Mathematics, 29.07.2019 12:00 heyItsLuna234

The table represents the change in the boiling point of water at different altitudes. altitude (in thousands of feet) boiling point of water (fahrenheit) (sea level) 0 212 0.5 211.1 1.0 210 2.0 208.4 2.5 207.5 3.0 206.6 4.0 204.8 4.5 203.9 determine the dependent and independent variables if this data were plotted. what would the slope of the graph represent?

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Answers:

1) The dependent variable is the boiling point of water and the independent variable is the altitude.

2) The slope would represent the average decrease of the boiling point of water per every one thousand feet that the altitude increase.

Explanation:

1) given

Table:

Altitude (in thousands of feet)   Boiling Point of Water (Fahrenheit)

(sea level) 0   212
0.5                                               211.1
1.0                                              210
2.0                                               208.4
2.5                                               207.5
3.0                                              206.6
4.0                                              204.8
4.5                                              203.9

2) The independent variable is the input of the function, and the dependent variable is the output of the function.

The input determines the output once the rule is established.

Therefore:

a) the independent variable is the altitude, and
b) the dependent variable is the boiling point of water in Farenheit.

3) The slope of the graph would be:

                 change in the dependent variable          change in boiling point
slope = =
                 change in the independent variable          change in altitude

Therefore, the slope represents the average change in the boiling boilin point of water every one thousand feet on change of altitude.

If the relationship is not linear, then the slope is not constant, and you will have different slopes for different parts.

If the slope is negative, means that as the altitude increase the boiling point of water decrease.

You can calculate the slope using any two pair of points (data)

              212 - 210           2
slope = =   = - 2
                0 - 1            - 1

or, using other pair of points:

                204.8 - 210           -5.2
slope = =   = -2.6
                  4.0 - 2.0               2.0

As you see, the slope is not constant. So, the function is not linear.

Answer from: Quest

i think it is c, not positive though

step-by-step explanation:

Answer from: Quest

$r(x)=-\frac{1}{50}x^2+14x$

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

$x=200,p=10$

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

$m=-\frac{1}{50}$

now, we can use point slope form of line

$p(x)=mx+b$

now, we can plug values

$p(x)=-\frac{1}{50}x+b$

we can use point

$x=200,p=10$

and find b

$10=-\frac{1}{50}\times 200+b$

$10=-4+b$

$b=14$

now, we can plug it back

and we get

$p(x)=-\frac{1}{50}x+14$

now, we can find revenue

we know that

revenue = price*quantity

so, we get

$r(x)=x\times p(x)$

$r(x)=x\times (-\frac{1}{50}x+14)$

$r(x)=-\frac{1}{50}x^2+14x$

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