Answer:
See Below.
Step-by-step explanation:
We want to verify the identity:
Note that the left-hand side is a perfect square trinomial pattern. Namely:
If we let <em>a</em> = csc(x) and <em>b</em> = cot(x), we can factor it as such:
Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):
Combine fractions:
Square (but do not simplify yet):
Now, we can make a substitution. Let <em>u</em> = <em>x</em> / 2. So, <em>x</em> = 2<em>u</em>. Substitute:
Recall that cos(2u) = 1 - sin²(u). Hence:
Simplify:
Recall that sin(2u) = 2sin(u)cos(u). Hence:
Square:
Cancel:
Since sin(u) / cos(u) = tan(u):
We can substitute <em>u</em> back for <em>x</em> / 2:
Hence proven.
The anwser for this question is B
Part A
t 0 1 2 3
H(t) 12 44 44 42
g(t) 10 25 40 56
Set H(t) = g(t) yields 16t^2 -32t -2 which shows its zeroes or points of intersections are at 0.6 and 2.1 seconds
Part B
H(t) = g(t) intersect at (x,y) points (0.6 secs, 9.1 feet) and (2.1 secs, 42.1 feet)
H(t) is a parabola that opens downward which shows the cannonball arches upwards then falls downward.
g(t) is a straight linear line which slopes positive upwards and intersects G(t) in two places.
This problem can be solved with a series of additions and subtractions.
The starting value is 500 and we first subtract 120 because on Monday they withdrew 120 dollars which leaves us with 380 dollars.
Next, we add 50 because on Wednesday they deposited 50 dollars which results in 430.
And, If I am not mistaken, we are done because when Braxton bought their basketball ticket, they used their debt card and did not withdrew from their checking account.
So, the answer is 430 dollars.
