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Len [333]
3 years ago
14

This is URGENT. Please answer this question including every step thanks.

Mathematics
2 answers:
Xelga [282]3 years ago
7 0
Area of stone path that students plan to cover is 80ft².
x-width of a path
xft*8ft+(xft*16ft-xft*xft)=80ft²
8x+16x-x²=80, -x²+24x-80=0
x²-24x+80=0, x₁,₂=(24⁺₋√(24²-4*80))/2
x₁,₂=(24⁺₋16)/2, x₁=16, x₂=4
a. Width of stone path is 4ft.
b. I choose 4ft because it cannot be other solution which is 16ft. The length  of hole rectangular area is 16 ft so the only logical solution of those two is 4ft.
Likurg_2 [28]3 years ago
5 0
(a) x = 4  
First, let's calculate the area of the path as a function of x. You have two paths, one of them is 8 ft long by x ft wide, the other is 16 ft long by x ft wide. Let's express that as an equation to start with. 
A = 8x + 16x
 A = 24x 
 But the two paths overlap, so the actual area covered will smaller. The area of overlap is a square that's x ft by x ft. And the above equation counts that area twice. So let's modify the equation by subtracting x^2. So:
 A = 24x - x^2 
 Now since we want to cover 80 square feet, let's set A to 80. 80 = 24x - x^2 
 Finally, let's make this into a regular quadratic equation and find the roots.
 80 = 24x - x^2
 0 = 24x - x^2 - 80
 -x^2 + 24x - 80 = 0 
 Using the quadratic formula, you can easily determine the roots to be x = 4, or x = 20. 
 Of those two possible solutions, only the x=4 value is reasonable for the desired objective. 
 (b) There were 2 possible roots, being 4 and 20. Both of those values, when substituted into the formula 24x - x^2, return a value of 80. But the idea of a path being 20 feet wide is rather silly given the constraints of the plot of land being only 8 ft by 16 ft. So the width of the path has to be less than 8 ft (the length of the smallest dimension of the plot of land). Therefore the value of 4 is the most appropriate.
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Step-by-step explanation:

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(-1,1)

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Step-by-step explanation:

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Find the final amount in each of these retirement accounts, in which the rate
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Answer:

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:

FV = PV(1 + r/m)mt

or

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

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reff = (1 + r/m)m - 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

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r eff =(1 + rnom /m)m = (1 + 0.098/12)12 - 1 = 0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

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and

D = P × (1 + r)k - R × [(1 + r)k - 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

n = log[x / (x – P × r)] / log (1 + r)

where Log is the logarithm in any base, say 10, or e.

Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n - 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be

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Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

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Number 7
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3 years ago
A father is 1 year older than 3 times the age of his son the son is 20 years old
blsea [12.9K]
20 x 3= 60 + 1 = 61 is your answer
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2 years ago
Read 2 more answers
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