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Since both is equal to p(a), you can set them as equal to each other:
15 = 2a - 3
18 = 2a
9 = a
Answer:
Per child admission costs $8.5
Per Adult admission costs $13.5
Step-by-step explanation:
Let x be the amount of admission per child and y be the amount of admission per adult
For Tom's party:
13x+2y=137.50 (Equation 1)
For Lisa's Party:
9x+2y=105.50 (Equation 2)
Using Elimination Method:
Add Equation 1 & 2
13x+2y=137.50
9x+2y=105.50
- - = - (Change of Signs)
---------------------------------
4x+0y=34.00
x=34/4
x=8.5
Putting the value of x in Equation 2
13(8.5)+2y=137.50
110.5+2y=137.50
2y=137.50-110.50
2y=27
y=27/2
y=13.5
The point (2, 5) is not on the curve; probably you meant to say (2, -5)?
Consider an arbitrary point Q on the curve to the right of P, 
, where 
. The slope of the secant line through P and Q is given by the difference quotient,
where we are allowed to simplify because 
.
Then the equation of the secant line is
Taking the limit as 
, we have
so the slope of the line tangent to the curve at P as slope 2.
- - -
We can verify this with differentiation. Taking the derivative, we get
and at 
, we get a slope of 
, as expected.
