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____
2 days ago
13

Jenna saves $2,500 per year in an account that earns 10% interest per year, compounded annually. Jenna will have(A $411,234) (B

$425,352) (C $449,739) saved in 30 years. Her account balance is a result of Jenna’s(A annuity payments)(B lump-sum payment) .
Mathematics
1 answer:
Leona [9.2K]2 days ago
3 0

Response:

The result is $43623.50

Detailed explanation:

This query involves compound interest.

The formula for calculating compound interest is

A=P(1+r)^t

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Provided information

P= $2,500

r= 10/100= 0.1

t= 30 years

Inserting values into the compound interest formula and calculating A gives us

A=2500(1+0.1)^30

A=2500(1.1)^30

A=2500*17.449

A=$43623.50

The total amount is $43623.50

The balance in her account comes from Jenna’s (A annuity payments)

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If g(x)=4x^2-16 were shifted 5 units to the right and 2 down, what would the new equation be?
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When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is t
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The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

\boxed{u \ or \ v_i = initial \ velocity}

\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}

\boxed{a = acceleration \ (constant)}

\boxed{d = distance \ travelled}

We know the flea attains a takeoff velocity of 1.0 m/s over a distance of 0.50 mm.

The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

\boxed{ \ v^2 = u^2 + 2ad \ }

  • a = acceleration (m/s²)
  • u = initial speed = 0 m/s
  • v = takeoff velocity = 1.0 m/s
  • d = displacement = 0.50 mm

First, convert 0.50 mm to meters: \boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}

Solution steps:

Rearrange the formula to isolate acceleration (a).

\boxed{ \ v^2 = u^2 + 2ad \ }

\boxed{ \ v^2 - u^2 = 2ad \ }

\boxed{ \ 2ad = v^2 - u^2 \ }

\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }

Insert the given values into the rearranged equation.

\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }

\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }

\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }

\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }

This yields the flea's acceleration as 1,000 m/s².

Additional resources

  1. Scientific notation: brainly.com/question/7263463
  2. Determining substance mass: brainly.com/question/4053884
  3. Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

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