Respuesta :
Quadratic equations is an equation that has a standard form of a·x² + b·x + c = 0
The correct values are presented as follows;
(a) If the pottery makes 5 bowls a week, the number of plates that can be made is 18 plates
(b) The maximum number bowls produced in a week is 15 Bowls
The reason the above values are correct are as follows:
The given relation between the number of bowls, B, and plates, P, that can be made in a week is presented as follows;
2·B² + 5·B + 25·P = 525
(a) Required: The number of plates that can be made if five (5) bowls are made each week
Solution:
To find out the number of plates that can be made, the given number of bowls (5) is placed in the equation as follows;
When B = 5, we get;
2 × 5² + 5 × 5 + 25·P = 525
25·P = 525 - (2 × 5² + 5 × 5) = 450
P = 450/25 = 18
P = 18
If the pottery makes 5 bowls a week, the number of plates that can be made, P = 18 plates
(b) Required: To find the maximum number of bowls that can be produced each week
Solution:
The given relation is rewritten as follows;
2·B² + 5·B + 25·P = 525
Given that the sum of the bowls B, produced and plates, P, produced is a constant, the maximum number of bowls is produced when the minimum number of plates are made
Therefore, when no plates are made, we get;
P = 0
2·B² + 5·B + 25×0 = 525
2·B² + 5·B = 525
2·B² + 5·B - 525 = 0
Factorizing with a graphing calculator, or by the quadratic formula, gives;
Calculator: (B - 15)·(2·B + 35) = 0
Quadratic formula: B = (-5 ± √(5² - 4 × 2 × (-525)))/(2 × 2)
∴ The maximum number bowls, B = 15 or -35/2
The positive value of B is used, therefore;
The maximum number bowls produced in a week = 15 Bowls
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