ratio of adults to students can be written as a fraction
adult tickets / student tickets
140/210 can be simplified to 14/21
14/21 can be simplifed to 2/3
Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
Answer:
No solution
Step-by-step explanation:
Unfortunately your screenshot has cut off the final answer choice, if it says "no solution" you should choose that because these two lines are parallel. Meaning they will never intersect, and the point of intersection is usually the solution.
<u>Part A</u>
<u />
<u>Part B</u>
The vertex of the graph will be a maximum because the leading coefficient is negative.
The x coordinate of the vertex is 
.
When x=15/8, 
.
So, the vertex has coordinates 
<u>Part C</u>
Plot the two x-intercepts and the vertex and then draw a curve in the shape of a parabola passing through them.
The graph is in the attached image.
