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As far as I understand A)

4 0

3 years ago

You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 1536cm3. Deter

Katen [24]

Answer:

The dimensions of the box are:

Length = 11.53cm

Breadth = 11.53cm

Height = 11.53cm

Step-by-step explanation:

The volume of the box can be calculated with this formula:

The volume of the box = area of square base X height of the box.

We are given that the length of one side of the square base is = x cm, and its height is h cm.

Area of square base = $x^{2}cm^{2}$

The surface area of the box will be minimized if the height of the box, is the same as its length. hence, we can take the height of the box to be x cm also.

In this case, the volume of the box will be $x^{3}=1536cm^{3}$

from this, $x =3\sqrt{1536}= 11.53cm$

There fore, the box has its length, height, and width all having the same values.

The dimensions of the box are:

Length = 11.53cm

Breadth = 11.53cm

Height = 11.53cm

8 0

3 years ago

In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. If the perimeter of MNPQ is 68 inches, t

Svetlanka [38]

Answer: NP = 9 inches

Step-by-step explanation:

In a parallelogram, the opposite sides are equal.

If the length of the longer side is MN, it means that the length of the two opposite longer sides is 2MN.

If the length of the shorter side is NP, it means that the length of the two opposite shorter sides is 2NP.

The perimeter is 2MN + 2NP

If the perimeter of MNPQ is 68 inches, it means that

2MN + 2NP = 68- - - - - - - - - - - -1

In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. It means that

MN = 2NP + 7- - - - - - - - - - -2

Substituting equation 2 into equation 1, it becomes

2(2NP + 7) + 2NP = 68

4NP + 14 + 2NP = 68

4NP + 2NP = 68 - 14

6NP = 54

NP = 54/6

NP = 9 inches

6 0

3 years ago

Help please it’s a text

nikitadnepr [17]

Answer:

D

please mark brainlist!!! please

4 0

3 years ago

Read 2 more answers

Write an equation of the line through each pair of points in slope-intercept form.

ASHA 777 [7]

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

7 0

3 years ago