Answer:
A = (100 - y)y
Maximum area = 2500 sq. feet.
Step-by-step explanation:
Let the length of the combined rectangular area is y feet and the shared width is x feet.
So, perimeter of the two rectangle together is (3x + 2y) = 200 {Given}
⇒ 2y = 200 - 3x
⇒
...... (1).
a) Now, area of the total plot in sq. feet is
........ (2)
So, this is the expression for area A in terms of length of shared side x.
b) For area to be maximum the condition is ![\frac{dA}{dx} = 0](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdx%7D%20%3D%200)
Now, differentiating equation (2) on both sides with respect to x we get
![\frac{dA}{dx} = 100 - 3x = 0](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdx%7D%20%3D%20100%20-%203x%20%3D%200)
⇒ x = 33.33 feet.
So, from equation (1) we get ![y= \frac{1}{2} (200 - 3x)](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28200%20-%203x%29)
⇒ x = 50 feet.
So, the value of maximum area = 50 × 33.33 = 1666.5 sq. feet. (Answer)
Congrats to all seniors!!!
Answer:
j=3
j=4
j=5
Step-by-step explanation:
10≥ j+5
Subtract 5 from each side
10-5≥ j+5-5
5≥ j
All solutions will satisfy the inequality
Answer:
1. subtract
2. quotient
3. multiply
4. times
Step-by-step explanation:
Answer:
d. -38
Step-by-step explanation:
Arithmetic sequence concepts:
The general rule of an arithmetic sequence is as follows:
![a_{n+1} = a_{n} + d](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20a_%7Bn%7D%20%2B%20d)
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
![a_{n} = a_{1} + (n-1)*d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29%2Ad)
In this question:
![a_{1} = 10, d = -3](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2010%2C%20d%20%3D%20-3)
17th term:
![a_{17} = a_{1} + (17-1)*d = 10 + 16*(-3) = -38](https://tex.z-dn.net/?f=a_%7B17%7D%20%3D%20a_%7B1%7D%20%2B%20%2817-1%29%2Ad%20%3D%2010%20%2B%2016%2A%28-3%29%20%3D%20-38)
So the correct answer is:
d. -38