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Arisa [49]
3 years ago
10

Starting at point​ A, a ship sails 18.9 km on a bearing of 190 degrees and ​then turns and sails 47.2km on a bearing of 318 degr

ees. Find the distance of the ship from point A. (Use trigonometry)

Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0

Answer:

Approximately 38.56 kilometers

Step-by-step explanation:

So, from the picture, we want to find <em>x</em>.

To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:

c^2=a^2+b^2-2ab\cos(C)\\

The <em>c </em>in this equation is our <em>x, </em>and the <em>C</em> is the angle we need to find.

From the picture, you can see that angle <em>C </em>is the sum of the red and blue angles.

From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.

From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.

Therefore, angle <em>C </em> is 42+10 which equals 52 degrees. Now we can plug this into our formula:

x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}

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What is 25% Of 30% Of 400?
marta [7]

Answer:

25% of 30% of 400 = 30

33% decrease in value

Step-by-step explanation:

You can either get 30% of 400 first then 25% of 400 or you can get the total percentage of 400.

Method 1:

30% of 400 = 0.3 of 400 = 0.3 * 400 = 120

25% of 120 = .25 of 120 = .25 * 120 = 30

Method 2:

30% of 25% = 0.3 * 0.25 = 0.075 = 7.5% of 400

7.5% of 400 = 0.075 of 400 = 0.075 * 400 = 30

5.) To find the percentage  of the new price, you can build the equation below.

\frac{new price}{original price} = \frac{percent}{100}

\frac{200,000}{300,000}  = \frac{x}{100}

20,000,000 = 300,000x

x = 66.667

The percentage decrease in price is then 100% of the original price - 66.667% of the original price = 100% - 66.67% = 33.33% = 33% decrease.

3 0
2 years ago
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collecte
allsm [11]

Answer:

The degrees of freedom are given by;

df =n-1= 5-1=4

The significance level is 0.1 so then the critical value would be given by:

F_{cric}= 7.779

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

Step-by-step explanation:

For this case we have the following observed values:

Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100

For this case the expected values for each day are assumed:

E_i = \frac{100}{5}= 20

The statsitic would be given by:

\chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}

Where O represent the observed values and E the expected values

The degrees of freedom are given by;

df =n-1= 5-1=4

The significance level is 0.1 so then the critical value would be given by:

F_{cric}= 7.779

If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays

5 0
2 years ago
JK=4x+7 and KL=3x+14 find JL
Lena [83]

Answer:

Step-by-step explanation:

4x + 7 = 3x + 14

x + 7 = 14

x = 7

4(7) + 7 + 3(7) + 14

28 + 7 + 21 + 14

35 + 35 = 70

5 0
2 years ago
Can someone help me with this please!
Vinil7 [7]

Answer:

This is really easy, take away all 1s and multiplication sign.

Step-by-step explanation:

And then it means 25=25

3 0
2 years ago
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kherson [118]
I'm pretty sure it is figure A
3 0
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