Answer:
Practical domain: ![v\in[0,230]\ or\ 0\leqslant v\leqslant 230](https://tex.z-dn.net/?f=v%5Cin%5B0%2C230%5D%5C%20or%5C%200%5Cleqslant%20v%5Cleqslant%20230)
Roger can earn $510 at most.
Step-by-step explanation:
We are given the function
![E(v)=50+2v](https://tex.z-dn.net/?f=E%28v%29%3D50%2B2v)
Which gives the earnings of Roger when he sells v videos. Since the play’s audience consists of 230 people and each one buys no more than one video, v can take values from 0 to 230, i.e.
![v\in[0,230]\ or\ 0\leqslant v\leqslant 230](https://tex.z-dn.net/?f=v%5Cin%5B0%2C230%5D%5C%20or%5C%200%5Cleqslant%20v%5Cleqslant%20230)
That is the practical domain of E(v)
If Roger is in bad luck and nobody is willing to purchase a video, v=0
If Roger is in a perfectly lucky night and every person from the audience wants to purchase a video, then v=230. It's the practical upper limit since each person can only purchase 1 video
In the above-mentioned case, where v=230, then
![E(230)=50+2(230)=50+460=510](https://tex.z-dn.net/?f=E%28230%29%3D50%2B2%28230%29%3D50%2B460%3D510)
Roger can earn $510 at most.
Answer:
b. 495
Step-by-step explanation:
Given
15, 21, 27, 33, 39, ...., 75
Number of terms = 11
Required
Evaluate
To evaluate means to add up all term of the series above;
The first step is to determine if the series is arithmetic or exponential;
If its arithmetic, then the difference between successive terms must be equal;
In other words;
21 - 15 = 27 - 21 = 33 - 27 = 39 - 33 = 6
<em>Since the result of the above expression gives 6, then it is an arithmetic series;</em>
<em></em>
The sum of n terms of an arithmetic series is calculated as this
![S_n = \frac{n}{2}(a + T_n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28a%20%2B%20T_n%29)
Where n = 11
a = First term = 15
T_n = Last term = 75
The formula becomes
![S_{11} = \frac{11}{2}(15 + 75)](https://tex.z-dn.net/?f=S_%7B11%7D%20%3D%20%5Cfrac%7B11%7D%7B2%7D%2815%20%2B%2075%29)
![S_{11} = \frac{11}{2}(90)](https://tex.z-dn.net/?f=S_%7B11%7D%20%3D%20%5Cfrac%7B11%7D%7B2%7D%2890%29)
![S_{11} = \frac{11 * 90}{2}](https://tex.z-dn.net/?f=S_%7B11%7D%20%3D%20%5Cfrac%7B11%20%2A%2090%7D%7B2%7D)
![S_{11} = \frac{990}{2}](https://tex.z-dn.net/?f=S_%7B11%7D%20%3D%20%5Cfrac%7B990%7D%7B2%7D)
![S_{11} = 495](https://tex.z-dn.net/?f=S_%7B11%7D%20%3D%20495)
Hence, the series when evaluated is 495
Answer:
a) Minimize ![Cost=90x_1+120x_2](https://tex.z-dn.net/?f=Cost%3D90x_1%2B120x_2)
subject to
![0.2x_1+0.3x_2\geq8](https://tex.z-dn.net/?f=0.2x_1%2B0.3x_2%5Cgeq8)
![0.2x_1+0.25x_2\geq6](https://tex.z-dn.net/?f=0.2x_1%2B0.25x_2%5Cgeq6)
![0.15x_1+0.1x_2\geq5](https://tex.z-dn.net/?f=0.15x_1%2B0.1x_2%5Cgeq5)
![x_1\geq0\\x_2\geq0](https://tex.z-dn.net/?f=x_1%5Cgeq0%5C%5Cx_2%5Cgeq0)
b) Attached
c) The optimum value that minimizes cost is x1=28 and x2=8.
Step-by-step explanation:
The objective function is the cost of extraction and needs to be minimized.
The cost of extraction is the sum of the cost of extraction of ore type 1 and the cost of extraction of ore type 2:
![Cost=90x_1+120x_2](https://tex.z-dn.net/?f=Cost%3D90x_1%2B120x_2)
Being x1 the tons of ore type 1 extracted and x2 the tons of ore type 2.
The constraints are the amount of minerals that need to be in the final mix
Copper:
![0.2x_1+0.3x_2\geq8](https://tex.z-dn.net/?f=0.2x_1%2B0.3x_2%5Cgeq8)
Zinc
![0.2x_1+0.25x_2\geq6](https://tex.z-dn.net/?f=0.2x_1%2B0.25x_2%5Cgeq6)
Magnesium
![0.15x_1+0.1x_2\geq5](https://tex.z-dn.net/?f=0.15x_1%2B0.1x_2%5Cgeq5)
Of course, x1 and x2 has to be positive numbers.
![x_1\geq0\\x_2\geq0](https://tex.z-dn.net/?f=x_1%5Cgeq0%5C%5Cx_2%5Cgeq0)
The feasible region can be seen in the attached graph.
The orange line is the magnesium constraint. The red line is the copper constraint. The green line is the zinc constraint.
The optimal solution is found in one of the intersection points between two constraints that belong to the limits of the feasible region.
In this case, the cost can be calculated for the 3 points that satisfies the conditions.
The optimum value that minimizes cost is x1=28 and x2=8.
Answer:
Here you go! :]
Step-by-step explanation:
Answer: The angles inside a triangle are called interior angles. ... The three interior angles in a triangle will always add up to 180°. At each corner the exterior and interior angles are on a straight line, so at each corner these two angles add up to 180°.
Step-by-step explanation:
Sal proves that the angles of an equilateral triangle are all congruent (and therefore they all measure 60°), and conversely, that triangles with all congruent angles are equilateral.