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2 years ago

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Hurry quickly and answer as fast as possible!!! Three years ago, Isabel got her first job after graduating from college. Once sh

e began earning a steady monthly income, she decided to start saving for a new car. To help her stay on track with her savings, Isabel set up a savings account at her bank and arranged to automatically transfer money into it. On the 15th of every month, the bank transfers $200 from her checking account to her savings account. The interest on her savings account is 1.70% compounded monthly.
Which term best describes the savings account that Isabel has set up, given its purpose?

Select the correct answer.
emergency fund
mutual fund
rainy-day fund
sinking fund

1 answer:

mrs_skeptik [129]2 years ago

7 0

Answer:

.

Step-by-step explanation:

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A 400 gallon tank initially contains 100 gal of brine containing 50 pounds of salt. Brine containing 1 pound of salt per gallon

posledela

Answer:

The amount of salt in the tank when it is full of brine is 393.75 pounds.

Step-by-step explanation:

This is a mixing problem. In these problems we will start with a substance that is dissolved in a liquid. Liquid will be entering and leaving a holding tank. The liquid entering the tank may or may not contain more of the substance dissolved in it. Liquid leaving the tank will of course contain the substance dissolved in it. If Q(t) gives the amount of the substance dissolved in the liquid in the tank at any time t we want to develop a differential equation that, when solved, will give us an expression for Q(t).

The main equation that we’ll be using to model this situation is:

Rate of change of <em>Q(t)</em> = Rate at which <em>Q(t)</em> enters the tank – Rate at which <em>Q(t)</em> exits the tank

where,

Rate at which Q(t) enters the tank = (flow rate of liquid entering) x

(concentration of substance in liquid entering)

Rate at which Q(t) exits the tank = (flow rate of liquid exiting) x

(concentration of substance in liquid exiting)

Let y<em>(t)</em> be the amount of salt (in pounds) in the tank at time <em>t</em> (in seconds). Then we can represent the situation with the below picture.

Then the differential equation we’re after is

$\frac{dy}{dt} = (Rate \:in)- (Rate \:out)\\\\\frac{dy}{dt} = 5 \:\frac{gal}{s} \cdot 1 \:\frac{pound}{gal}-3 \:\frac{gal}{s}\cdot \frac{y(t)}{V(t)} \:\frac{pound}{gal}\\\\\frac{dy}{dt} =5\:\frac{pound}{s}-3 \frac{y(t)}{V(t)} \:\frac{pound}{s}$

$V(t)$ is the volume of brine in the tank at time <em>t. </em>To find it we know that at time 0 there were 100 gallons, 5 gallons are added and 3 are drained, and the net increase is 2 gallons per second. So,

$V(t)=100 + 2t$

We can then write the initial value problem:

$\frac{dy}{dt} =5-\frac{3y}{100+2t} , \quad y(0)=50$

We have a linear differential equation. A first-order linear differential equation is one that can be put into the form

$\frac{dy}{dx}+P(x)y =Q(x)$

where <em>P</em> and <em>Q</em> are continuous functions on a given interval.

In our case, we have that

$\frac{dy}{dt}+\frac{3y}{100+2t} =5 , \quad y(0)=50$

The solution process for a first order linear differential equation is as follows.

Step 1: Find the integrating factor, $\mu \left( x \right)$ , using $\mu \left( x \right) = \,{{\bf{e}}^{\int{{P\left( x \right)\,dx}}}$

$\mu \left( t \right) = \,{{e}}^{\int{{\frac{3}{100+2t}\,dt}}}\\\int \frac{3}{100+2t}dt=\frac{3}{2}\ln \left|100+2t\right|\\\\\mu \left( t \right) =e^{\frac{3}{2}\ln \left|100+2t\right|}\\\\\mu \left( t \right) =(100+2t)^{\frac{3}{2}$

Step 2: Multiply everything in the differential equation by $\mu \left( x \right)$ and verify that the left side becomes the product rule $\left( {\mu \left( t \right)y\left( t \right)} \right)'$ and write it as such.

$\frac{dy}{dt}\cdot \left(100+2t\right)^{\frac{3}{2}}+\frac{3y}{100+2t}\cdot \left(100+2t\right)^{\frac{3}{2}}=5 \left(100+2t\right)^{\frac{3}{2}}\\\\\frac{dy}{dt}\cdot \left(100+2t\right)^{\frac{3}{2}}+3y\cdot \left(100+2t\right)^{\frac{1}{2}}=5 \left(100+2t\right)^{\frac{3}{2}}\\\\\frac{dy}{dt}(y \left(100+2t\right)^{\frac{3}{2}})=5\left(100+2t\right)^{\frac{3}{2}}$

Step 3: Integrate both sides.

$\int \frac{dy}{dt}(y \left(100+2t\right)^{\frac{3}{2}})dt=\int 5\left(100+2t\right)^{\frac{3}{2}}dt\\\\y \left(100+2t\right)^{\frac{3}{2}}=(100+2t)^{\frac{5}{2} }+ C$

Step 4: Find the value of the constant and solve for the solution y(t).

$50 \left(100+2(0)\right)^{\frac{3}{2}}=(100+2(0))^{\frac{5}{2} }+ C\\\\100000+C=50000\\\\C=-50000$

$y \left(100+2t\right)^{\frac{3}{2}}=(100+2t)^{\frac{5}{2} }-50000\\\\y(t)=100+2t-\frac{50000}{\left(100+2t\right)^{\frac{3}{2}}}$

Now, the tank is full of brine when:

$V(t) = 400\\100+2t=400\\t=150$

The amount of salt in the tank when it is full of brine is

$y(150)=100+2(150)-\frac{50000}{\left(100+2(150)\right)^{\frac{3}{2}}}\\\\y(150)=393.75$

6 0

2 years ago

Which triangle defined by three points on the coordinate plane is congruent with the triangle illustrated, and why?

HACTEHA [7]

The triangle defined by three points on the coordinate plane is congruent with the triangle illustrated:

C) (4,2); (8,2); (4,8) because the corresponding pairs of sides and corresponding pairs of angles are congruent.

If we plot these points we can observe that they are congruent, we should also solve for the distance of each point between each other to conclude their congruency.

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2 years ago

Read 2 more answers

General solution of equation sin x + sin 5x = sin 2x + sin 4x is

zaharov [31]

Answer:

x=nπ3, n∈I

Step-by-step explanation:

sin x + sin 5x = sin 2x + sin 4x

⇒⇒ 2 sin 3x cos 2x = 2 sin 3x cos x

⇒⇒ 2 sin 3x(cos 2x - cos x) = 0

⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I

or cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x

⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3 , n∈I, n∈I

But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I

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2 years ago

The geometric average of -12%, 20%, and 25% is _________.

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<span>20.28% is the answer</span>

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2 years ago

Louise begins factoring the polynomial, which has four terms.

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Louise wants to factorize completely the given polynomial $4x^{3}+12x^{2}+5x+15$

Grouping first, second terms together and third, fourth terms together

= $4x^{3}+12x^{2}+5x+15$

Taking $4x^{2}$ common from first and second terms of the given expression and taking 5 common from the third and fourth terms.

= $=4x^{2}(x+3)+5(x+3)$

Taking (x+3) common from the given expression,

= $=(4x^{2}+5)(x+3)$ is the completely factored form.

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2 years ago