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vladimir2022 [97]
2 years ago
5

Can someone help please?

Mathematics
2 answers:
tangare [24]2 years ago
7 0

Answer:

s=26

Step-by-step explanation:

anzhelika [568]2 years ago
7 0

Answer:

26

Step-by-step explanation:

hope it helps

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Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br
Lina20 [59]

Answer:

The differential equation for the amount of salt A(t) in the tank at a time  t > 0 is \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t

where, \text{R}_i_n = concentration of salt in the inflow \times input rate of brine solution

and \text{R}_o_u_t = concentration of salt in the outflow \times outflow rate of brine solution

So, \text{R}_i_n = 4 lb/gal \times 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

                                                = 3 gal/min - 2 gal/min

                                                = 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, \text{R}_o_u_t = concentration of salt in the outflow \times outflow rate of brine solution

             = \frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min} = \frac{2A(t)}{500+t} \text{ lb/min }

Now, the differential equation for the amount of salt A(t) in the tank at a time  t > 0 is given by;

= \frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }

or \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

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What is the product of the polynomials below? (4x^2-2x-4)(2x+4)
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Answer:  8x³ + 12x² - 16x - 16

<u>Step-by-step explanation:</u>

  (4x² - 2x - 4)(2x + 4)

= (2x + 4)(4x² - 2x - 4)

= 2x(4x² - 2x - 4)  +  4(4x² - 2x - 4)

=   8x³ - 4x² - 8x   +  16x² - 8x - 16

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You can find slope by using the slope formula. Because we are already given two coordinate points, we can use that to find our slope. The slope formula is \frac{y^{2}-y^{1}  }{x^{2}-x^{1} }. This also refers to \frac{5-(-5)}{0-4} or 10/-4 or -5/2. Any coordinate with the x-value as 0 means that that coordinate is the y-intercept. Because (0,5) has 0 as its x-value, the y-intercept is 5.

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