The solution is 20 days, found as follows:
Each of the three friends initially makes 4 bags of dough. After 10 days, each of these bags is split into 4 new bags:
3 friends × 4 bags = 12 bags, and 12 bags × 4 = 48 bags
Then in the following 10 days, 48 bags are again divided into 4 bags each:
48 × 4 = 192 bags
Adding the periods: 10 days + 10 days = 20 days
Therefore, 192 bags are created after 20 days.
Take note of the image below
the riverbank requires no fencing due to the river's presence
so the pen's perimeter can be calculated as 2w + l, or w + w + l
thus

derive P(w), set it to zero, locate any critical points, and perform a first-derivative test for minimum values.
Answer:



Step-by-step explanation:
Given



Solving for (a): n
To find n;
We will utilize

Substituting values for XY and XZ



Dividing by -6

Solving for (b) XY

Substituting 3 for n



Solving for (c): XZ


The statements labeled 1 and 4 are accurate. To easily see the center and radius of the circle, we can modify the given equation to fit its standard format. Once in standard form, we can contrast it with the standard equation to find the circle's center and radius. The coordinates for the center are determined to be (1,0) and the radius is represented by

. With this understanding, we can evaluate each statement. 1. The circle's radius is 3 units—this is true. 2. The circle's center is located on the y-axis—this is incorrect, as the center at (1,0) indicates it is on the x-axis. 3. The standard equation is (x - 1)² + y² = 3—this is false; the correct equation is (x - 1)² + y² = 9. 4. The circle's radius matches that of the circle with the equation x² + y² = 9—this statement is correct, as both radii equal 3.