Someone please help me ASAP

Answer:

Box Dimensions:

L  = 15.15 ul

W = 7.15 ul

h = x = 2.43 ul

V(max) =    263.22 cu

Step-by-step explanation:

We call x the length of the square to be cut in the corners then:

Are of the base of the box is:

(20 - 2*x)  is the future length of the box and

(12 - 2*x) will be the width

The heigh is x  then the volume of the box is:

V = ( 20 - 2*x )* ( 12 - 2*x ) * h

And the volume as a function of x is:

V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x     or   V(x) = (240 -40*x -24*x + 4*x²) * x

V(x) =  240*x - 64*x² + 4*x³

Taking derivatives on both sides of the equation we get:

V´(x) = 240 - 128*x + 12*x²

V´(x)  =  0              240 - 128*x + 12*x²  = 0    or     60 - 32*x + 3*x²

3*x²  -  32*x  +  60  = 0

Solving:

x₁,₂  =  32  ± √ (32)² - 4*3*60 ]/ 2*3

x₁,₂  =  32  ± √ 1024 - 720 )/6

x₁,₂  = ( 32  ± √ 304 )/6

x₁,₂  = ( 32  ± 17.44 )/6

x₁  =  8.23      ( we dismiss this solution because is not feasible 2*x > 12

x₂ = 2.43  u.l ( units of length)

Then

L  =  20 - 2*x      L  = 20  - 4.85     L  = 15.15 ul

W =  12 - 2*x      W = 12 - 4.85      W = 7.15 ul

h  =  2.43 ul

V = 2.43*7.15*15.15  cubic units

V =  263.22 cu

To see if when x = 2.43   function V has a maximum we go to the second derivative

V´´(x)  = - 128  + (24)*2.43

V´´(x) = - 69.68      as        V´´(x)  < 0   then we have a maximum for V(x) in the point x = 2.43

y= -1x -3

that's equation of the line

Answer:

B. 2.618 units

Step-by-step explanation:

the arc length = (5π/6) / 2π × 2×3.14×1

= 5/12 × 6.28

= 31.4/ 12

= 2.618 units

The arc length is = 2.618 units

Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc. Arc length is a fraction of the circumference of the circle.

Given : r=1, [tex]\theta[/tex]= 5π/6

Now, arc length

= [tex]\theta[/tex]/ 2π * 2πr

= (5π/6) / 2π × 2×3.14×1

= 5/12 × 6.28

= 31.4/ 12

= 2.618 units

Learn more about arc length here:

https://brainly.com/question/1577784

#SPJ2

Step-by-step explanation:

the lines on the graph of inequality second option

Answer:

110°

Step-by-step explanation:

Each tick line in a protractor shows 10°. So the next is 110° inclined.

Answer:

110 degrees hope this helps

Step-by-step explanation:

Answer:

I think it is 2 points for this .

Answer:

Step-by-step explanation:

8(1 + 2i) -  (7 - 3i) = 8*1 + 8*2i + 7*(-1) - 3i*(-1)

                          = 8 + 16i -7 + 3i

                          = 8 - 7 + 16i + 3i

                          = 1 + 19i

Daniel forgot to multiply 2i by 8

Answer:

A , He did not apply the distributive property correctly for 8(1 + 2i).

on edge

Step-by-step explanation:

Answer:

HCF X LCM= product of two numbers

14 x 840 = 42 x other number

other number= 14x840/42=280

Answer:

70 degrees

Step-by-step explanation:

It's a whole 540 degrees

So y = 70 degrees

Answer: y=2/4x+6

I think it´s right sorry if it is´nt

Answer:

[tex] V_{cone} = 4000\pi \: {cm}^{3} [/tex]

Step-by-step explanation:

Height of the cone (h) = 30 cm

Radius of the cone (r) = 20 cm

[tex]V_{cone} = \frac{1}{3} \pi {r}^{2} h \\ \\ = \frac{1}{3} \pi \: {(20)}^{2} (30) \\ \\ = \pi(400)(10) \\ \\ V_{cone} = 4000\pi \: {cm}^{3} [/tex]

Answer:

the answer to the question is 12cm

Answer:

W'(10/3, 6), X'(4, 16/3), Y'(-4, 2) and Z'(2/3, -8/3)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.

