Answer:
20 ft by 60 ft
Step-by-step explanation:
"What should the dimensions of the garden be to maximize this area?"
If y is the length of the garden, parallel to the stream, and x is the width of the garden, then the amount of fencing is:
120 = 3x + y
And the area is:
A = xy
Use substitution:
A = x (120 − 3x)
A = -3x² + 120x
This is a downward facing parabola. The maximum is at the vertex, which we can find using x = -b/(2a).
x = -120 / (2 · -3)
x = 20
When x = 20, y = 60. So the garden should be 20 ft by 60 ft.
Let the value of the car be represented by V and the amount of years by y.
This gives us the following formula:
V = 25,635 - 3000y
(This is because we start with a value of $25,635 and the value decreases by $3,000 every year 'y')
Now, we want to know when the car is worth $3,135, so we know V = 3,135
Now we can make up our equation:
25,365 - 3,000y = 3,135
Collecting terms gives us:
-3,000y = -22,500
Finally we divide by -3,000 to find 'y'
y = -22,500 / -3,000 = 7.5
Hence, the car will be worth $3,135 after 7.5 years.
Answer:
(1.5, 10.5)
Step-by-step explanation:
Answer:
A = 48
B = 5
C = 54
Step-by-step explanation:
Segment in the direction from A to C
Initial Point: A=(9,5)=(xa,ya)→xi=xa=9, yi=ya=5
Final point: C=(-7,1)=(xc,yc)→xf=xc=-7, yf=yc=1
B=(xb,yb)=?
Proportion: r=AB/BC=3:1=3/1→r=3
xb=(xi+r*xf)/(1+r)
Replacing xi=xa=9, xf=xc=-7 and r=3
xb=[9+3*(-7)]/(1+3)
xb=(9-21)/4
xb=(-12)/4
xb=-3
yb=(yi+r*yf)/(1+r)
Replacing yi=ya=5, yf=yc=1 and r=3
yb=[5+3*(1)]/(1+3)
yb=(5+3)/4
yb=8/4
yb=2
B=(xb,yb)→B=(-3,2)
Answer: B=(-3,2)
