5 degrees above is 5°F
3 degrees below is -3°F
6 degrees above is 6°F
2 3/4 below is -2.74°F
Answer:
I got this answer hope works...
Answer:
The standard equation of the parabola is:
![y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
![y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2](https://tex.z-dn.net/?f=y-y_%7Bvertex%7D%3Da%5C%2C%28x-x_%7Bvertex%7D%29%5E2%5C%5Cy-6%3Da%5C%2C%28x-4%29%5E2)
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
![y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}](https://tex.z-dn.net/?f=y-6%3Da%5C%2C%28x-4%29%5E2%5C%5C0-6%3Da%5C%2C%282-4%29%5E2%5C%5C-6%3Da%5C%2C4%5C%5Ca%3D-%5Cfrac%7B6%7D%7B4%7D%20%3D-%5Cfrac%7B3%7D%7B2%7D)
Then the equation of the parabola becomes:
![y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%5C%2C%28x-4%29%5E2%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%28x%5E2-8x%2B16%29%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-24%5C%5Cy%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
Answer:
The answer is 120 feet.
Step-by-step explanation:
The area of the field (A) is:
A = w · l (w - width, l - length)
It is known:
A = 12,000 ft²
l = w - 20
So, let's replace this in the formula for the area of the field:
12,000 = w · (w - 20)
12,000 = w² - 20
⇒ w² - 20w - 12,000 = 0
This is quadratic equation. Based on the quadratic formula:
ax² + bx + c = 0 ⇒
In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000
Thus:
So, width w can be either
or
Since, the width cannot be a negative number, the width of the field is 120 feet.