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maria [59]
3 years ago
9

You deposited $10,000 in an account. Write an equation to determine the amount, A, you will have in t years if the account pays

5.75% interest compounded quarterly.
Mathematics
1 answer:
Alona [7]3 years ago
3 0

Answer:

10000 x (1.001438)^4t

Step-by-step explanation:

Using the compound interest formula Accrued Amount = P (1 + r/n)^n t

where Accrued amount is to be determined

P = principal; $10000

r = 5.75% = 0.0575

n = number of times interest is applied annually = 4 for quarterly

t = number of years

Therefore

Accrued Amount (A) = 10000 x (1 + (0.0575/4))^(4t)

= 10000 x (1 + (0.001438))^(4t)

= 10000 x (1.001438)^4t

which can then be solved by varying t, the number of years

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It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel
Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

<u><em>Solution:</em></u>

The speed is given by formula:

speed = \frac{distance}{time}

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

<em><u>The total distance travelled by the train across the bridge is given by:</u></em>

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

<em><u>Therefore, the speed is given as:</u></em>

speed = \frac{2x+ 1260}{60}

<em><u>The total distance travelled by the train through the tunnel is given by:</u></em>

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

<em><u>Therefore, the speed is given as:</u></em>

speed = \frac{2x+ 2010}{90}

The speed of the train was the same in both cases.

Equate both speeds

\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}

\frac{x+630}{30} = \frac{x+1005}{45}

45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120

Thus length of train is 120 meters

<em><u>Find the speed of train:</u></em>

speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25

Thus speed of train is 25 meter per second

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Answer:

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