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spayn [35]
2 years ago
13

From the top of a vertical cliff 80m high, the angles of depression of 2 buoys lying due west of the cliff are 23° and 15° respe

ctively. How far are the buoys apart?​
Engineering
1 answer:
Umnica [9.8K]2 years ago
6 0

Answer:

  110 m

Explanation:

The geometry of the problem can be modeled by a right triangle. The height of the cliff forms one leg, and the distance to a buoy forms the other leg. The angle of depression is opposite the height of the cliff. An appropriate trig relation is ...

  Tan = Opposite/Adjacent

Solving for the Adjacent side (the distance to the buoy), we find ...

  Adjacent = Opposite/Tan

  distance to buoy 1 = (80 m)/tan(23°) ≈ 188.468 m

  distance to buoy 2 = (80 m)/tan(15°) ≈ 298.564 m

Then the distance between the buoys is ...

  298.564 -188.468 m ≈ 110 m

The buoys are about 110 meters apart.

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A biotechnology company produced 225 doses of somatropin, including 11 which were defective. Quality control test 15 samples at
Radda [10]

Answer:

  • <u>0.59</u>

Explanation:

The <em>batch</em> is <em>rejected</em> if any of the <em>random samples are found defective</em>, or, what is the same, it will be accepted only if all 15 samples are good.

The probability that none be defective is the same probability that all the samples are good. Thus, start to calculate the probability that the batch is accepted.

The probability that the first sample is good is 214 /225, because there are 225 - 11 = 214 good samples in 225 doses.

The probability that the second samples is good too is 213/224, because there is 1 less good sample, in the 224 remaining samples.

By the same process, you conclude that the consecutive probabilities of selecting a good sample are: 212/223, 211/222, 210/221, . . . up to 199/211.

The joint probability of all the samples are good is the product of each probability:

\frac{214}{225}\cdot\frac{213}{224}\cdot\frac{212}{223}\cdot\frac{211}{222}\cdot\frac{210}{221}\cdot\frac{209}{220}\cdot\frac{208}{219}\cdot\frac{207}{218}\cdot\frac{206}{217}\cdot\frac{205}{216}\cdot\frac{204}{215}\cdot\frac{203}{214}\cdot\frac{202}{213}\cdot\frac{201}{212}\cdot\frac{200}{211}\cdot\frac{199}{210}

The result is: 0.41278 ≈ 0.41

The conclusion is that the probability that all the samples are good and the batch is accepted is 0.41.

Therefore, <em>the probability that the batch is rejected</em> is 1 - 0.41 = 0.59.

4 0
3 years ago
. In one stroke of a reciprocating compressor, helium is isothermally and reversibly compressed in a piston + cylinder from 298
andriy [413]

Answer:

5.7058kj/mole

Explanation:

Please see attachment for step by step guide

5 0
3 years ago
You are hitting a nail with a hammer (mass of hammer =1.8lb) the initial velocity of the hammer is 50 mph (73.33 ft/sec). The ti
Archy [21]

Answer:

The nail exerts a force of 573.88 Pounds on the Hammer in positive j direction.

Explanation:

Since we know that the force is the rate at which the momentum of an object changes.

Mathematically \overrightarrow{F}=\frac{\Delta \overrightarrow{p}}{\Delta t}

The momentum of any body is defines as \overrightarrow{p}=mass\times \overrightarrow{v}

In the above problem we see that the moumentum of the hammer is reduced to zero in 0.023 seconds thus the force on the hammer is calculated using the above relations as

\overrightarrow{F}=\frac{m(\overrightarrow{v_{f}}-\overrightarrow{v_{i}})}{\Delta t}

\overrightarrow{F}=\frac{m(0-(-73.33)}{0.23}=\frac{1.8\times 73.33}{0.23}=573.88Pounds

6 0
3 years ago
A seamless pipe 800mm diameter contains a fluid under a pressure of 2N/mm2. If the permissible tensile stress is 100N/mm2, find
Bad White [126]

Answer:

8 mm

Explanation:

Given:

Diameter, D = 800 mm

Pressure, P = 2 N/mm²

Permissible tensile stress, σ = 100 N/mm²

Now,

for the pipes, we have the relation as:

\sigma=\frac{\textup{PD}}{\textup{2t}}

where, t is the thickness

on substituting the respective values, we get

100=\frac{\textup{2\times800}}{\textup{2t}}

or

t = 8 mm

Hence, the minimum thickness of pipe is 8 mm

3 0
3 years ago
The best saw for cutting miter joints is the
ZanzabumX [31]

Answer:

The best saw for cutting miter joints is the backsaw.

Add-on:

i hope this helped at all.

6 0
3 years ago
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