If a point A(x, y) is dilated by a scale factor of k, the new point is A'(kx, ky). If a point A(x, y) is reflected over line y = x, the new point is A'(y, x).

Given the vertices W(-3,5), X(8,6),  Y(3,-6), and Z(-4,1). If it is dilated by a scale factor of 2/3, the new point is at W*(-6, 10/3), X*(16/3, 4), Y*(2, -4) and Z*(-8/3, 2/3). If it is then reflected over the line y = x, the new point is W'(10/3, 6), X'(4, 16/3), Y'(-4, 2) and Z'(2/3, -8/3).

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that he pulls out a red marble = number of red marbles / total number of marbles

= 4/20 = 1/5

Answer:

12

Step-by-step explanation:

Since they are parallel then

(7x - 8) + (11x - 28) = 180

18x - 36 = 180

18x = 216

x = 12

Answer:

-4 square inches

Step-by-step explanation:

its because the 5 pictures together make 21

Answer:

where is the Venn diagram plz insert Venn diagram then I should solve

Answer:

No solution is possible

Step-by-step explanation:

You didn't indicate the number of adults and children.

Answer: Choice D)  [tex]0 \le y \le 5[/tex]

This is because the smallest y can get is y = 0, while the largest it can get is y = 5. It can be anything in between these y values as well.

Visually, we look for the lowest and highest points. The range is the set of all possible y outputs. In contrast, the domain is the set of all allowed x inputs.

Answer:

in my opinion it's A.. hope it will help you.

Answer:

A

Step-by-step explanation:

Write the nunber in scientific notation which we need to add -1 to 10 power to made it 3.07.

Answer:

C

Step-by-step explanation:

just round up to nearest number and 7/8 is 0.87 so it coloser to 1 than half and the others are way to big.

Answer:

y=3    x=1

Step-by-step explanation:

Answer:

above one is correct. I think so

Answer:

(4,5)

Step-by-step explanation:

Hi there!

We are given the system of equations:

5x+2y=30

-5x+4y=0

and we need to find the solution

there are 3 ways to solve a system of equations, but let's use the elimination method, where we will add the systems together to clear one variable out, solve for the other variable, and use the value of the solved variable to find the other variable

When we clear a variable, the coefficients need to be opposites (ex. 2 and -2). In this case, the coefficients in front of x are 5 and -5 in the first and second equation respectively

5x+2y=30

-5x+4y=0

add the equations together

6y=30

divide both sides by 6

y=5

we found the value of y

now we need to find the value of x

substitute 5 as y into either one of the equations (ex. the first one) to solve for x

5x+2(5)=30

multiply

5x+10=30

subtract 10 from both sides

5x=20

divide both sides by 5

x=4

so the answer is x=4, y=5; as a point, it's (4,5)

Hope this helps! :)

Answer:

true

Step-by-step explanation:

because your susy

Answer:

jennifer won 15 time and mark won 24

if the answer is wrong i am really sorry

Answer:

ss

Step-by-step explanation:

s

Answer:

x = 8/3, 2/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(x + 1)² - 25/9 = 0

Step 2: Solve for x

Step-by-step explanation:

Hey there!

Given equation is:

(x+1)² - 25/9 = 0

Then;

(x+1)² - (5/3)² = 0 ( since 5² = 25 and 3² = 9)

or, {(x+1)+5/3} { (x+1)-5/3} = 0. { use a² - b² = (a+b)(a-b) formula}

[tex]( \frac{3x + 3 + 5}{3} )( \frac{3x + 3 - 5}{3} ) = 0[/tex]

[tex]( \frac{3x + 8}{3} )( \frac{3x - 2}{3}) = 0[/tex]

Now;

Either;

( \frac{3x + 8}{3}= 0

or, X = 8/3

Or,

( \frac{3x -2}{3} = 0

x = 2/3

Therefore, X = 8/3 or 2/3.

Hope it helps!