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valkas [14]
2 years ago
13

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
Mathematics
2 answers:
xxMikexx [17]2 years ago
5 0
If we let
x as the distance traveled by the boat
y as the distance between the boat and the lighthouse.

Then, we have:
tan 18°33' = 200 / (x + y)
and
tan 51°33' = 200 / y

Solving for y in the second equation:
y = 200 / tan 51°33'

Rearranging the first equation and substituting y
x = 200 / tan 18°33' - 200 / tan 55°33'
x = 458.81 ft

Therefore, the boat traveled 458.81 ft before it stopped.
patriot [66]2 years ago
4 0

Answer: 437.21 ft

Step-by-step explanation:

First off, change all minutes to degrees.

18°33’ = 18.55°

51°33’ = 51.55°

When the boat is first spotted:

Tan(x)=opp/adj

Tan(18.55°)=200/x

x=200/tan(18.55)

x=596.01ft

When the boat stops:

Tan(51.55)=200/x

x=158.80ft

Find the difference:

596.01-158.0=437.21

Yay! It’s very simple once you understand the parttern :)

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the chef is making 10.5 batches of dinner rolls. For each batch, he kneaded dough for 0.7 and let the dough rest for 1.6 hours.
Sergeeva-Olga [200]

Answer: 2.7 hours

Step-by-step explanation:

Hi, to answer this question we simply have to calculate the amount of time that takes making one batch of dinner rolls, by adding the individual times of, kneading, resting and baking.  

Mathematically speaking  

0.7 hours +1.6 hours +0.4 hours = 2.7 hours  

It takes 2.7 hours to make each batch of dinner rolls.

6 0
2 years ago
The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number
geniusboy [140]

Answer:

Reasonable estimation for constant of variation is 0.25 kWh per day.    

Step-by-step explanation:

We are given the following information in the question:

  • The graph represents the function where electricity usage.
  • Electricity usage in kilowatts per hour of a clock radio varies directly with the number of days.
  • The x-axis shows the number of days and usage in kilo-watt per hour is showed on the y-axis.
  • Some coordinates of the graph are: (0,0), (2,0.5) and (6,1.5)

Formula for constant of variation:

\displaystyle\frac{y_2-y_1}{x_2-x_1}

Putting the values from the coordinates (2,0.5) and (6,1.5), we get:

\displaystyle\frac{1.5-0.5}{6-2} = \frac{1}{4} = 0.25\text{ kilowatt-hours per day}

Hence, reasonable estimation for constant of variation is 0.25 kWh per day.

7 0
2 years ago
Read 2 more answers
What is the volume of 1.60 grams of O2 gas at STP?
Mariulka [41]
The answer is 1.12 or d
5 0
2 years ago
Read 2 more answers
For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr
anastassius [24]

Answer:

For k = 36, there is 0 solutions

For other values of k, there is 1

We never got infinite solutions on the system.

Step-by-step explanation:

We have 2 unknowns and 2 equations:

E1     8x1 + x2 = 18

E2    k*22 x1 + 9 x2 = 18

If we multiply the E1 by 9 we obtain

E3     72 x1 + 9x2 = 162

if we substract E3 with E2 we obtain

(72- 2k) x1 = 144

Thus,

x1 = 144/ (72-2k)

That is, if 72-2k = 0, otherwise there is no solution. And 72-2k = 0 when k = 72/2 = 36.

If k is not 36, then

x1 = 144/(72-2k) and we can replace this value to obtain x2 by using E1

x2 = 18-8x1 = 18- 8 * (144/72-2k)

Which is a specific number that depends only on k. Thus,

for k = 36, there is 0 solutions

for other values of k, there is unique solution.

4 0
2 years ago
Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this p
goldfiish [28.3K]

Answer:

0.0406, 0.8284,0.7887

Step-by-step explanation:

Given that Mattel Corporation produces a remote-controlled car that requires three AA batteries

X is N(34, 5.5)

Hence sample size of 25 would follow a t distribution with df = 24

This is because sample size <30

t distribution with df 24 would be bell shaped symmetrical about the mean and unimodal.

Std error of sample mean = std dev /sqrt n=\frac{5.5}{5} \\=1.1

Prob (X>36) = P(t>\frac{36-34}{1.1} ) = P(t>1.82)\\= 0.04063

i.e nearly 4.1% of the sample would have a mean useful life of more than 36 hours

X>33.5 implies t>-0.45

=0.82837

=0.8284 proportion will have a mean useful life greater than 33.5 hours

Proportion between 33.5 and 36 hours

= 0.3284+0.4593=0.7887

6 0
2 years ago
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