Answer: See Annex
z (max) = 190
x = 10
y = 20
Step-by-step explanation:
z = 5*x + 7*y to maximize
Subject to:
x + y ≤ 30
2*x + y ≤50
2*x - y ≥ 0
x≥= y ≥0
Use the Distributive Property to expand this expression.
2 answers:
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Answer: area = 379.7 mm²
Perimeter = 95.84 mm
Step-by-step explanation:
The composite shape contains a semi circle and a trapezoid.
The area of a semi circle is
1/2 × πr²
Radius = diameter/2
Radius = 20/2 = 10 mm
Area = 1/2 × 3.14 × 10 = 15.7 mm²
Area of trapezoid is expressed as
1/2(a + b)h
Area = 1/2 × (20 + 32)14
Area = 1/2 × 52 × 14) = 364mm²
Area of the composite shape is
15.7 + 364 = 379.7 mm²
Formula for determining the perimeter of the semicircle is
1/2 × πd
Perimeter = 1/2 × 3.14 × 20 = 31.4mm
Looking at the attached photo, we would determine the slant height,h, by applying Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 12² + 14² = 340
h = √340/= 18.44
Perimeter of the composite shape is
31.4 + 14 + 32 + 18.44 =95.84 mm
