Check the picture.
The bases of the 2 prisms are on 2 parallel planes,
a and
b.
Let
c be a third plane, between
a and
b, parallel to both.
Then,
the cross-sections
A and
B , of the 2 prisms, formed by plane c, have
Equal Areas,
this is by
Cavalier's Principle.
Answer:
Step-by-step explanation:
<u>Given Equation is:</u>
Adding 9 to both sides
=> 
=> 
Multiplying 2 to both sides
=> -3x = -18 * 2
=> -3x = -36
Dividing both sides by -3
=> x = 12
Answer:
(x, y) = (7, 4) meters
Step-by-step explanation:
The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.
The perimeter of the floor is the sum of all side lengths, so is 4x +2y.
The given dimensions tell us ...
x^2 -y^2 = 33
4x +2y = 36
From the latter equation, we can write an expression for y:
y = 18 -2x
Substituting this into the first equation gives ...
x^2 -(18 -2x)^2 = 33
x^2 -(324 -72x +4x^2) = 33
3x^2 -72x + 357 = 0 . . . . write in standard form
3(x -7)(x -17) = 0 . . . . . factor
Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.
y = 18 -2(7) = 4
The floor dimension x is 7 meters; the inset dimension y is 4 meters.
{x-(-3/4)}^2=3^2
(x+3/4)^2=9
{(4x+3)/4}^2=9
(4x+3)^2/16=9
(4x+3)^2=9*16
16x^2+2*4x*3+3^2=144
16x^2+24x+9=144
16x^2+24x+9-144=0
16x^2+24x-135=0
The answer to the question is b
