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3 years ago

687 is greater than 587. How much greater? Explain how you know without multiplying.

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

You know that if you are multiplying a number by 5, and multiplying the same number by 6, 6 is going to be bigger

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A gym charges a membership fee of $10 per month plus a $100 application fee. Which equation best models the total cost for a gym

MatroZZZ [7]

Answer:

10(m)+100

Step-by-step explanation:

$10 is multiplied by m becuase that price depends on how many months you want the memberhsip, plus the $100 for applying.

I hope I helped <33

3 0

2 years ago

Initially tank I contains 100 litres of salt brine with a concentration of 1 kilogram per litre, and tank II contains 100 litres

Gala2k [10]

Answer:

a) $A1(t)=\frac{100000000}{(100-t)(100+t)^{2} } \\C1(t)=\frac{A1(t)}{100+t}$

b) C1 = 0.8348 [kg/lt]

Step-by-step explanation:

Explanation

First of all, the rate of change of the amount of salt in the tank I is equal to the rate of change of salt incoming less the rate change of the salt leaving, so:

$\frac{dA1(t)}{dt}= R_{in}C_{in}-R_{out}C_{out}$

We know that the incoming rate is greater than the leaving rate, this means that the fluid in the tank I enters more than It comes out, so the total rate is :

$R_{total}=R_{in}-R_{out}=\frac{2 lt}{min} - \frac{1 lt}{min}= \frac{1 lt}{min}$

This total rate means that 1 lt of fluid enters each minute to the tank I from the tank II, with the total rate we can calculate the volume in the tank I y tank II as:

$V_{I}=100 lt + Volumen_{in}= 100 lt + (\frac{1lt}{min})(t) =100+t$

$V_{II}=100 lt - Volumen_{out}= 100 lt - (\frac{1lt}{min})(t) =100-t$

Now we have the volume of both tanks, the next step is to calculate the incoming and leaving concentration. The concentration is the ratio between the amount of salt and the volume, so:

$C(t)=C_{out} =\frac{A1(t)}{V_{I} }=\frac{A1(t)}{100+t }$

Since fluid is pumped from tank I into tank II, the concentration of the tank II is a function of the amount of salt of the tank I that enters into the tank II, thus:

$C_{in} =\frac{(A1(t)/V_{I})(t)}{V_{II} }=\frac{A1(t)}{V_{I} V_{II}}(t)$

$C_{in} =\frac{A1(t)}{(100+t)(100-t)}(t)=\frac{A1(t)}{(10000-t^{2} )}(t)$

If we substitute the concentrations and the rates into the differential equation we can get:

$\frac{dA1(t)}{dt}= R_{in}C_{in}-R_{out}C_{out}\\\frac{dA1(t)}{dt}= (2)(\frac{(t)A1(t)}{10000-t^{2} })-(1)(\frac{(A1(t)}{100+t })$

$\frac{dA1(t)}{dt}= A1(t)(\frac{2t}{10000-t^{2} }-\frac{1}{100+t })$

$\frac{dA1(t)}{dt}- (\frac{2t}{10000-t^{2} }-\frac{1}{100+t })A1(t)=0$

The obtained equation is a homogeneous differential equation of first order and the solution is:

a) $A1(t)= \frac{100000000}{(100-t)(100+t)^{2} }$

and the concentration is:

$C1(t)= \frac{100000000}{(100-t)(100+t)^{3}}$

This equations A1(t) and C1(t) are only valid to 0<=t<100 because to t >=100 minutes the tank II will be empty and mathematically A1(t>=100) tends to the infinite.

b) To calculate the concentration in the tank I after 10 minutes we have to substitute t=10 in C1(t), thus:

$C1(10)= \frac{100000000}{(100-10)(100+10)^{3}}=0.8348 kg/lt$

7 0

3 years ago

Jeff ran 2 miles in 12 minutes. Ju Chan ran 3 miles in 18 minutes. Did Jeff and Ju Chan run the same number of miles per minute?

kenny6666 [7]

12/2=6mpm 18/3=6mpm yes they ran at the same rate

4 0

3 years ago

Read 2 more answers

What do the numbers represent in a linear equation in slope-intercept form?

Contact [7]

Answer:

The numbers represent in a linear equation in slope-intercept form are described

Solution:

We have to know about what do the numbers represent in a linear equation in slope-intercept form

We know that,

In the equation of a straight line when the equation is written as "y = mx + b" is called slope intercept form

The slope is the number " m " that is multiplied on the x, and " b " is the y - intercept (that is, the point where the line crosses the vertical y-axis).

And, x, y are the coordinates set representing the points a particular line which is represented by given line equation.

Hence, numbers in slope intercept form are described

5 0

3 years ago

Find the slope of the line passing through the points (-2,5) and (1,-4).

Dennis_Churaev [7]

Answer:

-3/1

Step-by-step explanation:

-4-5 -9

____ = ___ = -3/1

1-(-2) 3

5 0

3 years ago

6*87 is greater than 5*87. How much greater? Explain how you know without multiplying.

687 is greater than 587. How much greater? Explain how you know without multiplying.