Answer:
B. 3.
Step-by-step explanation:
OK lets try again.
The slope of the secant = slope of the tangent at a certain point ( The Mean Value Theorem).
Slope of the secant = f(5) - f(2) / (5 - 2)
= [(25-3) / (5-1) - (4-3) / (2-1)] / 3
= (22/4 - 1) / 3
= 9/2 / 3
= 9/6
= 3/2.
The derivative at c = the slope of the tangent at c.
Finding the derivative:
f'(x) = [2x(x - 1) - (x^2 - 3) ]/ (x - 1)^2 (where x = c).
= (x^2 - 2x + 3)/ (x - 1)^2 = the slope.
So equating the slopes:
(x^2 - 2x + 3) / (x - 1)^2 = 3/2
2x^2 - 4x + 6 = 3x^2 - 6x + 3
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 90
x = 3 , -1
x can't be -1 because we are working between the values 2 and 5 so
x = c = 3.
Answer:
30100-2150x and it would take 14 minutes to reach the ground.
Step-by-step explanation:
30100 feet is out starting y coordinate, and since 2150 is always changing depending on the amount of time we multiple it by x (the amount of minutes) therefor we can create the equation 30100-2150x and when we plus in 14 the equation would equal 0
Answer:
Required total charge is 
coulombs per square meter.
Step-by-step explanation:
Given electric charge is dristributed over the disk,
so that the charge density at (x,y) is,
To find total charge on the disk let Q be the total charge and 
so that,
where A is the surface of disk.
![=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%7D%7B3%7D%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%28%5Csin%5Ctheta%2B%5Ccos%5Ctheta%29%5CBig%5Br%5E3%5CBig%5D_%7B0%7D%5E%7B4%7Dd%5Ctheta%2B2%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%5CBig%5B%5Cfrac%7Br%5E4%7D%7B4%7D%5CBig%5Dd%5Ctheta)
![=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi](https://tex.z-dn.net/?f=%3D%5Cfrac%7B128%7D%7B3%7D%5CBig%5B%5Csin%5Ctheta-%5Ccos%5Ctheta%5CBig%5D_%7B0%7D%5E%7B2%5Cpi%7D%2B128%5Ctimes%202%5Cpi)
![=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi](https://tex.z-dn.net/?f=%3D%5Cfrac%7B128%7D%7B3%7D%5CBig%5B%5Csin%202%5Cpi-%5Ccos%202%5Cpi-%5Csin%200%2B%5Ccos%200%5CBig%5D%2B256%5Cpi)
Hence total charge is coulombs per square meter.
The given matrix equation is,
![1.5\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y\left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]](https://tex.z-dn.net/?f=%201.5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%266%5C%5C8%264%5Cend%7Barray%7D%5Cright%5D%20%2By%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%264%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20)
.
Multiplying the matrices with the scalars, the given equation becomes,
![\left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%269%5C%5C12%266%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dy%264y%5C%5C3y%262y%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20)
Adding the matrices,
![\left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%2By%269%2B4y%5C%5C12%2B3y%266%2B2y%5Cend%7Barray%7D%5Cright%5D%20%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20)
Matrix equality gives,
Solving the equations together,
We can see that the equations are not consistent.
There is no solution.
