Answer:
Step-by-step explanation:
Let
x -----> the number of minutes
y ----> the balloon's height in feet
we know that
The linear equation in slope intercept form is equal to
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem we have that
The slope is equal to
----> is negative because is a decreasing function
Remember that the y-intercept is the value of y when the value of x is equal to zero
In this context the y-intercept is the height of the balloon when the time is equal to zero (initial height)
substitute
F = t ⇨ df = dt
dg = sec² 2t dt ⇨ g = (1/2) tan 2t
⇔
integral of t sec² 2t dt = (1/2) t tan 2t - (1/2) integral of tan 2t dt
u = 2t ⇨ du = 2 dt
As integral of tan u = - ln (cos (u)), you get :
integral of t sec² 2t dt = (1/4) ln (cos (u)) + (1/2) t tan 2t + constant
integral of t sec² 2t dt = (1/2) t tan 2t + (1/4) ln (cos (2t)) + constant
integral of t sec² 2t dt = (1/4) (2t tan 2t + ln (cos (2t))) + constant ⇦ answer
The x coordinate of S will be 1/2 * 2a = a.
and since the half triangle is 30-60-90 the y coordinate will be sqrt3 a
so S is (a , sqrt3a)
Answer:
C. G
Step-by-step explanation:
