Answers:
4) r = √[V/(πh)]; d ≈ 5 in
5) 1.25x + 2.50y = 25.00 ; 11 combinations
Explanation:
4) (a) Formula for radius
V = πr²h Divide each side by πh
V/(πh) = r² Take the square root of each side.
r = √[V/(πh)]
(b) Diameter of tuna can
(i) Data:
V = 66 in³
h = 3.3 in
(ii) Calculations
r = √[V/(πh)]
= √[66/(π × 3.3)]
= √(20/π)
= 2√(5/π)
d = 2r
= 4√(5/π)
≈ 5 in
5) Hot dogs and hamburgers
(a) The equation
Let x = the number of hot dogs
and y = the number of hamburgers
Then
1.25x + 250y + 7 × 0.50 = 28.50
1.25x + 250y + 3.50 = 28.50 Subtract 3.50 from each side
1.25x + 2.50y = 25.00
(b) Plot the graph
Let x = 0. Then
2.50y = 25.00 Divide each side by 2.50
y = 10
Plot a point at (0, 10).
Let y = 0. Then,
1.25x = 25.00 Divide each side by 1.25
x = 20
Plot a point at (20, 0).
Draw a straight line between the two points.
Your graph should look like the one below.
(c) Hot dog/hamburger combinations
The possible hot dog/hamburger (x/y) combinations are:
0x + 10y, 2x + 9y, 4x + 8y, 6x + 7y, 8x + 6y, 10x + 5y, 12x + 4y, 14x + 3y, 16x + 2y, 18x + 1y, 20x + 0y
Thus, there are 11 different combinations that Zeke and his friends can buy for $28.50.
It works like this, because one hamburger costs $2,50 and a hamburger half as much.
You can replace one hamburger with two hot dogs (or vice versa) and still spend the same amount of money,.