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bixtya [17]
4 years ago
8

Rewrite the formula for the circumference of a circle C=2xpix r in terms of its diameter d. Show your work.

Mathematics
2 answers:
ozzi4 years ago
7 0
Hi there!

The answer is
circumference \:  = d\pi
In this formula d represents the diameter.

We know that 2 times the radius equals the diameter, hence
2r = d

Therefore we can replace the 2r in the original formula by d, and then we get the following:
circumference = 2\pi \: r = 2r\pi = d\pi
Keith_Richards [23]4 years ago
3 0
Diameter = 2·radius

С = 2·π·r   ⇒    С = π·d   
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As part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each
Finger [1]

Answer:

Option d)$401,447.24

Step-by-step explanation:

We are given that as part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each year at rate of 6% compounded annually for 20  years

So first of all we need to find the future value of annuity using the formula as shown below :

FV= p\frac{[(1+\frac{r}{n})^{(n)(t)}-1)]}{\frac{r}{n}}

Here, FV = future value of annuity

         p = $35000   (annual deposit)

         r is rate = 6% = 0.06

         n = number of compounding = 1 ( as we are compounding annually )

        t = number of years = 20

So plugging in all the values in the formula , we get

FV= 35000\frac{[(1+\frac{0.06}{1})^{(1)(20)}-1)]}{\frac{0.06}{1}}

Simplifying further , we get

FV= 35000\frac{[(1+0.06)^{20}-1)]}{0.06}

Plugging in the given values in the calculator , we get

FV = $ 1287495.69

So far we have got the Total amount for annuity , from here we need to use the concept of compound interest and find the principal amount to be deposited to get the required total amount of $ 1287495.69

The formula for compound interest when compounded annually is given by:

A=P(1+r)^t

Here A = 1287495.69  (Total amount required)

         P =   ( principal amount to be deposited to meet the required total amount )

         r = 6% = 0.06

        t = 20

So plugging in all the known values in the formula , we get

1287495.69= P(1+0.06)^{20}

simplifying further, we get

\frac{1287495.69}{(1.06)^{20}}= P

so required amount to be deposited is given by :

P = $401,447.24

Hope it was helpful !:)




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