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3 years ago

What is the distance between the points (2,6) and (5,8)? Round to the

Mathematics

1 answer:

lidiya [134]3 years ago

8 0

The distance between given points is 3.6 units.

Step-by-step explanation:

Given points are;

(2,6) and (5,8)

Here;

$x_1=2\\y_1=6\\x_2=5\\y_2=8$

Distance between two points is calculated by;

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\Distance = \sqrt{(5-2)^2+(8-6)^2}\\\\Distance = \sqrt{(3)^2+(2)^2}\\\\Distance = \sqrt{(9+4)}\\\\Distance = \sqrt{13}\\\\Distance=3.6\ units$

The distance between given points is 3.6 units.

Keywords: distance, points

Learn more about distance at:

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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;

31.1° and 40.9°

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

14.5 miles

<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, d, 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 ≈ 31.1

θ₂ ≈ 180° - 108° - 31.1° ≈ 40.9°

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 A represent the island that has an angle of elevation to the helicopter

of 15°, and let B 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 14.5 miles

Learn more about the Law of Sines and Cosines here:

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7 0

2 years ago

Express f(x) =3\x²- 1 in partial fraction

BARSIC [14]

3/(x ² - 1) = 3/((x - 1) (x + 1)) = a/(x - 1) + b/(x + 1)

==> 3 = a (x + 1) + b (x - 1)

==> 3 = (a + b) x + a - b

==> a + b = 3 and a - b = 0

==> a = b

==> a + b = 2a = 3 ==> a = 2/3 and b = 2/3

So you have

3/(x ² - 1) = 2/(3(x - 1)) + 2/(3(x + 1))

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3 years ago

Out of 24 cookies, 3 4 are chocolate chip. How many cookies are chocolate chip?

Yanka [14]

Answer:

18 cookies

Step-by-step explanation:

3/4 = 75%

75% = 0.75

Multiply this by 24 = 18 cookies

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3 years ago

How many square inches are in 60 square feet?

antoniya [11.8K]

Answer:

8640

Step-by-step explanation:

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3 years ago

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Nataly_w [17]

The correct answer is B.
$\frac{7}{6}$
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3 years ago

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