First convert yards to feet.
1 yard = 3 feet.
100 x 3 = 300 feet long.
53 x 3 = 159 + 1 = 160 feet wide.
Now use the Pythagorean theorem to find the diagonal.
x^2 = 300^3 + 160^2
x^2 = 90000 + 25600
x^2 = 115600
x = √115600
x = 340 feet
Answer:
The slope is -2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (10-14)/(2-0)
= -4/2
= -2
The slope is -2
Answer:
I'm just going to take a guess and say 36?
Step-by-step explanation:
Answer:
a. The critcal points are at
![x=0,-5,3](https://tex.z-dn.net/?f=x%3D0%2C-5%2C3)
b. Then,
is a maximum and
is a minimum
c. The absolute minimum is at
and the absolute maximum is at ![x = -5.](https://tex.z-dn.net/?f=x%20%3D%20-5.)
Step-by-step explanation:
(a)
Remember that you need to find the points where
![f'(x)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D0)
Therefore you have to solve this equation.
![20x^4 + 40x^3 - 300x^2 = 0](https://tex.z-dn.net/?f=20x%5E4%20%20%2B%2040x%5E3%20-%20300x%5E2%20%3D%200)
From that equation you can factor out
and you would get
![20x^2 ( x^2 +2x - 15) = 0](https://tex.z-dn.net/?f=20x%5E2%20%28%20%20x%5E2%20%20%2B2x%20-%2015%29%20%20%3D%200)
And from that you would have
, so
.
And you would also have
.
You can factor that equation as ![x^2 +2x -15 = (x+5)(x-3) = 0](https://tex.z-dn.net/?f=x%5E2%20%2B2x%20-15%20%3D%20%28x%2B5%29%28x-3%29%20%3D%200)
Therefore
.
So the critcal points are at
![x=0,-5,3](https://tex.z-dn.net/?f=x%3D0%2C-5%2C3)
b.
Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since
![f''(x) = 80x^3 + 120x^2 -600x\\f''(-5) = 80(-5)^3 + 120(-5)^2 -600(-5) = -4000 < 0\\\\f''(3) = 80(3)^3 + 120(3)^2 -600(3) = 1440 > 0 \\](https://tex.z-dn.net/?f=f%27%27%28x%29%20%3D%2080x%5E3%20%2B%20120x%5E2%20-600x%5C%5Cf%27%27%28-5%29%20%3D%2080%28-5%29%5E3%20%2B%20120%28-5%29%5E2%20-600%28-5%29%20%3D%20-4000%20%3C%200%5C%5C%5C%5Cf%27%27%283%29%20%3D%2080%283%29%5E3%20%2B%20120%283%29%5E2%20-600%283%29%20%3D%201440%20%3E%200%20%5C%5C)
Then,
is a maximum and
is a minimum
c.
The absolute minimum is at
and the absolute maximum is at ![x = -5.](https://tex.z-dn.net/?f=x%20%3D%20-5.)