I cant see all the question but this is how you find the derivative of your function using the product rule.
Here you use the extension of the product rule to 3 factors which we'll write as:-
f(x), g(x) and h(x):-
Derivative = f'(x) g(x) h(x) + f(x) g'(x) h(x) + f(x) g(x) h'(x)
(3x - 1)(x + 4)(2x - 1)
derivative = 3(x + 4)(2x - 1) + (3x + 1)(1)(2x - 1) + (3x - 1)(x + 4)(2)
= 3(x + 4)(2x - 1) + (3x + 1)(2x - 1) + 2(3x - 1)(x + 4)
Answer:
4 inches²
144 inches²
0.64 inches²
Yes, the area of a square and the length of its side directly proportional quantities.
Step-by-step explanation:
In this question, we have to find the area of square by changing the lengths of a side. Given lengths are: 2, 12, 0.8. I will evaluate the area of each side and try to find out the relation between area and length of side.
First, we start with the smallest length (a=0.8 inches)
Area of a square is calculated by taking the square of single side (since both sides are equal).
Area of square = a²
Area of square = 0.8²
Area of square = 0.64 inches²
Area of square with smallest side length (a=0.8 inches) = 0.64 inches²
Secondly, we start with the 2nd highest length (a=2 inches)
Area of square = a²
Area of square = 2²
Area of square = 4 inches²
Area of square with second largest side length (a=2 inches) = 4 inches²
Thirdly, we start with the highest length (a=12 inches)
Area of square = a²
Area of square = 12²
Area of square = 144 inches²
Area of square with highest side length (a=12 inches) =144 inches²
As we can see, with the increase in the length of a side, area of square is also increasing. Therefore, yes the area of a square and the length of its side are directly proportional quantities as the area increases or decreases when the length of the side increases or decreases.
Answer:
They are directly proportional quantities.
Step-by-step explanation:
DEFINITION
Two quantities are said to be directly proportional if an increase in one quantity lead to an increase in the other quantity.
Area of a Square =
Area of a Square of Length 2 inch =
Area of a Square of Length 12 inch =
Area of a Square of Length 0.8 inch =
Arranging the sides and corresponding area in ascending order:
(0.8, 2, 12) = (0.64, 4, 144)
We notice that as the length increases, the area also increases.
Therefore, the area of a square and the length of its side are directly proportional quantities.