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2 years ago

Suppose ABCD is a rectangle. Find AB and AD if point M is the midpoint of BC,

Mathematics

1 answer:

Anit [1.1K]2 years ago

4 0

Answer:

Step-by-step explanation:

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A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into t

inn [45]

Answer:

The number A(t) of pounds of salt in the tank at time 't' is;

${A(t)}= -2,100 \times e^{\dfrac{-t}{100} } + 2,100$

Step-by-step explanation:

In the question, we have;

The volume of pure water initially in the tank = 700 gal

The concentration of brine pumped into the tank = 3 pounds per gallon

The rate at which the brine is pumped into the tank, = 7 gal/min

The rate at which the well mixed solution is pumped out = The same 7 gal/min

The number of pounds of salt in the tank at time 't' is found as follows;

The rate of change in A(t) with time = The rate of salt input - The rate of salt output

$The \ rate \ of \ change \ in \ A(t) \ with \ time = \dfrac{dA}{dt}$

The rate of salt input = 7 gal/min × 3 lbs/gal = 21 lbs/min

The rate of salt output = (A(t)/700) lb/gal × 7 gal/min = (A(t)/100) lb/min

Therefore, we have;

$\dfrac{dA}{dt} = 21 - \dfrac{A(t)}{100}$

Therefore;

$\dfrac{dA}{dt} + \dfrac{A(t)}{100}= 21$

The integrating factor is $e^{\int\limits {\frac{1}{100} } \, dx } = e^{\frac{x}{100} }$

$e^{\dfrac{t}{100} } \times \dfrac{dA}{dt} + e^{\dfrac{t}{100} } \times\dfrac{A(t)}{100}= e^{\dfrac{t}{100} } \times21$

$\dfrac{d}{dt} \left[ e^{\dfrac{t}{100} } \times{A(t)}{} \right]= e^{\dfrac{t}{100} } \times21$

Using an online tool, we get;

${A(t)}= c_1 \times e^{\dfrac{-t}{100} } + 2,100$

At time t = 0, A(t) = 0

We get;

$0= c_1 \times e^{\dfrac{-0}{100} } + 2,100$

c₁ = -2,100

Therefore, the number A(t) of pounds of salt in the tank at time 't' is given as follows;

${A(t)}= -2,100 \times e^{\dfrac{-t}{100} } + 2,100$

8 0

3 years ago

-12,60,-300,1500 what are the next two number s

larisa86 [58]

Answer:-7500, 37,500

Step-by-step explanation:

The patter is multiply by negative 5 -12*5=60, 60*-5=-300... so 1500* -5=-7500, and -7500*-5=37,500

3 0

3 years ago

Read 2 more answers

Steps on how to solve the expression -17.8 divided by 1/6

Lubov Fominskaja [6]

Dividing a number is really just multiplying by the conjugate of the divisor. Thus, -17.8 divided by 1/6 equals -17.8 * 6, which equals -106.8

4 0

3 years ago

Pls help<br> 16x^2-64x=0

Slav-nsk [51]

the answer is above one

x=4

x=0

5 0

3 years ago

Tony is 21 years older than his sister Danielle. In 13 years he will be twice as old as Danielle. How old is each of them now?

Bess [88]

x-y=21 ⇒ x=y+21

x+13=2y

Substitute y+21 for x into the equation x+13=2y

So y+21+13=2y

Simplify 34=y

So Danielle is 34 years old. Plug y back in to the original equation

x-34=21

x=55

Tony is 55 years old

3 0

4 years ago