Homer made an error in step 2
When completing the square, it's necessary to apply the adjustments to both sides of the equation
Solution:
The provided equation for the circle:
First, let’s determine the center and the radius and identify where the mistake occurred
Step 1:
Group the terms
Step 2:
However, Homer’s second step is:
Thus, Homer committed an error during this step
When completing the square, the values must be added to both sides of the equation
However, Homer neglected to add 49 and 1 to the right side of the equation
Correct steps are:
By comparing with the general equation of a circle,
It follows that the center coordinates are ( 7, -1) and the radius measures 8.66
Answer:
The amount of ovens that must be produced in a week to earn a $1610 profit is 70.
Step-by-step explanation:
Given:
A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:
with 0 ≤ x ≤ 200.
The target profit is $1610
So, set P = 1610, then solve for x:
Multiply both sides by 10:
Next, factor the quadratic:
Solving for x gives:
Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.
Hence, the valid solution is x=70.
Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.
Answer:
3/2
Step-by-step explanation:
Given that AC = BC, this is an isosceles triangle.
Since CD is perpendicular to AB, we find AD = DB = 0.5AB = 3/2
Now considering triangle ACD,[TAG_17]]
we will use Pythagoras' theorem,
AC =
AC = 3/2