Which equation has a constant of proportionality equal to 8?
1 answer:
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Answer:
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
Step-by-step explanation:
Geometrically speaking, the area of a rectangle (), in square centimeters, is described by following expression:
(1)
Where:
- Width, in centimeters.
- Height, in centimeters.
By Differential Calculus, we find an expression for the rate of change of the area of the rectangle (), in square centimeters per second:
(2)
Where:
- Rate of change of the width of the rectangle, in centimeters per second.
- Rate of change of the length of the rectangle, in centimeters per second.
If we know that ,
,
and
, then the rate of change of the area of the rectangle is:
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
Answer:
x³ + 7x² + 15x + 9
Step-by-step explanation:
Given that the volume (V) of a rectangular pyramid is
V = A h ( A is the area of base and h the height ), then
V = (3x² + 12x + 9)(x + 3) ← factor out 3 from A
= × 3(x² + 4x + 3)(x + 3)
= (x² + 4x + 3)(x + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x² (x + 3) + 4x(x + 3) + 3(x + 3) ← distribute parenthesis
= x³ + 3x² + 4x² + 12x + 3x + 9 ← collect like terms
= x³ + 7x² + 15x + 9
Thus the expression for the volume is
V = x³ + 7x² + 15x + 9