![z^3=64(\cos219^\circ+i\sin219^\circ)](https://tex.z-dn.net/?f=z%5E3%3D64%28%5Ccos219%5E%5Ccirc%2Bi%5Csin219%5E%5Ccirc%29)
Note that
![64=4^3](https://tex.z-dn.net/?f=64%3D4%5E3)
. The third roots are then given by
![z=4\left(\cos\left(\dfrac{219+360k}3\right)^\circ+i\sin\left(\dfrac{219+360k}3\right)^\circ\right)](https://tex.z-dn.net/?f=z%3D4%5Cleft%28%5Ccos%5Cleft%28%5Cdfrac%7B219%2B360k%7D3%5Cright%29%5E%5Ccirc%2Bi%5Csin%5Cleft%28%5Cdfrac%7B219%2B360k%7D3%5Cright%29%5E%5Ccirc%5Cright%29)
where
![k=0,1,2](https://tex.z-dn.net/?f=k%3D0%2C1%2C2)
, so that
On the coordinate (0,7) the value of P is maximum 280.
What is a Linear Inequality?
In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.
Solution:
First of all to solve the Linear Inequality we need to plot the graph of the given equations.
Kindly find the attached graph
To maximise the equation P = 30x + 40y
we need to find the corner values of x and y.
According to the graph, the corner values of (x,y) are
(5,0), (3,4) and (0,7)
putting the values in the equation P = 30x + 40y
at x = 5 and y = 0
P = 150
at x = 3 and y = 4
P = 250
at x = 0 and y = 7
P = 280
So, on the cordinate (0,7) the value of P is maximum i.e. 280.
To learn more about <u>Linear Inqualities</u> from the given link
brainly.com/question/24372553
#SPJ1
-13/5. The equation to find the slope between 2 points is y sub 2-y sub 1/x sub 2-x sub 1. Or in this case, -6-7/2+3. -6-7=-13, 2+3=5. So the slope is -13/5.
Answer:
The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.
Step-by-step explanation:
Let the random variable <em>X</em> represent the lengths of the classes.
The random variable <em>X</em> is uniformly distributed within the interval 49.0 and 54.0 minutes.
The probability density function of <em>X</em> is:
![f_{X}(x)=\frac{1}{b-a};\ a](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Cfrac%7B1%7D%7Bb-a%7D%3B%5C%20a%3CX%3Cb%2C%5C%20a%3Cb)
Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:
![P(50.75](https://tex.z-dn.net/?f=P%2850.75%3CX%3C51.25%29%3D%5Cint%5Climits%5E%7B51.25%7D_%7B50.75%7D%7B%5Cfrac%7B1%7D%7B54-49%7D%7D%5C%2C%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%5Ctimes%20%5Bx%5D%5E%7B51.25%7D_%7B50.75%7D%5C%5C%5C%5C%3D%5Cfrac%7B51.25-50.75%7D%7B5%7D%5C%5C%5C%5C%3D0.10)
Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.
The lowest common denominator would be twelve.