A hotdog costs $3 and a corndog costs $1.5 . If was collected, write a mathematical sentence to represent this information.
2 answers:
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Answer:
Therefore the width is 25 feet for getting maximum area.
The maximum area of the rectangle is 625 square feet.
Therefore the range is 0≤A≤625.
Step-by-step explanation:
Given function is
A = - x²+50x
We know that ,
If y = ax²+bx+c
For the maximum
Here a = -1 , b= 50 and c=0
Therefore the width
Therefore the width is 25 feet for getting maximum area.
The maximum area =[ -(25)²+50.25] square feet
= 625 square feet
The area can not be negative and maximum area is 625 square feet.
Therefore the range is 0≤A≤625.
Answer:
x = 2
Step-by-step explanation:
These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.
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<h3>Squaring</h3>The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.
The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.
x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true
x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution
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<h3>Substitution</h3>Another way to solve this is using substitution for one of the radicals. We choose ...
Solutions to this equation are ...
u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution
The value of x is ...
x = u² -2 = 2² -2
x = 2 . . . . the solution to the equation
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<em>Additional comment</em>
Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.
