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2 years ago

What is the missing polynomial?

Mathematics

2 answers:

Mekhanik [1.2K]2 years ago

4 0

Answer:

C. 40-4x-12x^2

Step-by-step explanation:

got it right on the quiz

Andre45 [30]2 years ago

3 0

Very simple

? – (20 – 4x – 5x2) = 20 – 7x2, so ? = 20 – 7x2 + (20 – 4x – 5x2)
? = 20 – 7x2 + (20 – 4x – 5x2)=20-7x²+20-4x-5x²=40-12x²-4x
the answer is C. 40-4x-12x^2

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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 Q(t) = Rate at which Q(t) enters the tank – Rate at which Q(t) 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(t) be the amount of salt (in pounds) in the tank at time t (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 t. 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 P and Q 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

Now let the figure show a scale drawing of a park. The scale is 1 unit : 25 meters. What is the horizontal distance across the p

insens350 [35]

The question is missing the figure. So, the figure is attached below.

Answer:

C. 350 m

Step-by-step explanation:

Given:

Scale is given as:

1 unit : 25 meters

This means that 1 unit on the grid is equivalent to 25 meters in actual.

Now, from the figure, the horizontal distance across the park is 14 units.

1 unit = 25 meter

Now, we can find the actual distance using unitary method and thus multiplying 25 and 14 to get the actual distance across the park horizontally.

∴ 14 units = $25\times 14=350$ meters.

Therefore, the horizontal distance across the park is 350 m in actual.

So, the correct option is option C.

7 0

2 years ago

At the Hardey Fitness Center, the management did a survey of their membership. The average age of the female members was 40 year

faust18 [17]

Answer:

5 / 8

Step-by-step explanation:

Given :

Average age of male = 25

Average age of female = 40

Average age of entire membership = 30

The ratio of female to male students :

Male students : Female students

25 : 40

5 : 8

5/8

8 0

2 years ago

Andrea's family stopped at the gas station to get gas. At gas stations, the price of gas per gallon is given to the nearest thou

Lelechka [254]

One hundredth is 0.01. If a number is above 4 it is rounded up. If it is below five, it is rounded down. 3 is rounded down to $2.49. 8 is rounded up to give $2.50. 5 is rounded up to give $2.51. 9 is rounded up to give $2.51. The answer is $2.498.

6 0

2 years ago

Read 2 more answers

If x and y satisfy both 9x+2y=8 and 7x+2y=4, then y=?

Alex

Answer:

The value of y is -5

Step-by-step explanation:

we have

$9x+2y=8$ ------> equation A