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aleksklad [387]
3 years ago
14

A 6-foot piece of ribbon costs $15.84. What is the price per inch?

Mathematics
2 answers:
sleet_krkn [62]3 years ago
6 0

Answer:

$0.22/inch

Step-by-step explanation:

6 ft = 72 inches

15.84/72 =0.22

yan [13]3 years ago
5 0
$15.84 divided by 6 =$2.64
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The equation of the function is Y=4x+5.Find the value of y when<br> x=3<br> x=-2
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<h2><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>

The equation of the function is y = 4x + 5. Find the value of y when

x = 3

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<h2><u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u>:-</h2>

<h3>Given:-</h3>

y = 4x + 5 [Equation]

<h3>To Find:-</h3>

The value of y when x = 3 , x = -2

<h2>Solution:-</h2>

y = 4x + 5 [Given equation]

\therefore When x = 3 ,

y = 4 × 3 + 5 [Value of x is 3]

y = 12 + 5

<h3>y = 17 [Answer]</h3>

Again, when x = -2 ,

y = 4 × (-2) + 5 [Value of x is -2]

y = -8 + 5

<h3>y = -3 [Answer]</h3>

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Step-by-step explanation:

The method of Lagrange multipliers can solve this quickly. For objective function f(x, y) and constraint function g(x, y)=0 we can set the partial derivatives of the Lagrangian to zero to find the values of the variables at the extreme of interest.

These functions are ...

  f(x,y)=4x+2y\\g(x,y)=2x^2+y-4

The Lagrangian is ...

  \mathcal{L}(x,y,\lambda)=f(x,y)+\lambda g(x,y)\\\\\text{and the partial derivatives are ...}\\\\\dfrac{\partial \mathcal{L}}{\partial x}=\dfrac{\partial f}{\partial x}+\lambda\dfrac{\partial g}{\partial x}=4+\lambda (4x)=0\ \implies\ x=\dfrac{-1}{\lambda}\\\\\dfrac{\partial \mathcal{L}}{\partial y}=\dfrac{\partial f}{\partial y}+\lambda\dfrac{\partial g}{\partial y}=2+\lambda (1)=0\ \implies\ \lambda=-2

  \dfrac{\partial\mathcal{L}}{\partial\lambda}=\dfrac{\partial f}{\partial\lambda}+\lambda\dfrac{\partial g}{\partial\lambda}=0+2x^2+y-4=0\ \implies\ y=4-2x^2\\\\\text{We know $\lambda$, so we can find x and y:}\\\\x=\dfrac{-1}{-2}=0.5\\\\y=4-2\cdot 0.5^2=3.5

Since x and y are in thousands, maximum profit is to be had when the company produces ...

  500 Type A souvenirs, and 3500 Type B souvenirs

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