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cestrela7 [59]
3 years ago
7

What is the conjugate? Sqrt 8 - sqrt 9

Mathematics
2 answers:
jarptica [38.1K]3 years ago
4 0
<span> </span><span>The conjugate of an irrational number is the number you have to multiply it by in order to arrive at a rational number. 
</span>
Dafna1 [17]3 years ago
4 0

Answer:

\frac{-1}{(\sqrt{8}+\sqrt{9})}

Step-by-step explanation:

We are given the expression \sqrt{8}-\sqrt{9}.

So, the conjugate is given by,

(\sqrt{8}-\sqrt{9})\times \frac{(\sqrt{8}+\sqrt{9})}{(\sqrt{8}+\sqrt{9})}

i.e. \frac{(\sqrt{8})^{2}-(\sqrt{9})^{2}}{(\sqrt{8}+\sqrt{9})}

i.e. \frac{8-9}{(\sqrt{8}+\sqrt{9})}

i.e. \frac{-1}{(\sqrt{8}+\sqrt{9})}

Thus, the conjugate of the expression is given by \frac{-1}{(\sqrt{8}+\sqrt{9})}.

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Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)
vredina [299]

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.

__

<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.

__

<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.

3 0
2 years ago
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