PLEASE HELP QUICK I HAVE NO CLUE

Solution :

Let x, y, z be the dimensions of the rectangle.

Volume of the rectangle (V) = xyz

Given that the vertex should lie on ellipse [tex]$4x^2 + y^2+4z^2=4$[/tex] .......(i)

So here the volume xyz must be maximum with constraints above.

We solve this using Lagranches method with variable λ

Lagranches function is

[tex]$F : xyz + \lambda(4x^2+y^2+4z^2-4)=0$[/tex] .....(ii)

To find λ, [tex]$\frac{dF}{dx}=0; \frac{dF}{dy}=0;\frac{dF}{dz}=0$[/tex]

[tex]$\frac{dF}{dx}=0 \Rightarrow yz+\lambda(16x)=0 \Rightarrow \lambda = -\frac{yz}{16x}$[/tex] .............(iii)

[tex]$\frac{dF}{dy}=0 \Rightarrow xz+\lambda(2y)=0 \Rightarrow \lambda = -\frac{xz}{2y}$[/tex] ..................(iv)

[tex]$\frac{dF}{dz}=0 \Rightarrow xy+\lambda(16z)=0 \Rightarrow \lambda = -\frac{xy}{16z}$[/tex] ...............(v)

Equating (iii) and (iv)

[tex]$-\frac{yz}{16x}=-\frac{xz}{2y} \Rightarrow y^2=8x^2 \Rightarrow y = \sqrt8 x$[/tex] ...............(vi)

Equating (iii) and (v)

[tex]$-\frac{yz}{16x}=-\frac{xy}{16z} \Rightarrow z^2=x^2 \Rightarrow z = x$[/tex] ....................(vii)

Substitute (vi) and (vii) in (i),

From (i),

[tex]$4x^2 + (\sqrt8 x)^2+4x^2 = 4$[/tex]

[tex]$\Rightarrow 4x^2 +8x^2+4x^2 = 4 \Rightarrow x = \frac{1}{4}$[/tex]

From (vi),

[tex]$y = \sqrt8 x$[/tex]

[tex]$\Rightarrow y= \sqrt8 \times \frac{1}{4} \Rightarrow y =\frac{\sqrt8}{4}$[/tex]

[tex]$\Rightarrow y =\frac{\sqrt{2\times4}}{4} \Rightarrow y = \frac{1}{\sqrt2}$[/tex]

From (vii),

z = x

[tex]$z =\frac{1}{4}$[/tex]

Therefore, for maximum volume the dimensions of a rectangle box are

[tex]$x =\frac{1}{4} ; y = \frac{1}{\sqrt2} ; z =\frac{1}{4}$[/tex]

Step-by-step explanation:

(1 point)

No, there isn't a more efficient way to solve this system.

Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.

Yes, a more efficient way is to multiply the first equation by −4, add to eliminate y, then solve for x.

Yes, a more efficient way is to multiply the first equation by −4, add to eliminate x, then solve for y.

Answer: B

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Domain (and range) don't necessarily have to be in smallest to largest order unless your teacher requires it, so don't worry about the order.

Let's remind ourselves that the domain is the input value, or the x value, and y is the output value, or the y value. We know that in an ordered pair, the first # is x and the second # is y (because x comes before y in the alphabet). Lets look at our ordered pairs and see what the x values are.

{(8, -2), (4, -2), (-3, 2), (-5, -3)}

The x values are 8, 4, -3, and -5, therefore:

Domain: {8,4,-3,-5}

Range would equal all the y values. Remind yourself that if an x value is repeated to only write it down ONCE.

Remember, the order does not matter, so the answer would be C.

Hope this helped!

Answer:

15 is 9 because the ratio is 3:15 in 1 hour, so you multiply by 3(hours) and you get 9

Step-by-step explanation:

I apologise but I'm too rusty at the other questions to be able to answer them anywhere close to accurate D:

9514 1404 393

Answer:

  13. 3/15 = 1/5

  14. 1/5 (or 3 Bieber songs per hour)

  15. 9

Step-by-step explanation:

13. The requested ratio is ...

  (3 Bieber songs)/(15 total songs) = 3/15 = 1/5

__

14. 1/5 is the "unit rate" for the ratio in problem 13. Its units are "Bieber songs per song played."

(IMO, this "unit rate" is pointless. For the purpose of problem 15, the applicable "unit rate" is Bieber songs per hour. That is 3 songs per hour.)

__

15. At a rate of 3 Bieber songs per hour, in 3 hours one might expect ...

  (3 songs/hour)(3 hours) = 9 songs . . . . by Bieber

Answer:

He would make 300 dollars.

Step-by-step explanation:

15 x 5 = 75

75 x 4 = 300.

Answer:

answer is 300

Step-by-step explanation:

Because if your doing it for 1 day you would have to 15*5 which five you 75. Then you multiple that 75 with the 4 and give you 300 within the 4 days..

Hopes this help.

Answer:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.

Step-by-step explanation:

I believe that the answer B,D,and E

Answer:

A, D, and E (I think)

Step-by-step explanation:

I'm pretty sure those would be the right answers, sorry that this isn't much of an explanation lol

Answer:

y=20

Step-by-step explanation:

8x

8(2.5)

8×2=16

8×0.5=4

16+4=20

y=20 in this equation

Answer:

12950

Step-by-step explanation:

Answer:

1,-4

Step-by-step explanation:

The vertex is always that little spot there at the tip of a nonlinear function.

Answer:

y=4/2m-3 OR y=2m-3

Step-by-step explanation:

Answer:A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:

Answer:

=  -24576/7

or

-3510.857142

both are the correct answer

The value of x will be;

⇒ x = 3.75

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5x - 12 + 3x + 30 = 48

Now,

Solve the expression for x as;

The expression is,

⇒ 5x - 12 + 3x + 30 = 48

⇒ 8x - 12 + 30 = 48

⇒ 8x + 18 = 48

Subtract 18 both side as,

⇒ 8x - 18 = 48 - 18

⇒ 8x = 30

Divide by 8 as;

⇒ x = 30/8

⇒ x = 3.75

Thus, The value of x will be;

⇒ x = 3.75

Learn more about the mathematical expression visit:

brainly.com/question/1859113

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Answer:

its D

Step-by-step explanation:

Answer: the scale factor is 1/2

And the missing side is 5.5

Step-by-step explanation:

The larger triangle is twice the smaller triangle

The scale factor is 1/2 and the length of the missings side is 5.5 after using the concept of the scale factor.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that:

The two rectangles are shown in the picture:

Part A what is the scale factor used when going from the larger rectangle to the smaller one?

The scale factor = 8/16 = 1/2

The length of the missings side = 1/2(11) = 5.5

Thus, the scale factor is 1/2 and the length of the missings side is 5.5 after using the concept of the scale factor.

Learn more about the scale factor here:

brainly.com/question/22312172

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Answer:

15

Step-by-step explanation:

just cause

Answer:

I'm guessing that when you graph it, the graph changes direction when it's not on the x-axis. the "real zeros" of a graph are the ones that go through the x-axis and then imaginary ones are the ones that don't.

Step-by-step explanation:

Answer:

the whole

Step-by-step explanation:

Answer:

Y-3/5x+2

Step-by-step explanation:

Answer:

1<x<4

Step-by-step explanation:

this helps me out a lot in my math class

Answer:

x=4 and thats your answer thanks for helping you but if using the z-score it's 0

Step-by-step explanation:

1<x<4

Answer:

um what?

Step-by-step explanation:

What the heck are all these numbers

Answer:

v = 2

Explanation:

8(2 − 6v) + 19 = −61

[ Simplify both sides of the equation ]

8(2 − 6v) + 19 = −61

(8)(2) + (8)(−6v) + 19 = −61 (Distribute)

16 + −48v + 19 = −61

(−48v) + (16 + 19) = −61 (Combine Like Terms)

−48v + 35 = −61

−48v + 35 = −61

[ Subtract 35 from both sides ]

−48v + 35 − 35 = −61 − 35

−48v = −96

[ Divide both sides by -48 ]

−48v / -48 = −96 / -48

v = 2

- PNW

Answer:

[tex]\frac{5}{14}[/tex]

Step-by-step explanation:

First subtract the two terms by setting the first term as a fraction.

3 * [tex]\frac{5}{5}[/tex] = [tex]\frac{15}{5}[/tex]

Then subtract the terms.

[tex]\frac{15}{5}[/tex][tex]-\frac{1}{5}[/tex] = [tex]\frac{14}{5}[/tex]

Finally, flip the numerator and the denominator.

Answer:

B

Step-by-step explanation: