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3 years ago

What is the additive identity of a

Mathematics

1 answer:

Lady_Fox [76]3 years ago

6 0

Answer:

a+0 (or just 0)

Step-by-step explanation:

The additive identity is when you add any number by zero. This is because an additive identity is what number do you add to make the same number (since it's additive it is zero, if it were multiplicative, it'd be 1)

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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

What value of n makes the<br> statement true?<br> nx(7 + 8) = (5 x 7) + (5 x 8)

Sindrei [870]

Answer:

n=5

Step-by-step explanation:

i hope this helps :)

3 0

3 years ago

Can anyone help out with the first question so I can get an idea with the others?

Oksanka [162]

As you can see, the first number line is divided into tenths (0.1, 0.2, 0.3). So, put 8.152 in between 8.1 and 8.2.

Then, the ends of the next number line should be 8.1 at the start, and 8.2 at the end. You keep going smaller to find the exact spot. So, move 5 places inwards and place the 8.153, between 8.15 and 8.16.

Afterwards, the ends of the last number line should be 8.15 and 8.16. Now, it is divided into thousandths. So, find the third spot. Now, it should be 8.153 correctly labeled.

7 0

4 years ago

ANSWERS NOW HELP OR ELSE

vekshin1

Answer:

obama in brazil

Step-by-step explanation:

brazil

5 0

3 years ago

A number m is formed by writing all the prime numbers between 0 and 10 in ascending order. another number n is formed by writing

Brums [2.3K]

Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are 1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

3 0

2 years ago