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3 years ago

HELP PLEASE!!!

Mathematics

2 answers:

Marina CMI [18]3 years ago

8 0

Answer:

The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

= -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

= -31.72x^2 + 2,030x+126.96x - 26,391

Combine like terms

= -31.72 x^2 + 2156.96 x - 26391

This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391

-36668.32+73336.64-26391

10277.32

Luba_88 [7]3 years ago

5 0

Answer:

Max profit is: $10,277.32

Selling price: $951.52

Step-by-step explanation:

Profit = Revenue - Cost

Profit = (-31.72x² + 2,030x) - (-126.96x + 26,391)

Profit = -31.72x² + 2156.96x - 26391

= -31.72(x² - 68x + 34² - 34²) - 26391

= -31.72(x² - 2(34)(x) + 34²) + 31.72(34²) - 26391

= -31.72(x - 34)² + 10277.32

Max profit is: $10,277.32

When x = 34

Revenue = -31.72(34²) + 2030(34)

= 32351.68 for 34 bags

Per bag:

32351.68/34

$951.52

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Answer:

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Step-by-step explanation:

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If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Sauron [17]

<h2>Answer:</h2>

$2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}$

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

$\vec{u}=(5,-7) \ and \ \vec{v}=(-11,3)$

So we need to find two things:

$2\vec{v}-6\vec{u}$

and:

$||2\vec{v}-6\vec{u}||$

FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

$2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}$

SECOND:

If we name:

$\vec{w}=2\vec{v}-6\vec{u}$

Then, $||2\vec{v}-6\vec{u}||$ is the magnitude of the vector $\vec{w}$ . Therefore:

$||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}$

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