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3 years ago

Jayden invested $22,000 in an account paying an interest rate of 2.5% compounded

Mathematics

1 answer:

Gemiola [76]3 years ago

3 0

Answer:

12.9

Step-by-step explanation:

30400=

\,\,22000e^{0.025t}

22000e

0.025t

Plug in

\frac{30400}{22000}=

22000

30400

\,\,\frac{22000e^{0.025t}}{22000}

22000

22000e

0.025t

Divide by 22000

1.3818182=

\,\,e^{0.025t}

0.025t

\ln\left(1.3818182\right)=

ln(1.3818182)=

\,\,\ln\left(e^{0.025t}\right)

ln(e

0.025t

)

Take the natural log of both sides

\ln\left(1.3818182\right)=

ln(1.3818182)=

\,\,0.025t

0.025t

ln cancels the e

\frac{\ln\left(1.3818182\right)}{0.025}=

0.025

ln(1.3818182)

\,\,\frac{0.025t}{0.025}

0.025

0.025t

Divide by 0.025

12.9360062=

12.9360062=t

t = 12.9

12.9

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Air containing 0.04% carbon dioxide is pumped into a room whose volume is 6000 ft3. The air is pumped in at a rate of 2000 ft3/m

borishaifa [10]

Answer:

the concentration at 10 minutes= 0.4+0.0133= 0.4133%

Step-by-step explanation:

Air containing 0.04% carbon dioxide

V, volume of room is 6000 ft3.

Q, rate of air 2000 ft3/min,

initial concentration of 0.4% carbon dioxide,

determine the subsequent amount in the room at any time.

What is the concentration at 10 minutes?

firstly, we find the time taken for air to completely filled the room

Q = V/t

t = V/Q = 6000/2000 = 3min

so, its take 3mins for air to be completely filled in the room and for exhaust air to move out.

there is an initial concentration of 0.4% carbon dioxide, and the air pump in is 0.04%.

therefore,

3mins = 0.04% of CO2

3*60 =180sec = 0.04%

1sec = 0.04/180 = 0.00022%/sec

so at any time the concentration of CO2 is 0.4 + 0.00022 =0.40022%/sec

What is the concentration at 10 minute

the concentration at 10minutes = the concentration for 1minute because at every minutes, the concentration moves in is moves out. = concentration for 2000ft3.

for 0.04% = 6000ft3

? = 2000ft3

= 2000* 0.04)/6000 =0.0133%

the concentration at 10 minutes= 0.4+0.0133= 0.4133%

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3 years ago

How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.

Svetllana [295]

Answer:

Given : Expression - $x^3y^3+343$

To find : How would the sum of cubes formula be used to factor given expression? Explain the process. Do not write the factorization.

Solution :

The formula of sum of cubes is,

$a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$

First we convert the given expression in $a^3+b^3$

$x^3y^3+343$

Apply exponent rule : $a^mb^m=(ab)^m$

$x^3y^3=(xy)^3$

Rewrite $343=7^3$

Therefore, $x^3y^3+343$ could be written as $=\left(xy\right)^3+7^3$

On comparison with the formula,

a=xy , b=7

$\left(xy\right)^3+7^3=(xy+7)(xy^2-xy(7)+7^2)$

$\left(xy\right)^3+7^3=(xy+7)((xy)^2-7xy+49)$

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3 years ago

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Plz help!!<br> Consider the given right triangle.

aalyn [17]

Answer:

b = 8

c = 16

Step-by-step explanation:

From the given right triangle,

a = $8\sqrt{3}$ , m(∠B) = 30°

By applying sine rule in the given triangle,

cos(B) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

cos(B) = $\frac{BC}{AB}$

cos(30°) = $\frac{8\sqrt{3}}{c}$

$\frac{\sqrt{3} }{2}= \frac{8\sqrt{3} }{c}$

c = 16

Further we apply tangent rule,

tan(B) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(30°) = $\frac{b}{a}$

$\frac{1}{\sqrt{3}}=\frac{b}{8\sqrt{3} }$

b = 8

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3 years ago

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Sever21 [200]

Answer:

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Step-by-step explanation:

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Answer:

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3 years ago

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