Question

Can you guys help me with this math questions

Answer 1

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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Question 2

Given information:

• Previous sales = 300 shirts at $20 each
• For every $1 increase in price, the number of sales diminishes by 5

Let $x$ = number of $1 increases

Let $y$ = total revenue (in dollars)

From the given information:

• Price change of shirt:  $(20 + x)$

• Number of sales change:  $(300 - 5x)$

Therefore, we can create a quadratic equation with the given information:

$\implies y = (20+x)(300-5x)$

As we need to find the maximum amount of revenue, we need to find the vertex of $y$.  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).

$\begin{aligned}y & =0\\\implies (20+x)(300-5x) & =0\\\implies (20+x) & =0 \implies x=-20\\\implies (300-5x) & = 0 \implies x=60\end{aligned}$

$\textsf{Midpoint}=\dfrac{-20+60}{2}=20$

Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:

$\implies \ 20 + 20 \times \ 1 = \ 40\: \sf per\:shirt$

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Question 3

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:  $y=a(x-h)^2+k$

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)

$\implies y=a(x-15)^2+10$

We know that when $x = 0, y = 0$.  Therefore, substitute these values into the equation and solve for a:

$\implies 0=a(0-15)^2+10$

$\implies 0=225a+10$

$\implies 225a=-10$

$\implies a=-\dfrac{10}{225}$

$\implies a=-\dfrac{2}{45}$

Therefore, the equation of the parabola is:

$\implies y=-\dfrac{2}{45}(x-15)^2+10 \quad \quad \textsf{for }0\leq x\leq 30$

The horizontal distance at 5 m right of the middle is:

$\implies \dfrac{30}{2}+5=20\:\sf m$

Therefore, to find the height at this point, input $x=20$ into the equation and solve for y:

$\implies -\dfrac{2}{45}(20-15)^2+10=\dfrac{80}{9}\:\sf m$

Therefore, the height of the bridge at 5 m to the right of the middle is:

$\dfrac{80}{9}\:=8.9\: \sf m\:(nearest\:tenth)$