25p+40q=375 Solve for p and q?

What do you think the hypervolume of a hypercube is? Why?

gavmur [86]

Answer:

$a^4$ Where (a) is the side length of the hypercube

Step-by-step explanation:

A dimension can be simply defined as a direction in which matter can move it.

We live in a 3-dimensional world, matter can move in three basic directions. The formula for finding the volume of a cube is the following: ( $a^3$ ). In the second dimension, a flat world, the area for the volume of a square is as follows: ( $a^2$ ). However, a hypercube is a paradox, as it exists in 4-dimensions, thus it cannot exist in our world. However, scientists propose "String theory" which requires that matter can move in more directs than the (3) we know of in our world. In essence, there can be more than 3 dimensions. A hypercube is the 4-dimensional version of a cube. If it follows the area pattern that a square-object follows in all preceding dimensions then the area of a hypercube is ( $a^4$ ).

Bear in mind that the area patter for a square-object is generally the following:

$a^n$

Where (a) is the side length of the square-object

(n) is the dimension the object is in.

Please keep in mind, this answer was written in the June of 2021, as science keeps progressing and new discoveries are made, this theory can be disproven. Therefore, this answer might be considered correct now, but it can be proven incorrect in the future.

6 0

2 years ago

Home CoworkHelper

9966 [12]

Answer:

See below.

Step-by-step explanation:

PROBLEM A

The formula for the volume of a cylinder is

V = πr²h, where πr² is the area of the base.

V = area of base x height

Choose any four numbers that are less than 10 for the height.
Then, substitute into the formula and isolate "r". 10 = πr²h
Double "r" to find the diameter.
The area of the base is found (bolded) while you solve πr².

*I will use the calculator button for pi (π)

Cylinder A: h = 1

10 = πr²h

10 = πr²(1)

10 = πr² Area of the base is 10m².

r = √ (10/π)

r = 1.78 Radius is 1.78m.

d = 2r = 1.78*2 = 3.56 Diameter is 3.56m.

Cylinder B: h = 2

10 = πr²h

10 = πr²(2)

5 = πr² Area of the base is 5m².

r = √ (5/π)

r = 1.26 Radius is 1.26m.

d = 2r = 1.26*2 = 2.52 Diameter is 2.52m.

Cylinder C: h = 4

10 = πr²h

10 = πr²(4)

2.5 = πr² Area of the base is 2.5m².

r = √ (2.5/π)

r = 0.89 Radius is 0.89m.

d = 2r = 0.89*2 = 1.78 Diameter is 1.78m.

Cylinder D: h = 5

10 = πr²h

10 = πr²(5)

2 = πr² Area of the base is 2m².

r = √ (2/π)

r = 0.80 Radius is 0.8m.

d = 2r = 0.80*2 = 1.6 Diameter is 1.6m.

The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.

There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.

PROBLEM B

Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.

We need the radius, which is half the diameter. r = d/2 = 10/2 = 5

Choose a random number for volume that divides easily by 25.
Substitute "V" and "r²" (r² = 25).
Isolate "h".
The area of the base is 78.54 cm² every time (A = πr²).

Cylinder A: V = 100

100 = π25h

4 = πh

h = 1.27 The height is 1.27m.

Cylinder B: V = 200

200 = π25h

8 = πh

h = 2.55 The height is 2.55m.

Cylinder C: V = 75

75 = π25h

3 = πh

h = 0.95 The height is 0.95m.

Cylinder D: V = 125

125 = π25h

5 = πh

h = 1.59 The height is 1.59m.

The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.

6 0

3 years ago

Simplify this expression : 2x(x-1)-3x^2-(5x-4)

Setler [38]

Answer:

-x^2 - 7x + 4

Step-by-step explanation:

2x(x - 1) - 3x^2 - (5x - 4)

= 2x^2 - 2x - 3x^2 - 5x + 4

Adding like terms, we get:-

-x^2 - 7x + 4 (answer).

6 0

3 years ago

5 /9 of students at a school are girls. If there are 4041 students at the school, how many are boys?

mash [69]

Answer:

1796 students are boys.

Step-by-step explanation:

If 5/9 of students are girls, then 4/9 of the students are boys.

4/9 * 4041 = 1796

7 0

2 years ago

Read 2 more answers

Solve the system of equations: -5x+y-4z=60 2x+4y+3z=-12 6x-3y-2x=-52

Bogdan [553]

Answer:

The answer to your question is:

x = -8; y = 1 ; z = -4

Step-by-step explanation:

Δ = $\left[\begin{array}{ccc}-5&1&-4\\2&4&3\\6&-3&-2\end{array}\right]$

= 40 + 24 + 18 - (-4 + 45 - 96)

= 82 + 55

= 137

Δx = $\left[\begin{array}{ccc}60&1&-4\\-12&4&3\\-52&-3&-2\end{array}\right]$

= - 480 - 144 - 156 - ( 24 - 540 + 832)

= -780 -316

= - 1096

Δy = $\left[\begin{array}{ccc}-5&1&-4\\2&4&3\\6&-3&-2\end{array}\right]$

= 40 + 24 + 18 - ( - 4 + 45 - 96)

= 82 + 55

= 137

Δz = $\left[\begin{array}{ccc}-5&1&60\\2&4&-12\\6&-3&-52\end{array}\right]$

= 1040 - 360 - 72 - ( - 104 - 180 + 1440)

= 608 - 1156

= -548

x = -1096/ 137 = -8

y = 137 / 137 = 1

z = -548 / 137 = -4

6 0

3 years ago