What type of angle is this pls hurry!

Answer:

a) [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

b) The volume of the box is maximized when 'x' is approximately 1.585 feet

Step-by-step explanation:

a) Let 'a' represent the length of the rectangular sheet of paper and let 'b' represent the with of the rectangular sheet of paper, we have;

The length of the side of the square cut from the corners of the rectangular sheet of paper = x

The length of the box formed after cutting the square sides are;

The length of the box, l = a - 2·x

The width of the box, w =  b - 2·x

The height of the box, h = x

The volume of the box, V = l × w × h = (a - 2·x)·(b - 2·x)·x = 4·x³ - 2·a·x² - 2·b·x² + a·b·x

The value of 'x' that gives the maximum volume of the box is given by finding the extremum of the volume, 'V', of the box as follows;

At the extremum, dV/dx = 0

∴ d(4·x³ - 2·a·x² - 2·b·x² + a·b·x)/dx = 12·x² - 4·a·x - 4·b·x + a·b = 0

12·x² - 4·(a + b)·x + a·b = 0

[tex]x = \dfrac{4\cdot (a + b) \pm \sqrt{(-4\cdot (a + b) )^2-4 \times12\times a \cdot b } }{2 \times 24} =\dfrac{a+b\pm\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

Found from part (b), the value of 'x' (in terms of 'a' and 'b') that maximizes the volume of the box is [tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex]

b), When a = 8.5 inches and b = 11 inches, we have;

x = (8.5 + 11 +√((8.5 + 11)² - 3×8.5×11))/6 = 4.914

x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

We get;

When x = 1.585, V = 4·1.585³ - 2·8.5·1.585² - 2·11·1.585² + 8.5·11·1.585 ≈ 66.15

When x = 4.914, V = 4·4.914³ - 2·8.5·4.914² - 2·11·4.914² + 8.5·11·4.914 ≈ -7.65

Therefore, the value of 'x' that gives the maximum volume of the box is x = (8.5 + 11 -√((8.5 + 11)² - 3×8.5×11))/6 ≈ 1.585

(The value of 'x' in terms of 'a' and 'b' is therefore;

[tex]x =\dfrac{a+b -\sqrt{(a + b)^2 - 3\cdot a \cdot b} }{6}[/tex])

The volume of the box is maximized when, x ≈ 1.585 feet

Answer:

No

Step-by-step explanation:

To find out if 2 is a solution, replace all the x's with 2.

4(2 - 1) - 3(2 - 2) =8

4(1) - 3(0) = 8

4 - 0 = 8

4 = 8

Nope!  False!  2 is not a solution.

true (I don't know if this is the answer but it would be my guess)

Answer:

Use n(u) formula of chapter sets

Step-by-step explanation:

Have a good day

11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.

Given that in a class of 25 students, 18 were math majors, 12 were computer science majors, and 7 were dual majors in math and computer science, to determine A) how many students were majoring in math only; B) how many students were not majoring in computer science; and C) how many students were not math or computer science majors; the following calculation must be performed:

Therefore, 11 students were majoring in math only; 13 students were not majoring in computer science; and 2 students were not math or computer science majors.

Learn more in https://brainly.com/question/20293703

Answer:

I can’t see the picture

Step-by-step explanation:

Answer:

270 KM

Step-by-step explanation:

180 divided by 2= 90

90*3= 270

Answer:

hope this will help

if correct please give brainliest

Answer:

Opps i am really sorry i donot know it

Answer:

Step-by-step explanation:

It's 5 units

Answer:

10

Step-by-step explanation:

I think I hope this helps

Answer:

D. 6

Step-by-step explanation:

Because a hexagon has 6 sides and when fully turned, it spin 360 degrees which is a whole circle!

Answer:

6

Step-by-step explanation:

Answer:

7 kittens did not finish their milk

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

x=-2 and y=-24

Step-by-step explanation:

Answer:

3

Step-by-step explanation: First, you find the mean of the data set. Then you take that mean and find the difference of that and each value, you add those up and find the mean of that number.

Answer:

0, -3

Step-by-step explanation:

So remember, when they say reflect over the x intercept, they do not mean to reflect the x value, they mean to reflect over the hirzontal line of the graph.(x axis)

This is the same with reflection over the y intrecept. This doesnt mean y is flipped, this means that whatever point or line you have is reflected over the vertical line on the graph(y axis)

So our orginal value is (0, 3). We need to reflect over the x axis, which means that y will now be -3, since that is the opposite of what we can see when we flip the x axis.

The 0 x, of course, stays the same since its 0.

So your answer is (0, -3)

Hope this helps! :)

Answer:

XY = 10

Step-by-step explanation:

By the definition of midpoint, XM would be equal to MY, so we can set both equations equal to each other;

XM = MY

8 - t = 5t - 10

=> Now add "t" to both sides of "="

8 = 6t - 10

=> add 10 from each side;

18 = 6t

=> Finally divide 6 on each side

3 = t

Now that we have the value for t, we can substitute 3 in place of "t" in any of the equation above and solve, when we have the answer, multiply it by 2 to get the value for XY.

=> 8 - 3

=> 5

=> XY = 5 * 2

=> XY = 10

Hope this helps!

Answer:

the product is 6/Y^8

Step-by-step explanation:

Answer:

(2,-3)

Step-by-step explanation:

2x + 2y = -2

3x - 2y = 12

Add the two equations to eliminate y

2x + 2y = -2

3x - 2y = 12

-----------------------

5x   = 10

5x/5 = 10/5

x = 2

Now find y

2x+2y = -2

2(2)+2y = -2

4+2y = -2

Subtract 4 from each side

4-4 +2y = -2-4

2y = -6

Divide by 2

2y/2 = -6/2

y = -3

(2,-3)

Answer:

y= 1500 -18t

Step-by-step explanation:

1500 is the number you are going to be subracting from so it goes first and 18 is the t because it decreases every year

Answer:

Nah i gotcha, I'm always helping around people, as long as i understand the question myself Imfao

Answer:

2411.52 mm²

Step-by-step explanation:

[tex]40^{2} =32^2+d^2[/tex]

→ [tex]d^2= 1600-1024[/tex]

→[tex]= 576[/tex]

→ [tex]d= 24[/tex]      [tex]so, (radius=12[/tex]

[tex]Total~ surface ~ area= (2\pi r)*height[/tex]

→ [tex](2*3.14*12*82)[/tex]

[tex]= 2411.52 mm^2[/tex]

-------------------------------

hope it helps...

have a great day!!

Answer:

2411.52 mm²

Step-by-step explanation:

hope its helpful

Answer:

24$

Step-by-step explanation:

its just 9$ + 15$ = 24$

Answer:

4. x=0 x=5

5. x=-4 x=8

Answer:mode

Step-by-step explanation:5+4+9+9+3+75+1=mode

Answer:

(-3,0)

Step-by-step explanation:

1) find the coordinate of x

x = -3

2) find the coordinate of y

the point lies on x axis so y = 0

The coordinates are (-3, 0)

:)

Answer:

$-23

77 - 100 = -23

Answer:

21 km/h

Step-by-step explanation:

Answer:

5/3 is the slope of the line.