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mario62 [17]
3 years ago
13

Question 8 (1 point)

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
6 0

Answer:

P_n=10+90n

Step-by-step explanation:

So it said it was linear and gave us two points on that line: (0,10) and (5,460).

y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line.  Our variables (x,y) are really (n,P) here.

The slope of the line can be computed using \frac{y_2-y_1}{x_2-x_1} where (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }.

You can also just line up the points vertically and subtract, then put 2nd difference over first difference.

Like this:

(5  ,  460)

-(0  ,    10)

--------------

5       450

So the slope is 450/5=90.

The y-intercept is where the line crosses the y-axis.  A graph crosses the y-axis when it's x value is 0.  Luckily, they give us the y-intercept which is (0,10) so b=10.  Your problem gave us this as well and was just asking for the slope of the line.

Anyways the equation is

y=90x+10

or

y=10+90x

or since we are using P and n:

P_n=10+90n

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__________________________
Given: <span>(x÷(y÷z))÷((x÷y)÷z) ;  without any specified values for the variables; 
_______________________
we shall simplify.
___________________
We have: 
__________
</span>(x÷(y÷z))  /  ((x÷y)÷z) .
_____________________________________
Start with the first term; or,  "numerator":  (x÷(y÷z)) ;
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x  ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) =  [(xz) / y ] 
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Then, take the second term; or "denominator":
_____________________________________
((x ÷ y) ÷z ) = (x / y) / z =  (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)]
_________________________________________
So (x÷(y÷z))  /  ((x÷y)÷z)  = (x÷(y÷z)) ÷  ((x÷y)÷z) =

 [(xz) / y ] ÷ [x / (zy)]  = [(xz) / y ] /  [x / (zy)] =
                                                                    [(xz) / y ] * [(zy) / x] ;
_______________________________________
                               The 2 (two) z's "cancel out" to "1" ; and
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And we are left with: z * z = z² .  The answer is:  z² .
______________________________________________


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