Area of a rectangle=length x width
You have two rectangles:
First rectangle (the biggest):
length=9 yd
width=12 yd-6 yd=6 yd
Area of the biggest rectangle=(9 yd)(6 yd)=54 yd²
Second rectangle (the smallest)
length=6 yd
width=3 yd
Area of the smallest rectangle=(6 yd)(3 yd)=18 yd²
Area of the ballroom=area of the biggest rectangle + area of the smallest rectangle.
area of the ballroom=54 yd² +18 yd²=72 yd²
Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2
angleD=(7b+1)angle E=(2b+1)and angle F=(b+8)
