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2 years ago

P viuen

Mathematics

1 answer:

Alex787 [66]2 years ago

3 0

Hello what do you exactly need help for

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The lovin lemon company sells a 4 gallon jug of lemonade for $24. the sweet and sour company sells an eight pack of 1quart bottl

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The one with gallons because that one is $6 and the other one is $2 so gallon has a higher unit price

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3 years ago

Suppose that G(x) = F(x + 9). Which statement best compares the graph of

Charra [1.4K]

C. The graph of G(x) is the graph of F(x) shifted 9 units to the left.

Inside changes do the opposite of what they seem like they'd do. "x+9" shifts it left 9 units.

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2 years ago

5. What would the graph of y= 3/4x -7/8 look like?

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2 years ago

The Ace Novelty company produces two souvenirs: Type A and Type B. The number of Type A souvenirs, x, and the number of Type B s

Molodets [167]

Answer:

500 type A; 3500 type B

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

3 0

2 years ago

A 90-inch length of ribbon is to be cut into three pieces. The longest piece is to be 30 inches longer than the shortest piece,

Free_Kalibri [48]

Lets name the shortest piece a, the medium b and the longest c

Together they are 90inches
$a + b + c = 90$
The longest is 30 inches longer than the shortest
$c = a + 30$
The third piece is half the lenght of the longest
$b = \frac{c}{2}$

So if you place c=a+30 in the other 2 equasions you get

$a + b + (a + 30) = 90 = 2a + b + 30$
And
$b = \frac{30 + a}{2}$
Now if you put this 2 toghether u get
$2a + \frac{30 + a}{2} + 30 = 90$
Multyplied by 2
$4a + 30 + a + 60 = 180$
$5a = 90$
Meaning that a=18inches

Now that we have the lenght of a we put it in the previous equasion

$b = \frac{30 + 18}{2}$
So b=48/2 which means b=24inches

And together they must be 90 so

$18 + 24 + c = 90$

C=48inches

6 0

3 years ago