Answer:
2) $40 per shirt
3) 80/9 m = 8.9 m (nearest tenth)
Step-by-step explanation:
The first question has been answered here: brainly.com/question/27846862
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<u>Question 2</u>
Given information:
- Previous sales = 300 shirts at $20 each
- For every $1 increase in price, the number of sales diminishes by 5
Let = number of $1 increases
Let = total revenue (in dollars)
From the given information:
- Price change of shirt:
- Number of sales change:
Therefore, we can create a <u>quadratic equation</u> with the given information:
As we need to find the maximum amount of revenue, we need to find the vertex of . As the equation is already factored, the quickest way to do this is to the find the mid-point of the zeros (since a quadratic curve is symmetrical).
Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:
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<u>Question 3</u>
Given information:
- Bridge is modeled as a parabola
- Width of bridge = 30 m
- Max height of bridge = 10 m high (in the middle)
As the bridge is modeled as a parabola, and we have been given the width and height, we can create a quadratic equation using the vertex form.
Vertex form:
where:
- x is the horizontal distance of the bridge
- y is the height of the bridge
- (h, k) is the vertex
- a is some constant
Middle of the bridge = 30 m ÷ 2 = 15 m
Max height of the bridge = 10 m
Therefore, the vertex of the parabola is (15, 10)
We know that when . Therefore, substitute these values into the equation and solve for a:
Therefore, the equation of the parabola is:
The horizontal distance at 5 m right of the middle is:
Therefore, to find the height at this point, input into the equation and solve for y:
Therefore, the height of the bridge at 5 m to the right of the middle is:
