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3 years ago

What is 40/17 rounded to the nearrst hundreth as a decimal

Mathematics

2 answers:

vaieri [72.5K]3 years ago

7 0

40 over 17 should be correct and can I get marked brainless

STatiana [176]3 years ago

4 0

Answer:

★ 40 over 17 is roughly 2.35294, which can be rounded to the nearest hundredth as 2.35

Step-by-step explanation:

Hope you have a great day :)

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A tank with capactity 500 gal originally contains 200 gal water with 100 lbs of salt mixed into it. Water containing 1 lb of sal

prisoha [69]

Answer:

The amount of salt in the tank at any moment $t$ is

$f(t)=-\frac {4\times 10^6}{(200+t)^2}+200+t$

The concentration of salt in the tank when it is at the point of overflowing is $0.968$ .

The theoretical limiting concentration of an infinite tank is $1$ lb per gallon.

Step-by-step explanation:

Let $f(t)$ be the amount of salt in the tank at any time $t.$

Then, its time rate of change, $f'(t)$ , by (balance law).

Since three gallons of salt water runs in the tank per minute, containing $1$ lb of salt, the salt rate is

$3.1=3$

The amount of water in the tank at any time $t$ is.

$200+(3-2)t=200+t,$

Now, the outflow is $2$ gal of the solution in a minute. That is $\frac 2{200+t}$ of the total solution content in the tank, hence $\frac 2{200+t}$ of the salt salt content $f(t)$ , that is $\frac{2f(t)}{200+t}$ .

Initially, the tank contains $100$ lb of salt,

Therefore we obtain the initial condition $f(0)=100$

Thus, the model is

$f'(t)=3-\frac{2f(t)}{200+t}, f(0)=100$

$\Rightarrow f'(t)+\frac{2}{200+t}f(t)=3, f(0)=100$

$p(t)=\frac{2}{200+t} \;\;\text{and} \;\;q(t)=3$ Linear ODE.

so, an integrating factor is

$e^{\int p dt}=e^{2\int \frac{dt}{200+t}=e^{\ln(200+t)^2}=(200+t)^2$

and the general solution is

$f(t)(200+t)^2=\int q(200+t)^2 dt+c$

$\Rightarrow f(t)=\frac 1{(200+t)^2}\int 3(200+t)^2 dt+c$

$\Rightarrow f(t)=\frac c{(200+t)^2}+200+t$

Now using the initial condition and find the value of $c$ .

$100=f(0)=\frac c{(200+0)^2}+200+0\Rightarrow -100=\frac c{200^2}$

$\Rightarrow c=-4000000=-4\times 10^6$

$\Rightarrow f(t)=-\frac {4\times 10^6}{(200+t)^2}+200+t$

is the amount of salt in the tank at any moment $t.$

Initially, the tank contains $200$ gal of water and the capacity of the tank is $500$ gal. This means that there is enough place for

$500-200=300$ gal

of water in the tank at the beginning. As concluded previously, we have one new gal in the tank at every minute. hence the tank will be full in $30$ min.

Therefore, we need to calculate $f(300)$ to find the amount of salt any time prior to the moment when the solution begins to overflow.

$f(300)=-\frac{4\times 10^6}{(200+300)^2}+200+300=-16+500=484$

To find the concentration of salt at that moment, divide the amount of salt with the amount of water in the tank at that moment, which is $500$ L.

$\text{concentration at t}=300=\frac{484}{500}=0.968$

If the tank had an infinite capacity, then the concentration would be

$\lim\limits_{t \to \infty} \frac{f(t)}{200+t}= \lim\limits_{t \to \infty}\left(\frac{\frac{3\cdot 10^6}{(200+t)^2}+(200+t)}{200+t}\right)$

$= \lim\limits_{t \to \infty} \left(\frac{4\cdot 10^6}{(200+t)^3}+1\right)$

$=1$

Hence, the theoretical limiting concentration of an infinite tank is $1$ lb per gallon.

3 0

4 years ago

The graph of a function f crosses the x-axis at -1 and 3 and touches the x-axis at 5. Which equations could define this function

sattari [20]

Given:

The points where the graph crosses the x-axis are -1 and 3.

The point where the graph touches the x-axis is at 5.

The objective is to find the correct equation of the function.

Explanation:

The equation representing the point x = -1, crossing the x-axis can be represented as,

$\begin{gathered} x=-1 \\ (x+1)=0_{} \end{gathered}$

Similarly, the equation representing the point x = 3, crossing the x-axis can be represented as,

$\begin{gathered} x=3 \\ (x-3)=0 \end{gathered}$

Similarly, the equation representing the point x = 5, touching the x-axis can be represented as,

$\begin{gathered} x=5,x=5 \\ (x-5)(x-5)=0 \\ (x-5)^2=0 \end{gathered}$

By combining all the equations of the graph, the function can be represented as,

$f(x)=(x+1)(x-3)(x-5)^2$

Hence, option (B) is the correct answer.

5 0

1 year ago

Write an equation that expresses the following relationship.

Gnesinka [82]

Answer:

p = k(d)/u^2

Step-by-step explanation:

BRAINLIEST, PLEASE!

7 0

3 years ago

Pre-calculus Help Please! Express the complex number in trigonometric form.

lana66690 [7]

We have that

3 = 3 + 0i -----------> rewrite as 3(1 + 0i)

So now what we have to do is figure out which of the above expressions has cos a = 1 and sin a = 0. 
cos 0 = 1, and sin 0 = 0, so that's the answer that we want.

the answer is: 
3 = 3(cos 0 + i sin 0)

3 0

4 years ago

3(a - 4) ≤ 33 Help me solve

yaroslaw [1]

Answer:

a ≤ 15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

3(a - 4) ≤ 33

Step 2: Solve for a

Divide 3 on both sides: a - 4 ≤ 11
Add 4 on both sides: a ≤ 15

Here we see that any value a less than or equal to 15 would work as a solution to the inequality.

3 0

3 years ago

What is 40/17 rounded to the nearrst hundreth as a decimal ​

What is 40/17 rounded to the nearrst hundreth as a decimal