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3 years ago

URGENT!!!!! Work out the image attached Include Workings

Mathematics

1 answer:

Ann [662]3 years ago

6 0

9514 1404 393

Answer:

17.8 km
80.4 m

Step-by-step explanation:

The first attachment shows the sort of geometry involved. The line of sight from the top of the lighthouse makes a tangent with the earth's surface at the horizon (neglecting optical effects due to the atmosphere).

The hypotenuse of the relevant triangle is (r+h), and the angle is adjacent to the radius, r. Then the cosine relation applies:

Cos = Adjacent/Hypotenuse

cos(α) = r/(r+h)

We note that the radius is in km, and the length h is given in meters, so we need to do a conversion to put the numbers in this formula. We don't care so much about the angle itself, but we need its value to find the length of the arc along the earth's surface. That is ...

s = r·α

so, the distance of interest is found from ...

cos(α) = 6367/(6367 +0.025)

r·α = 6367·arccos(6367/6367.025) ≈ 17.84 . . . km

The horizon is about 17.8 km from the observer.

The second problem requires we find the height value that makes the distance 32 km.

32 = r·α = 6367·arccos(6367/(6367 +h))

Dividing by the earth's radius and taking the cosine, we have ...

cos(32/6367) = 6367/(6367 +h)

h = 6367 -6367/cos(32/6367) ≈ 6367.0804 -6367 = 0.0804 . . . km

The cliffs must be about 80.4 meters high for it to be possible to see that distance.

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2 years ago

Katherine paid $25.56 for12 gallons of gasoline. What is the price per gallon of gasoline? per gal

zloy xaker [14]

Answer:

$2.13

Step-by-step explanation:

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3 years ago

A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

The 95% confidence interval is $0.0503 < p < 0.1297$

The sample proportion is $\r p = 0.09$

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

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3 years ago

Which value of x makes the equation<br> -5x = -35 true?

WITCHER [35]

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2 years ago

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jarptica [38.1K]

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Step-by-step explanation:

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3 years ago

Read 2 more answers