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Dafna11 [192]
3 years ago
12

Your friend is investing in a 401(k) that promises 2% annual growth. He plans on investing $250 each month for 25 years. Excel r

eturns a value of $97,205.28 for the balance in the 401(k) after 25 years. How much interest is earned in the account after 30 years?
Mathematics
1 answer:
7nadin3 [17]3 years ago
7 0

Answer:

$33181.35

Step-by-step explanation:

The first to do would to calculate the balance in the investment account after 30 years.

=fv(rate,nper,pmt,-pv)

rate is the rate of return per month which is 2%/12

nper is 30 years multiplied by 12

pmt is the periodic payment in the investment account of $250

pv is the current balance is shown as zero

=fv(2%/12,30*12,250,0)=$123,181.35

Total interest is the balance in the account after 30 years minus amount invested.

total interest=$123,181.35-($250*12*30)

                     =$123,181.35-$90,000.00=$33181.35

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salantis [7]

Answer:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:                                                                     \displaystyle \lim_{x \to c} x = c

L'Hopital's Rule

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                    \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

We are given the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}

When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle  \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}

Plugging in <em>x</em> = 0 again, we would get:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}

Substitute in <em>x</em> = 0 once more:

\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

6 0
3 years ago
Ha: μ ≠ 30 we know that the sample standard deviation is 10 and the sample size is 70. for what sample mean would the p-value be
Andrew [12]

From the given problem the same size is n = 70. Df = n – 1 = 70 – 1 = 69.

The population mean is u = 30, sample standard deviation is s = 10 and the sample size is n = 70. Then,

t = x – u / s sqrt of n

1.995 = x – 30 / (10 sqrt of 70)

1.995 = x – 30 / 1.1952

X – 30 = 1.995 (1.1952)

X – 30 = 2.3844

X = 30 + 2.3844

X = 32.3844

 

The sample mean is 32.3844

<span> </span>

3 0
3 years ago
Volume of a cylinder 100ft width 40ft height
Romashka-Z-Leto [24]

Answer:

0.89 FT

Step-by-step explanation:

8 0
3 years ago
7th grade math help me pleasee
Verizon [17]
Your Answer is Two 2
8 0
3 years ago
It costs $35 to enter an amusement park and $0.89 to ride a ride. You have $75. Write an equation that represents the number r o
Yuri [45]
Answer:
A. $35+$0.89r=$75

Explanation:
It’s only $35 to get in, you don’t have to pay an extra $35 for anything, however, the $0.89 is changeable, that’s were the variable comes in. If you go on more rides you would multiply every ride with how much it costs. The last number is how much you spend (total)
Hope this helps !
7 0
3 years ago
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