%5C-5%266%5Cend%7Barray%7D%5Cright%5D%3D%20%5B-7%20%5C%20%20%5C%2020%5C%20%5C%2031%5D)
![\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%26-35%26-34%5C%5C16%26-11%26-13%5C%5C-7%2620%2631%5Cend%7Barray%7D%5Cright%5D)
![inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\](https://tex.z-dn.net/?f=inverse%20%5C%20matrix%20%3D-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C)
Solution of the matrix:
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-8%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B16%2A-21%20%7D%7B-81%20%7D%20%2B%20%5Cfrac%7B-7%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-35%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B-11%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B20%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-34%2A-10%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B-13%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B31%2A-25%20%7D%7B-81%20%7D%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B-162%7D%7B-81%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-1%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Therefore, the correct option is (1,-1,2)
No;
it is exponentially always increasing
Answer: your answer is 20.
Step-by-step explanation:
15 +4= 19 rounded to the nearest tenth is 20
