Y= -2(4x -1)(4x+1)
⇒ y= -2[(4x)^2 -1^2] (because (4x)^2 -1^2= (4x-1)(4x+1))
⇒ y= -2(16x^2 -1)
⇒ y= -2*16x^2 -2*(-1) (distributive property)
⇒ y= -32x^2+ 2
The final answer is y= -32x^2+ 2~
Answer:
The answer is below
Step-by-step explanation:
The volume of box = width * length * height
120 = x * x * y
120 = x²y
y=120/x²
The surface area (SA) = sum of the area of all faces side
SA = x² + x² + xy + xy + xy + xy
SA = 2x² + 4xy
substitute y =120/x²
SA = 2x² + 4x(120/x²)
SA = 2x² + 480/x
Taking the derivative:
SA' = 4x - 480/x²
making SA' = 0:
0 = 4x - 480/x²
480/x² = 4x
4x³ = 480
x³ = 120
x = 4.93 feet
y = 120 / x² = 120 / 4.93² = 4.93
Hence the width, length and height is 4.93 feet.
The number of pennies in bank is 42
<em><u>Solution:</u></em>
Given that ratio of pennies to quarters in a piggy bank is 14 : 3
Let 14x be the number of pennies in piggy bank
Let 3x be the number of quarters in piggy bank
<em><u>To find: number of pennies</u></em>
Given that there are 51 quarters
number of pennies in piggy bank + number of quarters in piggy bank = 51
14x + 3x = 51
17x = 51
x = 3
number of pennies = 14x = 14(3) = 42
Thus the number of pennies in bank is 42