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MrRissso [65]
4 years ago
15

The U.S. annual energy consumption is roughly 1 x 1020 joules per a year. If there are 350,000,000 people in the U.S., express t

his as per person per second. Round to the hundredths. (hint: start by finding out how much energy one person uses per year.)
Mathematics
1 answer:
AnnZ [28]4 years ago
4 0

Answer with Step-by-step explanation:

Given the total energy consumption for all of the population is

E=1\times 10^{20}Joules

Thus energy consumed by each person per year can be obtained by dividing the total energy consumed by the total population Thus we get

E_{per\cdot person}=\frac{1\times 10^{20}}{350\times 10^{6}}\\\\E_{per\cdot person}=28.57\times 10^{10}Joules/Year

Now the energy consumed in each second assuming that there are 365 days in each year equals

E_{second}=\frac{28.57\times 10^{10}}{365\times 24\times 3600}\\\\E_{second}=9059.49Joules

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Agata [3.3K]

Answer:

y intercept (-6,0), x-intercept (0,-8) : y = \frac{-4}{3}x -8

y intercept (0,-6), x-intercept (-2,0): y = -3x -6

y intercept (0,8), x-intercept (1.6,0): y = -5x + 8

y intercept (0,7), x-intercept (-1.4,0): y = 5x + 7

Step-by-step explanation:

y = mx + b

*note: b is the y intercept

<u>1. y intercept (-6,0), x-intercept (0,-8)</u>

m = \frac{-8 - 0}{0 - (-6)}= \frac{-8}{6}  = \frac{-4}{3}\\y =  \frac{-4}{3}x + b\\y = \frac{-4}{3}x -8

<u>2.y intercept (0,-6), x-intercept (-2,0)</u>

<u />m = \frac{0 - (-6)}{-2 - 0} = \frac{6}{-2}  = -3\\y = -3x + b \\y = -3x -6<u />

<u>3. y intercept (0,8), x-intercept (1.6,0)</u>

<u />m = \frac{0 - 8}{1.6 - 0}= \frac{-8}{1.6} = -5\\y = -5x + b\\y = -5x + 8<u />

<u>4. y intercept (0,7), x-intercept (-1.4,0)</u>

<u />m = \frac{0 - 7}{-1.4 - 0} = \frac{-7}{-1.4}= 5 \\y = 5x + b\\y = 5x + 7<u />

6 0
3 years ago
In a load of laundry, 60% of the socks are white. If there are 25 socks in the load, how many are white?
Firdavs [7]
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6 0
4 years ago
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Lera25 [3.4K]

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4 years ago
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Evaluate integral _C x ds, where C is
borishaifa [10]

Answer:

a.    \mathbf{36 \sqrt{5}}

b.   \mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}

Step-by-step explanation:

Evaluate integral _C x ds  where C is

a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)

i . e

\int  \limits _c \ x  \ ds

where;

x = t   , y = t/2

the derivative of x with respect to t is:

\dfrac{dx}{dt}= 1

the derivative of y with respect to t is:

\dfrac{dy}{dt}= \dfrac{1}{2}

and t varies from 0 to 12.

we all know that:

ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \  \ dt

∴

\int \limits _c  \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt

= \int \limits ^{12}_{0} \  \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2})  \ dt

= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0

= \dfrac{\sqrt{5}}{4}\times 144

= \mathbf{36 \sqrt{5}}

b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)

Given that:

x = t  ; y = 3t²

the derivative of  x with respect to t is:

\dfrac{dx}{dt}= 1

the derivative of y with respect to t is:

\dfrac{dy}{dt} = 6t

ds = \sqrt{1+36 \ t^2} \ dt

Hence; the  integral _C x ds is:

\int \limits _c \ x \  ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \  dt

Let consider u to be equal to  1 + 36t²

1 + 36t² = u

Then, the differential of t with respect to u is :

76 tdt = du

tdt = \dfrac{du}{76}

The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145

Thus;

\int \limits _c \ x \  ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \  dt

\mathtt{= \int \limits ^{145}_{0}  \sqrt{u} \  \dfrac{1}{72} \ du}

= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}

\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}

\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}

5 0
4 years ago
If x=6 , y=8 , and z=3<br><br> 2x+3y-z<br><br> Is the answer 33?
Oduvanchick [21]
Yes.
2x = 12
3y = 24
-z = -3

12 + 24 - 3 = 33
3 0
4 years ago
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