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3 years ago

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A factory can assemble 3,400 iPhones in an 8-hour shift. If the factory were to work around the clock, how long would it take th

em to assemble 100,000 iPhones? Round to the nearest whole number

2 answers:

grandymaker [24]3 years ago

8 0

Answer:

4200

Step-by-step explanation:

(*^^*) -_-|| ;-;

pshichka [43]3 years ago

6 0

Answer:

235 hours

Step-by-step explanation:

Let H represent phones per hour

8H = 3,400

H = 425

100,000 = 425 H

100,000 / 425 = 235.29 hours

Rounded to nearest whole number is 235 hours.

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Another florist has 16 yellow mums and 40 white carnations. Which question can be answered by finding the GCF of 16 and 40?

Naily [24]

Answer:

8

Step-by-step explanation:

4 0

3 years ago

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Which equation has no solution?

konstantin123 [22]

Answer:

B) 4x-5-3x=x+5 has no solution.

Step-by-step explanation:

A) 4x+4=4-4x

4x-(-4x)+4=4

4x+4x+4=4

8x+4=4

8x=4-4

8x=0

x=0/8

x=0

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

B) 4x-5-3x=x+5

4x-3x-5=x+5

x-5=x+5

x-x-5=5

-5=5

no solution.

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

C) 4x+15-9x=5x+15

4x-9x+15=5x+15

-5x+15=5x+15

-5x-5x+15=15

-10x+15=15

-10x=15-15

-10x=0

x=0/-10

x=0

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

D) 4x+2-x=4+3x-2

3x+2=3x+4-2

3x+2=3x+2

infinitely many solutions.

8 0

2 years ago

Steve collects oysters for a living and sells them to restaurants. While catching oysters, Steve keeps track of the total weight

Vlad1618 [11]

Answer:8 ounces of oysters per minute

Step-by-step explanation:

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3 years ago

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How to solve 10 1/8+(3 5/8+2 7/8)

jeyben [28]

Those are mixed fractions, so first you have to make them improper fractions, multiply the whole times the denominator and add the numerator, that will be you new numerator, then copy your denomminator.

81/8 + (29/8 + 23/8) Since they already have the same denominator use order of operations to proceed, 81/8+57/8 = 138/8 =17 2/8 = 17 1/4

7 0

4 years ago

Prove that dx/x^4 +4=π/8

insens350 [35]

$\displaystyle\int_0^\infty\frac{\mathrm dx}{x^4+4}$

Consider the complex-valued function

$f(z)=\dfrac1{z^4+4}$

which has simple poles at each of the fourth roots of -4. If $\omega^4=-4$ , then

$\omega^4=4e^{i\pi}\implies\omega=\sqrt2e^{i(\pi+2\pi k)/4}$ where $k=0,1,2,3$

Now consider a semicircular contour centered at the origin with radius $R$ , where the diameter is affixed to the real axis. Let $C$ denote the perimeter of the contour, with $\gamma_R$ denoting the semicircular part of the contour and $\gamma$ denoting the part of the contour that lies in the real axis.

$\displaystyle\int_Cf(z)\,\mathrm dz=\left\{\int_{\gamma_R}+\int_\gamma\right\}f(z)\,\mathrm dz$

and we'll be considering what happens as $R\to\infty$ . Clearly, the latter integral will be correspond exactly to the integral of $\dfrac1{x^4+4}$ over the entire real line. Meanwhile, taking $z=Re^{it}$ , we have

$\displaystyle\left|\int_{\gamma_R}\frac{\mathrm dz}{z^4+4}\right|=\left|\int_0^{2\pi}\frac{iRe^{it}}{R^4e^{4it}+4}\,\mathrm dt\right|\le\frac{2\pi R}{R^4+4}$

and as $R\to\infty$ , we see that the above integral must approach 0.

Now, by the residue theorem, the value of the contour integral over the entirety of $C$ is given by $2\pi i$ times the sum of the residues at the poles within the region; in this case, there are only two simple poles to consider when $k=0,1$ .

$\mathrm{Res}\left(f(z),\sqrt2e^{i\pi/4}\right)=\displaystyle\lim_{z\to\sqrt2e^{i\pi/4}}f(z)(z-\sqrt2e^{i\pi/4})=-\frac1{16}(1+i)$
$\mathrm{Res}\left(f(z),\sqrt2e^{i3\pi/4}\right)=\displaystyle\lim_{z\to\sqrt2e^{i3\pi/4}}f(z)(z-\sqrt2e^{i3\pi/4})=\dfrac1{16}(1-i)$

So we have

$\displaystyle\int_Cf(z)\,\mathrm dz=\int_{\gamma_R}f(z)\,\mathrm dz+\int_\gamma f(z)\,\mathrm dz$
$\displaystyle=0+2\pi i\sum_{z=z_k}\mathrm{Res}(f(z),z_k)$ (where $z_k$ are the poles surrounded by $C$ )
$=2\pi i\left(-\dfrac1{16}(1+i)+\dfrac1{16}(1-i)\right)$
$=\dfrac\pi4$

Presumably, we wanted to show that

$\displaystyle\int_0^\infty\frac{\mathrm dx}{x^4+4}=\frac\pi8$

This integrand is even, so

$\displaystyle\int_0^\infty\frac{\mathrm dx}{x^4+4}=\frac12\int_{-\infty}^\infty\frac{\mathrm dx}{x^4+4}=\frac12\frac\pi4=\frac\pi8$

as required.

6 0

4 years ago