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3 years ago

Answer ASAP. Please give correct answer. (Involves a bunch of circles and trig identities)

Mathematics

1 answer:

iren [92.7K]3 years ago

7 0

Answer:

45.40

Step-by-step explanation:

First of all, the shape of rope is not a parabola but a catenary, and all catenaries are similar, defined by:

y=acoshxa

You just have to figure out where the origin is (see picture). The hight of the lowest point on the rope is 20 and the pole is 50 meters high. So the end point must be a+(50−20) above the x-axis. In other words (d/2,a+30) must be a point on the catenary:

a+30=acoshd2a(1)

The lenght of the catenary is given by the following formula (which can be proved easily):

s=asinhx2a−asinhx1a

where x1,x2 are x-cooridanates of ending points. In our case:

80=2asinhd2a

40=asinhd2a(2)

You have to solve the system of two equations, (1) and (2), with two unknowns (a,d). It's fairly straightforward.

Square (1) and (2) and subtract. You will get:

(a+30)2−402=a2

Calculate a from this equation, replace that value into (1) or (2) to evaluate d.

My calculation:

a=353≈11.67

d=703arccosh257≈45.40

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3 years ago

What is the area of the region bounded by the lines x= 1 and y= 0 and the curve y=xe^x^2?

Mice21 [21]

Answer:

A = 0.859

Step-by-step explanation:

We want to find the area of the region bounded by the lines x = 1 and y = 0 and the curve y = xe^(x²).

At y = 0, let's find x;

0 = xe^(x²)

Solving this leads to no solution because x is infinity. Thus we can say lower bound is x = 0.

So our upper band is x = 1

Thus,lets find the area;

A = ∫xe(x²) dx between 1 and 0

A = (e^(x²))/2 between 1 and 0

A = ((e¹)/2) - (e^(0))/2)

A = 1.359 - 0.5

A = 0.859

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3 years ago

Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and an

Daniel [21]

Using the normal distribution, the percentages are given as follows:

a) 9.18%.

b) 97.72%.

c) 50%.

d) 4.27%.

e) 0.13%.

f) 59.29%.

g) 2.46%.

h) 50%.

i) 50%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For this problem, the mean and the standard deviation are given as follows:

$\mu = 247, \sigma = 60$

For item a, the proportion is the p-value of Z when Z = 167, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (167 - 247)/60

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

Hence the percentage is of 9.18%.

For item b, the proportion is the p-value of Z when Z = 367, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (367 - 247)/60

Z = 2.

Z = 2 has a p-value of 0.9772.

Hence the percentage is of 97.72%.

For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (247 - 247)/60

Z = 0

Z = 0 has a p-value of 0.5.

Hence the percentage is of 50%.

For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (350 - 247)/60

Z = 1.72

Z = 1.72 has a p-value of 0.9573.

1 - 0.9573 = 0.0427.

Hence the percentage is of 4.27%.

For item e, the proportion is the p-value of Z when Z = 67, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (67 - 247)/60

Z = -3.

Z = -3 has a p-value of 0.0013.

Hence the percentage is of 0.13%.

For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:

X = 300:

$Z = \frac{X - \mu}{\sigma}$

Z = (300 - 247)/60

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

X = 200:

$Z = \frac{X - \mu}{\sigma}$

Z = (200 - 247)/60

Z = -0.78.

Z = -0.78 has a p-value of 0.2177.

0.8106 - 0.2177 = 0.5929.

Hence the percentage is 59.29%.

For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:

X = 400:

$Z = \frac{X - \mu}{\sigma}$

Z = (400 - 247)/60

Z = 2.55.

Z = 2.55 has a p-value of 0.9946.

X = 360:

$Z = \frac{X - \mu}{\sigma}$

Z = (360 - 247)/60

Z = 1.88.

Z = 1.88 has a p-value of 0.97.

0.9946 - 0.97 = 0.0246

Hence the percentage is 2.46%.

For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.

More can be learned about the normal distribution at brainly.com/question/24808124

#SPJ1

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2 years ago

How do you equal 2 by only using four fours?

Lady bird [3.3K]

Four divided by four plus four decided by four

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3 years ago