Answer: $6
Step-by-step explanation:
Given: A trolley company charges a fixed amount plus a fee based on the distance traveled.
If y represents cost (dollars) charged by the company for x distance traveled (miles) .
then represents the total cost where c is the fixed charge and m is the fee for the distance traveled.
From, table we can see when x=0, y=6.
Hence, the fixed fee charged by the company is $6.
Example Question:
X²+6x-14=0
Quadratic equations are usually in the form Ax²+Bx=C. Completing the Square is a technique for rewriting this equation in the form (x+a²)+b.
The example I provided is in standard form.
Here's what I did:
Step 1: Move the "C" to the other side (in this case it's negative 14, so you add 14 to both sides of the equation to move it).
Step 2: Leave a blank after Ax²+Bx. In this case, it'll look like: X²+6x+_____= 14.
Step 3: Use the box to find the missing "C". Idk if you can see the photo after the 1st one, but I circled the spaces in green. Those spaces indicate 2 factors that add up for B (in this case, 6). Those same factors will eventually multiply each other to get 9.
Step 4: Give the new "C" to both sides of the equation. What this means is that after you multiply the factors on the outside of the box, you put the number on both sides. The 3rd picture I drew is the process of finding the outer factors (by plugging in 3x to the spaces that were circled).
If you can't see it, it's (X+3)•(X+3).
The 4th picture is me plugging the new "C" (9) to both sides of the equation. 3 times 3 is 9. You multiply the 3's on the outside to get the factors on the inside.
Step 5: Use Step 3 box to write (perfect square)² of left hand side.
What this means is that you take the factors on the outside and rewrite it in perfect square form. like shown in picture 5. If you can't see it, it's like this:
(X+3)•(X+3) turns to (X+3)²=23.
The 23 was from adding 14+9 together.
So the final Answer would be:
(X+3)²=23.
In order for <em>F</em> to be conservative, there must be a scalar function <em>f</em> such that the gradient of <em>f</em> is equal to <em>F</em>. This means
Integrate both sides of the first equation with respect to <em>x</em> :
Differentiate both sides with respect to <em>y</em> :
But we assume <em>g</em> is a function of <em>y</em>, which means its derivative can't possibly contain <em>x</em>, so there is no scalar function <em>f</em> whose gradient is <em>F</em>. Therefore <em>F</em> is not conservative.