Answer:
Correct integral, third graph
Step-by-step explanation:
Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.
Given : ∫ tan²(θ)sec²(θ)dθ
Applying u-substitution : u = tan(θ),
=> ∫ u²du
Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1
Substitute back u = tan(θ) : tan^2+1(θ)/2+1
Simplify : 1/3tan³(θ)
Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.
56÷6.2 equals 9.032≈9 the answer is 9 $
This is a compound interest problem so you cannot use the simple interest formula. Effectively the total amount is being compounded each year by 6%. There is a formula for compound interest but in this simple example you can work this out recursively.
year 1 = 6500
year2 = 6500*1.06 = 6890
year3 = 6890*1.06 = 7303
year4 = 7303*1.06 = 7741..
etc......
year12 = 11604*1.06 = 12338
Answer:
the function given 
for 4 units up, just add 4 as a constant
4 units up means, every old value will now be 4 more than previous value. at x=0, y=0 in the transformed curse it should x=0 and y=4, so just add it.
for 6 units left,
each old value of y should now occur 6 units before the old value of x i.e. X=x+6
for example, the point (0,0) should occur at (-6,0) in the transformed graph,
hence, 
so the final curve is
Answer:
Step-by-step explanation:
g(x) = x+4
g(8) = 8+4 = 12
