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Tomtit [17]
3 years ago
15

Write equation in slope intercept from of the line

Mathematics
1 answer:
Ymorist [56]3 years ago
4 0

Answer:

y= 1/2x + 3

Step-by-step explanation:

good luck lmk if u have any more questions

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1. A buoy floats 19 yards from the eastern most point of a boat and 15 yards from the western most point of a second boat. The a
Black_prince [1.1K]

The laws of cosines and law of sines can be used given that two sides

and an included angle, or two angles a side are known.

Response:

1. The other angles in the triangle formed by the buoy are approximately;

  • <u>31.1° and 40.9°</u>

2. Distance of the helicopter from the first island is approximately;

  • <u>14.5 miles</u>

<h3>How is the Law of Sines and Cosines used?</h3>

Given parameters are;

Distance of the buoy from the easternmost point of a boat = 19 yards

Distance of the buoy from the westernmost point of the other boat = 15 yards

Angle formed from the buoy to the two boats = 108°

Distance between the two boats, <em>d</em>, is given by the law of cosines, as follows;

d² = 19² + 15² - 2 × 19 × 15 × cos(108°) = 586 - 570·cos(108°)

d = √(586 - 570·cos(108°))

By the law of Sines, we have;

\dfrac{d}{sin(108^{\circ})} = \mathbf{\dfrac{15}{sin(Angle \ formed \ from \ the \ boat \ on \ the \ West, \ \theta_1)}}

Which gives;

sin(\theta_1) = \mathbf{ \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} }}

The o

\theta_1 = arcsin \left( \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} } \right) \approx   \mathbf{31.1^{\circ}}

The other angles formed in the triangle containing the buoy are;

  • θ₁ ≈ <u>31.1</u>
  • θ₂ ≈ 180° - 108° - 31.1° ≈<u> 40.9°</u>

2. Distance between the two islands = 20 miles

Angle of elevation with one island = 15°

Angle of elevation with the second island = 35°

Required:

The mileage (distance travelled) of the helicopter.

Solution:

Let <em>A</em> represent the island that has an angle of elevation to the helicopter

of 15°, and let <em>B</em> represent the other island.

Angle formed by the helicopter and the two island, θ, is found as follows;

θ = 180° - (15° + 35°) = 130°

By the Law of Sines, we have;

\dfrac{20}{sin(130^{\circ})} = \mathbf{ \dfrac{Distance \ from \  island \ A }{sin(35^{\circ})}}

Which gives;

Distance \ of \ helicopter \ from \  island \ A = \mathbf{ \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ})}

Mileage \ from \ island \ A =  \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ}) \times cos(15^{\circ}) \approx 14.5

  • The mileage of the helicopter from the first island is approximately <u>14.5 miles</u>

Learn more about the Law of Sines and Cosines here:

brainly.com/question/8242520

brainly.com/question/2491835

7 0
2 years ago
3x - y = 9<br> Slope-intercept??
hoa [83]

Answer:

Y= 3X-9

Step-by-step explanation:

4 0
3 years ago
"find the third length of the right triangle. give an exact answer and an approximation" HELP PLS
egoroff_w [7]
Well, as far as the approximation... so... make one :)

then, check the picture below.

3 0
3 years ago
The following is a parallelogram solve for the variables
Andrews [41]
X = 66 degrees. (Co interior angles are supplementary, add up to 180)

2y + 4 = y + 7
2y - y = 7 - 4
Y = 3
6 0
3 years ago
Farmer Gray has 30 flower pots. He plants 10 seeds in each pot. How many seeds does he plant?
Alex17521 [72]

Farmer Gray planted 300 seeds.

To find this, you simply multiply the number of flower pots (30) by the number of seeds in each pot (10). Thus making the answer 300.

I hope this helps!

5 0
3 years ago
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