Using product rule;
f(x)=(1+6x²)(x-x²)
f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1
Solving the bracket first;
f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4
f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1
2.5 x 10 = 25 m^2
1.5 x 10 = 15 m^2
2 x 10 = 20 m^2
0.5 x 1.5 x 2 = 1.5 m^2 (2 times)
Total = 63 m^2
So just fill in 63.
Hey
Area of first rectangle = 18 x 21 = 378 in^2
Area of second rectangle = 17 x 9 = 153 in^2
Total area = 378+153 = 531 in^2
Option 1
Hope this helps :)
<h2>
Hello!</h2>
The answer is:
The correct option is:
D. 40 feet.
<h2>
Why?</h2>
To solve the problem and calculate the width of the river, we need to assume that the distance from A to B and the angle formed between that distance and the distance from A to the other point (C) is equal to 90°, meaning that we are working with a right triangle, also, we need to use the given angle which is equal to 34°. So, to solve the problem we can use the following trigonometric relation:

Where,
alpha is the given angle, 34°
Adjacent is the distance from A to B, which is equal to 60 feet.
Opposite is the distance from A to C which is also equal to the width of the river.
So, substituting and calculating we have:


Hence, we have that the correct option is:
D. 40 feet.
Have a nice day!