Math- Please Help Us!
posted by Cole n Cynthia .
Diagram has 4 rectangular corrals with a barn above it. Sides (front to back) are attached to the barn. Fencing is not needed along the back of the barn.
P= 200 ft of fencing
If each corral is 16 ft long (front to back), how wide will each corral be, what will be the area of each corral and what will be the combined area of the 4 corrals?
y= 42/2= 21 ft
A= (16)(21)=336 ft^2
A=(336)(4)= 1,344 ft^2
These are the answers we got for the questions but, how would we get the (x,y) coordinates and plot it on the parabola if we used the function
A= 200x-5x^2. When we had to find the function for the combined area of 4 corrals if each corral is x feet long.
The function does not seem to go with the answers above.
Please help and explain. Thank you C-C
If your question is a follow-up to
I don't know how you got your first part equations
I had given you
A = 200x - 5x^2
we can complete the square, and thus find the vertex this downwards opening parabola
A = -5(x^2 - 40x + 400 - 400)
= -5( (x-20)^2 - 400)
= -5(x-20)^2 + 2000
so x = 20, and y = 200 - 5x = 100 (from my previous post)
so the whole large rectangle is 20 by 100 making each of the 4 corrals 20 by 25
for a total area of 2000 ft^2
I don't understand where you got 16 from, and did you notice that my area is larger than yours
check that my answer is correct:
take a value smaller than 20, say x = 19.9
then y = 200-5x = 102.5 , Area = 19.5 x 102.5 = 1998.75, which is less than 2000
take a value larger than 20 , say x = 20.3
then y = 200-5(20.3) = 98.5 , Area = 20.3 x 98.5 = 199.55 which is less than 2000
Sorry, we are doing multi-step questions and we understand how to graph the parabola, but if 16ft is the given side and we had to find the function for it and solve.
Would the function be y=200-5x^2 instead of y=200-5x?
We would use the y=200-5x and plug in x=16
to get y=120, area= 16 x 120= 1920. That would be the area for the rectangle and 1920/4= 480 ft for each corral area.
The first part equation function is probably wrong because we used a different function for the same diagram and the x=16 is the given side.
Thank you for clearing those questions up.
There is another question which said to graph the function y=200x-5x^2. We graphed that already, which is an upside down parabola but, then we needed to label the points from the first part onto the graph. That part confuses us. Would the (x,y)=(16,120)?