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AlladinOne [14]
3 years ago
14

Plz Help im horrible at math if someone can help that would be much appreciated

Mathematics
1 answer:
timurjin [86]3 years ago
6 0
We need to compute the slope of the graph shown

m = (y2 - y1)/(x2 - x1)
m = (25-10)/(5-2)
m = 15/3
m = 5

The slope of 5 means the graph tells us "she is walking 5 feet per second".

So the first part of her walk is at 4 feet per second, then the second part of her walk is at 5 feet per second. The second part of her walk is faster. As a story scenario, perhaps she realizes she is going to be late getting home which is why she is walking a bit faster now. 
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Express the illuminance on the floor as a composite function of t for 0 &lt; t &lt; 8.
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3 years ago
Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different
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Answer:

(a)  As time increases, the amount of water in the pool increases.

     11 gallons per minute

(b)  65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate.  Therefore, this can be modeled as a linear function.  

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

\textsf{let}\:(x_1,y_1)=(8, 153)

\textsf{let}\:(x_2,y_2)=(12,197)

Input these into the slope formula:

\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

y-y_1=m(x-x_1)

\implies y-153=11(x-8)

\implies y-153=11x-88

\implies y=11x-88+153

\implies y=11x+65

When Ann had added no water, x = 0.  Therefore,

y=11(0)+65

y=65

So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.

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