How many ways can you put the letters in "Utah" in order?

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. When the weight it rele

a_sh-v [17]

The motion can be modeled as
$x(t) =9 \, cos( \frac{2 \pi t}{T} )$
where
x = the position below the equilibrium position
T = the period of the motion
t = time

The weight returns to its equilibrium position when x = 0.
This occurs when
$\frac{2 \pi t}{T} = \frac{ \pi }{2}$
That is,
$t= \frac{T}{4}$

Because the weight returns to the equilibrium position when t = 3 s, therefore
T = 12 s
The motion is
$x(t) = 9 \, cos( \frac{ \pi t}{6} )$

When t = 1 s, the position of the weight from equilibrium is
$d = 9 \, cos( \frac{ \pi }{6} ) = 9( \frac{1}{2} ) = 4.5 \, in$

Answer:
$d = 9 \, cos( \frac{ \pi }{6} ) = 4.5 \, in$

3 0

3 years ago

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Find the value of x.

omeli [17]

Answer:

x=45.5

Step-by-step explanation:

sum of angles of a quadrilateral is 360°

so 3x - 11+x+8+x-8+2x+7+x=360°

or 8x-4=360

or, x=364÷8

hence

x=45.5

8 0

3 years ago

a rectanglar solid has a base with lint 2 cm and width 8 cm. If the volume of the solid is 106 cm 3 to the highest, find the hei

Vanyuwa [196]

The hint says that volume of a rectangular solid = l*w*h, where l = length, w = width, and h = height. Use this to solve for the height of the solid by plugging in the numbers you know.

You know that length, l = 2cm, width, w = 8cm, and, *EDITED* volume = 160 cm^3. Plug these values into the equation for volume (the hint) and solve for h, the height:
Volume = lwh
160 = (2)(8)(h)
160 = 16h
h = 10cm

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Answer: The height is 10 cm

4 0

3 years ago

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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estim

pogonyaev

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36$

And rounded up we have that n=656

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.20$ and $\alpha/2 =0.10$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.28$

Solution to the problem

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

Since we don't have prior info for the proportion of interest we can use $\hat p=0.5$ as estimator. And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got: