HELPPPPP MEH!! plzzzz

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]

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:

Y-3/5x+2

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:

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:

the whole

Step-by-step explanation:

Answer:

Hello there this is number 6 the graph and number 7. I am also doing this assignment and I was wondering if you had a graph for number 8? If so I have a question posted on my account and I would greatly appreciate you adding the graph, but if not have a nice day

Step-by-step explanation:

7.

root 2x+8=x-8

2x+8=x^2-16x+64

-x^2+18x-56=0

x^2-18x+56=0

x(x-4)-14(x-4)=0

(X-4)(x-14)=0

x=4 ,x=14

x=14

Hope that this helps, Peace and love. And if you are feeling kind will you please mark me the brainliest?

Answer:

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

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

just cause

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:

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Answer:

B

Step-by-step explanation:

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:

[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:

Step-by-step explanation:

0 would represent the surface of the water

4 seguall

3

2

1 above water

0-surface of the water

-1 in the water

-2

-3

-4

Answer:

on the surface, because 0 represents sea level.

Step-by-step explanation:

Hope this helps and good luck :)

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:

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Answer:

its D

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

parentheses first 12-8=4

3x4=12

12+5=17

u do parentheses then exponents then division then multiplication then add then subtract

hope this helps!!!

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:

2;4;3

Step-by-step explanation:

y=2x²+4x+3

Answer:

Time taken by kangaroo to travel 5 km = 4.27 minutes.

Step-by-step explanation:

Speed of kangaroo is 44 mph.

Speed of kangaroo = 44 mph = 44 x 1.6 = 70.4 kmph = 19.5 m/s

We need to find how much time it takes to travel 5 km

Distance traveled = 5 km = 5000 m

We have

          Distance traveled =  Speed x Time taken

          5000 = 19.5 x Time taken

          Time taken = 256.41 seconds

           Time taken = 4.27 minutes.

Answer:7.5

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

statements:

reasons:

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:

Answer:

24

Step-by-step explanation:

First things first you multiply 22inches of rain times 22 and that is how you get 24

Answer:

1,-4

Step-by-step explanation:

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