Can someone plz help me on this thank you and please stop giving me links
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
Let be "x" the cost in dollars of a hamburger and "y" the cost in dollars of a soft drink.
The cost of 4 hamburguers can be represented with this expression:
And the cost of 6 soft drinks can be represented with this expression:
Since the total cost for 4 hamburgers and 6 soft drinks is $34, you can write the following equation:
<em>[Equation 1]</em>
The following expression represents the the cost of 3 soft drinks:
According to the information given in the exercise, the total cost for 4 hamburgers and 3 soft drinks is $25. Then, the equation that represents this is:
<em> [Equation 2]</em>
Therefore, the <em>Equation 1 </em>and the <em>Equation 2 </em>can be used to determine the price of a hamburger and the price of a soft drink
It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>
</span><span>In notation we write respectively
</span>
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers