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3 years ago

On average, how much garbage does each person throw away in a week?

Mathematics

2 answers:

Rudiy273 years ago

4 0

Average in 1 day is 7.1 pounds

So for a week about

49.7 pounds of garbage thrown away for each person

3241004551 [841]3 years ago

3 0

4.4 pounds of garbage

You might be interested in

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

3 years ago

The area of a square garden is 100 square feet .how long is each side of the garden

aniked [119]

Answer:

Each side is 25

7 0

3 years ago

Find the approximate volume of this prism.

musickatia [10]

Answer:

62m³

Step-by-step explanation:

The question is incomplete. Find the diagram of the prism attached below.

Volume of a Prism = Base area × Height

Given height = 9m

Since the prism is a triangular based prism,

Base area = area of the equilateral triangle = 1/2bh

base of the triangle = 4m

Height can be gotten using Pythagoras theorem.

Slant side of the triangle is the hypotenuse = 4m

Adjacent = 1/2 of the base = 1/2(4)= 2m

Height = √4²-2²

Height = √16-4

Height of the triangle= √12 m

Base Area = 1/2×4×√12

Base Area = 2√12 m

Volume of the prism = 2√12 × 9

= 2×2√3×9

= 36√3 m³

= 62.2m³

Volume of the prism is approximately 62m³

7 0

3 years ago

For what equation is X equals 4.5 a solution

Rom4ik [11]

2x4.5=6.5smsnsmslxdmldod

6 0

3 years ago

Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 feet, 4 f

aksik [14]

Using Pythagoras theorem, we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

<h3>How to use Pythagoras theorem to prove a right triangle?</h3>

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

Therefore,

c²= a²+ b²

where

c = hypotenuse side
a and b are the other legs.

Therefore,

3² + 4² = 5²

Hence,

Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

learn more on Pythagoras's theorem here: brainly.com/question/20462170

#SPJ1

4 0

2 years ago