The dog house consists of two geometric objects, triangular prism and rectangular prism.
First, find the surface area of triangular prism
The triangular prism consists of
base of triangle (b) = 3 ft
height of triangle (h) = 2.5 ft
height of prism or length of rectangle (l) = 4 ft
side of triangle or width of rectangle (w) = 2.5 ft
Now, calculate the area
area of tp = area of two triangle + area of 2 rectangle
area of tp = (2 × 1/2 × b × h) + (2 × l × w)
area of tp = (2 × 1/2 × 3 × 2) + (2 × 4 × 2.5)
area of tp = 6 + 20
area of tp = 26 ft²
Second, find the surface area of rectangular prism
The rectangular prisms consists of
length (l) = 3 ft
width (w) = 4 ft
height (h) = 2 ft
Now, calculate the area
area of rp = area of back and front rectangle + area of left and right rectangle
area of rp = (2 × l × h) + (2 × w × h)
area of rp = (2 × 3 × 2) + (2 × 4 × 2)
area of rp = 12 + 16
area of rp = 28 ft²
Third, add both of the area
area = area of tp + area of rp
area = 26 + 28
area = 54 ft²
The area of the dog house is 54 ft²
Answer:
car covers distance of 450 km in 4hr and 30min
4hr and 30 min - (4*60)+ 30 equal to 270
distance covered by car in one minute equal to 450/270 equal to 1.6 km
speed of car equal to (1.6*60)/60 equal to 1.6 km /hr
4 hours for 18
7 hours for 25.50
Difference in hours: 7-4 = 3
Difference in cost: 25.50 - 18 = 7.50
7.50 / 3 = 2.50
A. They charge 2.50 per hour.
B. 2.50 x 4 = 10
18 - 10 = 8
The flat fee is 8 dollars
C. 8 + (2 x 2.50) = 13 dollars
She can arrange them in the following;
1 row of 36
2 rows of 18 (doesnt count because it says other and this has already been mentioned)
3 rows of 12
4 rows of 9 (doesnt count because it says other and this has already been mentioned)
6 rows of 6
Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
