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Korvikt [17]
3 years ago
13

Simplify V100 + V36 - V150

Mathematics
1 answer:
motikmotik3 years ago
5 0

Answer:

16  - 5 \sqrt{6}

Step-by-step explanation:

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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}.

4 0
3 years ago
Dvide. Give the quotient and the remainder.<br> 838/8
fiasKO [112]

Answer:

quotion is 104 and remainder is 6

4 0
2 years ago
Find the volume of the prism
weqwewe [10]
Using the formula V = bh

5 0
3 years ago
A​ 12-sided die is rolled. The set of equally likely outcomes is​ {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling
Nastasia [14]
<h3>Answer:  1/12</h3>

This is because there's one side we want (that's labeled "8") out of 12 sides total. This is of course if each side is equally likely.

Side note: this 12-sided die is known as a dodecahedron.

7 0
3 years ago
Can someone plz answer B and C
Shkiper50 [21]

B. 
When two lines intersect they form two pairs of opposite angles.
Vertical angles are always congruent, which means that they are equal.
so  m<7 = m<8 or m<3y + 19 = m<5y-29


C. solve for y and measure <7 and <8

 3y + 19 = 5y-29
5y - 3y = 19+29
2y = 48
y = 24

so
5y-29 = 5(24) - 29 = 91
3y + 19 = 3(24) + 19 = 91

so <7 = 180 - 91 = 89
<7 = <8 = 89
4 0
3 years ago
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