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olga_2 [115]
2 years ago
14

What’s the value of x

Mathematics
1 answer:
skelet666 [1.2K]2 years ago
5 0

Answer:

Step-by-step explanation:

You are given an angle, the adjacent side to the angle, and need the hypotenuse of the triangle.  Use Cos x  to find the missing side.

Cos α = (adjacent side)/(hypotenuse)

Cos 45 = 10/x

    x(Cos 45) = 10       (multiply both sides by x to get rid of the fraction)

       x = 10/(Cos 45)    (divide both sides by Cos 45 to isolate x

  Cos 45 = (√2)/2   so we have...

        x = 10/[(√2)/2]  

now simplify...

    x = 10*(2/√2)

       x =  20/√2

           x = (20√2)/[(√2)(√2)

               x = (20√2)/2

                      x = 10√2

                or x = 14.1421 if you use a calculator

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Step-by-step explanation:

Here is what the question is asking.  If Dominic buys 2 points (2% of the loan value) he will get a better rate and hence less payment.  The question is asking how long will it take him to save the initial investment of 2% of the loan value due to a smaller payment.  The monthly payment at 5.45% is  $1,146.43,  the monthly payment for 5.2% is  $1,118.66.  This is a difference of  $27.77 per month.  The 2 points will cost him  $3,752.00.  The question is asking how long will it take Dominic to re-coup his  $3,752.00 if he saves $27.77 per month.  Just divide the 2 numbers and you get  135.10 months.  If you divide that by 12 you get 11.26 years, which is roughly 11 years, 4 months.

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