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3 years ago

13

-6=-8+

{11} " align="absmiddle" class="latex-formula">

1 answer:

vekshin13 years ago

8 0

P=22 rewrite the question as -8+p/11=-6 then move all terms not containing p to the right side p/11=2 multiply both sides of the given equation by 11, the reciprocal, 11*p/11=11*2

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Emma drove 5 hours and 20 mins to her vacuum she left home at 10:15 am what time did she arrive

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Answer: 3:35

Step-by-step explanation:

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Archy [21]

(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

$s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}$

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

$v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}$

(b) The velocity after 3 seconds is

$v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}$

(c) The particle is at rest when its velocity is zero:

$\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}$

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

$\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|$

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt$

By definition of absolute value, we have

$|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)$

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt$

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to

$s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}$

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Read 2 more answers

Statistics please help I'm not good worth 50 points

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(a) I can't help you with using your calculator for this part, but if you have some familiarity with your device you can check your answer with mine.

The mean is simply the sum of all the house costs divided by the number of houses:

(75k + 75k + 150k + 155k + 165k + 203k + 750k + 755k)/8 = 291k

So the population mean is $291,000.

The population standard deviation is the square root of the population variance. To get the variance, you take the sum of all the squared differences between the cost and the mean cost, then divide that sum by the number of houses. That is,

[(75k - 291k)² + (75k - 291k)² + … + (755k - 291k)²]/8 = 581,286k

Note that the variances is measured in square dollars. Then the standard deviation is

√(581,286k) ≈ $762,421.1

(b) The median is just the price in the middle. There were 8 houses sold, so there are 2 "middle" prices. The median is the average of these:

(155k + 165k)/2 = 160k = $160,000

(c) Yes, the mode is the data that shows up most frequently. This happens at the lower end, with $75,000 appearing twice.

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