Volume= length*width*height = Area * height
<span>square region: A= 32^2= 1024 </span>
<span>circle region: A= pi*radius^2= pi*(diameter/2)^2= 15^2 pi= 225pi </span>
<span>rectangle region: A= 30*45= 1350 </span>
<span>Volume= (1024+ 1350 +225pi) *6 = 14,244 +1350pi </span>
<span>The units are ft^3 </span>
<span>1 yard = 3 feet </span>
<span>yard^3= 27 ft^3 </span>
<span>ft^3= 1/(27y^3) </span>
<span>Cost = price / unit *Volume +surcharge </span>
<span>Cost= 12.50/y^3 *(14,244 +1350pi)ft^3 +25 </span>
<span>= 12.50/27 *(14,244 +1350pi) +25 </span>
<span>~ $8583</span>
In order to have infinitely many solutions with linear equations/functions, the two equations have to be the same;
In accordance, we can say:
(2p + 7q)x = 4x [1]
(p + 8q)y = 5y [2]
2q - p + 1 = 2 [3]
All we have to do is choose two equations and solve them simultaneously (The simplest ones for what I'm doing and hence the ones I'm going to use are [3] and [2]):
Rearrange in terms of p:
p + 8q = 5 [2]
p = 5 - 8q [2]
p + 2 = 2q + 1 [3]
p = 2q - 1 [3]
Now equate rearranged [2] and [3] and solve for q:
5 - 8q = 2q - 1
10q = 6
q = 6/10 = 3/5 = 0.6
Now, substitute q-value into rearranges equations [2] or [3] to get p:
p = 2(3/5) - 1
p = 6/5 - 1
p = 1/5 = 0.2
x-------> the length of <span>a rectangular cookie sheet
we know that
area of </span><span>a rectangular cookie sheet=length*width
area of </span>a rectangular cookie sheet=192 in²
area of a rectangular cookie sheet=<span>x² + 4x-----> x*(x+4)
</span><span>Step 1: x² + 4x = 192
</span><span>Step 2: x(x +
4 ) = 192 The length is x. The width is
(x+4)
</span><span>Step 3: x² + 4x = 192=0
we have
</span>x² + 4x = 192
x² + 4x - 192=0
using a graph tool-----> to resolve the second order equation
see the aattached figure
the solution is
x=-16
x=12
(x+16)*(x-12)=0
the length is x=12 in
and the width is-----> (x+4)-----> 12+4----> 16 in
<span>Step 4: (x +
16) (x - 12) = 0
Because the length can't be -
16 the length is 12, and the width is
16</span>