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Answer:
The equation of the parabola is given to be : y = -x² + 36
So, the airplane will cut the rainbow if the graph of the equation of airplane intersects the graph of rainbow.
Now, to find the equation of airplane :
The points through which airplane passes are : (1,0) and (0,2)
⇒ Equation : 2x + y = 2
This equation will intersect the parabola at exactly two points.
And the points are the solution of these two equation :
(-4.916,11.832) and (6.916,-11.832)
The required table is :
x -4.916 11.832
y 6.916 -11.832
Answer:
- value: $66,184.15
- interest: $6,184.15
Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
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<h3>formula</h3>The formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
<h3>calculator</h3>The attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
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<h3>a) </h3>The future value of the annuity due is $66,184.15.
<h3>b)</h3>The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
