Answer:
y = - 10
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 2 when x = - 4, that is
2 = - 4k ( divide both sides by - 4 )
= k, that is
k = -
y = - x ← equation of variation
When x = 20, then
y = - × 20 = - 10
Answer:
-17x-1
Step-by-step explanation:
Proper fraction: 26 1/5
improper fraction: 131/5
Old price: p1 = $ 3.90;
New price: p2 = $ 3.40.
The percentual decrease is given by
d(%) = [ (p2 - p1) / p1 ] * 100 %
d(%) = [ (3.40 - 3.90) / 3.90 ] * 100 %
d(%) = [ - 0.50 / 3.90 ] * 100 %
d(%) = - 0.128 * 100 %
d(%) = - 12.8 % (approximately)
So the price fell 12.8 % approximately.
I hope this helps. =)
Volume
of a rectangular box = length x width x height<span>
From the problem statement,
length = 60 - 2x
width = 10 - 2x
height = x</span>
<span>
where x is the height of the box or the side of the equal squares from each
corner and turning up the sides
V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x
To maximize the volume, we differentiate the expression of the volume and
equate it to zero.
V = </span>4x^3 - 100x^2 + 600x<span>
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0</span>
<span>x^2 - 50/3x + 50 = 0
Solving for x,
x1 = 12.74 ; Volume = -315.56 (cannot be negative)
x2 = 3.92 ;
Volume = 1056.31So, the answer would be that the maximum volume would be 1056.31 cm^3.</span><span>
</span>
