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svet-max [94.6K]
3 years ago
11

Item 11 Identify the independent and dependent variables. The equation c=0.09s gives the amount c (in dollars) of commission a s

alesperson receives for making a sale of s dollars Item 11 Identify the independent and dependent variables. The equation c=0.09s gives the amount c (in dollars) of commission a salesperson receives for making a sale of s dollars
Mathematics
1 answer:
diamong [38]3 years ago
6 0

Answer:

C is dependent variable

S is independent variable

Step-by-step explanation:

Here, give the equation, we are told to identify the independent and the dependent variable

When we talk of the independent variable, it is that variable which values does not depend on whatever values the second variable in the equation has. It is that variable that is used to find the other variable in the equation

While the dependent variable depends on the values we input in the equation. It is the variable that we arrive at after plugging different values for the independent variable

now looking at the question, the equation we have is as follows;

c = 0.09s

To get the value of c which is the cost , we have to input different values of a. As is the amount in sales that we have that will yield the value of the commission to be received

Thus, we can categorically say that the values of the commission are dependent on the values we get from the sales

Hence, while commission represents the dependent variable, the values of the sales are the independent variables

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Assessing the situation:

Let's get a feel for the shape of the problem here: what step should we be aiming to get to by the end? We want to find out how long it will take, in minutes, for the tank to drain completely, given a drainage rate of 400 L/s. Let's name a few key variables we'll need to keep track of here:

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We're about ready to set up an expression using those variables, but first, we should address a subtlety: the question provides us with the drainage rate in liters per second. We want the answer expressed in liters per minute, so we'll have to make that conversion beforehand. Since one second is 1/60 of a minute, a drainage rate of 400 L/s becomes 400 · 60 = 24,000 L/min.

From here, we can set up our expression. We want to find out when the tank is completely drained - when the water volume is equal to 0. If we assume that it starts full with a water volume of V L, and we know that 24,000 L is drained - or subtracted - from that volume every minute, we can model our problem with the equation

V-24000t=0

To isolate t, we can take the following steps:

V-24000t=0\\ V=24000t\\ \frac{V}{24000}=t

So, all we need to do now to find t is find V. As it turns out, this is a pretty tall order. Let's begin:

Solving for V:

About units: all of our measurements for the cone-shaped tank have been provided for us in meters, which means that our calculations will produce a value for the volume in cubic meters. This is a problem, since our drainage rate is given to us in liters per second. To account for this, we should find the conversion rate between cubic meters and liters so we can use it to convert at the end.

It turns out that 1 cubic meter is equal to 1000 liters, which means that we'll need to multiply our result by 1000 to switch them to the correct units.

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V= \frac{1}{3}\pi r^2h

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