This is the Equation: 2x + 6
SA=2H(L+W)+LW for open box
20=2H(4+W)+4(W)
distribute
20=8H+2WH+4W
divide both sides by 2
10=4H+WH+2W
solve for 1 variable, pick W
10-4H=WH+2W
10-4H=W(H+2)
(10-4H)/(H+2)=W
V=LWH
subsitute 4 for V, subsitute H for H and (10-4H)/(H+2) for W
V=(4)(H)(10-4H)/(H+2)
V=(40H-16H²)/(H+2)
find max value
take deritivitive of this thing
V'=-16(H²+4H-5)/((H+2)²)
using sign chart
sign changes from positive to negative at H=1
so at H=1
find W
W=(10-4H)/(H+2)
W=2
the dimeionts are
length=4ft
width=2ft
height=1ft
(the volume is 8 cubic feet)
<span>1. </span><span>4x –y = 8, the point (-4, 3)
Let’s say y = 0
=> 4x – 8
=> 4x / 4 = 8 /4
=> x = 2
So the point is (2 , 0).
Now, we have 2 forms, the (2,0) and the (-4, 3)
=> (y2 – y1)(x2 – x1) = m
=> m = (0 - 3)(2-(-4))
=> m = (0 - 3)(2+4)
=> m = (-3)(6)
=> m = -1/2
Thus,
y = -1/2x + a
=> 0 = -1 + a so a = 1
y = -x/2 + 1</span>
Let <em>q</em> be the number of quarts of pure antifreeze that needs to be added to get the desired solution.
8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.
The new solution would have a total volume of 8 + <em>q</em> quarts, and it would contain a total amount of 3.2 + <em>q</em> quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means
(3.2 + <em>q</em>) / (8 + <em>q</em>) = 0.60
Solve for <em>q</em> :
3.2 + <em>q</em> = 0.60 (8 + <em>q</em>)
3.2 + <em>q</em> = 4.8 + 0.6<em>q</em>
0.4<em>q</em> = 1.6
<em>q</em> = 4
1. Over a period of 6 years (from 1980 to 1986) the house gained a value of 12000 dollars (109k-97k). 12000/6 gives you a rate of 2000 dollars per year. Because the initial price at t=0 is 97000, the function is 97000+2000t
