Answer:
Step-by-step explanation:
We have the two points (3<em>a</em>, 4) and (<em>a</em>, -3).
And we want to find the value of <em>a</em> such that the gradient of the line joining the two points is 1.
Recall that the gradient or slope of a line is given by the formula:
Where (<em>x₁, y₁</em>) is one point and (<em>x₂, y₂</em>) is the other.
Let (3<em>a, </em>4) be (<em>x₁, y₁</em>) and (<em>a</em>, -3) be (<em>x₂, y₂</em>). Substitute:
Simplify:
We want to gradient to be one. Therefore, <em>m</em> = 1:
Solve for <em>a</em>. Rewrite:
Cross-multiply:
Therefore:
The solution:
For the bread:
Area = π R²
16 in² = π R²
R² = 16 in² / π
Bun radius = √(16 in² / π) = 2.257 inches
For the meat:
Area = side²
16 in² = side²
Side = √16 in² = 4 inches
Diagonal of the square = 4 √2 = 5.657 inches
1/2 of the burgerdiagonal = 2.828 inches .
If the meat is placed on the center of the bun, then the
corner of the burger
extends to: (2.828 - 2.257) = 0.57 inch