Answer:
Step-by-step explanation:
Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola
![y=100-x^2](https://tex.z-dn.net/?f=y%3D100-x%5E2)
This parabola has vertex at (0,100) and symmetrical about y axis.
Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.
Hence coordinates of any rectangle are
![(a,0) (-a,0), (a, 100-a^2), (-a, 100-a^2)](https://tex.z-dn.net/?f=%28a%2C0%29%20%28-a%2C0%29%2C%20%28a%2C%20100-a%5E2%29%2C%20%28-a%2C%20100-a%5E2%29)
Length of rectangle = 2a and width = ![100-a^2](https://tex.z-dn.net/?f=100-a%5E2)
Area of rectangle = lw = ![2a(100-a^2)=200a-400a^3](https://tex.z-dn.net/?f=2a%28100-a%5E2%29%3D200a-400a%5E3)
To find max area, use derivative test.
![A' = 200-800a^2\\A"=-1600a](https://tex.z-dn.net/?f=A%27%20%3D%20200-800a%5E2%5C%5CA%22%3D-1600a%3C0)
Hence maxima when first derivative =0
i.e. when a =2
Thus we find dimensions of the rectangle are l =4 and w = 96
Maximum area = ![4(96) = 384](https://tex.z-dn.net/?f=4%2896%29%20%3D%20384)
Answer:
GCF of 18 and 54 is 18.
Step-by-step explanation:
Answer:
<h2>
![x\leq -1](https://tex.z-dn.net/?f=x%5Cleq%20-1)
</h2>
Step-by-step explanation:
Steps:
![12x+4-4\leq -8](https://tex.z-dn.net/?f=12x%2B4-4%5Cleq%20-8)
Subtract 4 from both sides:
![12x+4-4\leq -8-4](https://tex.z-dn.net/?f=12x%2B4-4%5Cleq%20-8-4)
Simplify:
![12x\leq \frac{-12}{12}](https://tex.z-dn.net/?f=12x%5Cleq%20%5Cfrac%7B-12%7D%7B12%7D)
Divide both sides by 12:
![\frac{12x}{12} \leq \frac{-12}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B12x%7D%7B12%7D%20%5Cleq%20%5Cfrac%7B-12%7D%7B12%7D)
Simplify:
![x\leq -1](https://tex.z-dn.net/?f=x%5Cleq%20-1)
Answer:
C
Step-by-step explanation:
200 x 5 = 1,000
100 x 10 = 1,000
C - 5 to 10 days
Answer:
29
Step-by-step explanation:
(x+12) + 100 + x = 180
2x + 112 = 180
Subtract 112 from both sides
2x = 58
Divide 2 from both sides
x = 29