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maxonik [38]
3 years ago
10

According to Newton's Second Law of Motion, the force acting on an object varies directly with the object's acceleration. Suppos

e that a force of 56 N results in an acceleration of 8 /ms2 . If the force is changed to 35 N , what will the object's acceleration become?
Mathematics
1 answer:
Marta_Voda [28]3 years ago
5 0
Repost this in science. this is physics not math. physics is science.
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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
Write 4=(-8) + 3x as a decimal
Marrrta [24]
4=(-8)+3x
4+8=3x
12=3x
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8 0
3 years ago
Read 2 more answers
Find the value of b to the shape
Aleonysh [2.5K]

Answer:

b=99°

Step-by-step explanation:

108°+72°+81°+b=360°

b=99°

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3 years ago
HELP!!! WILL GIVE BRAINLIEST!!!! 40 POINTS!!!!!! The agriculture department of a university works with individuals wanting to bu
alexgriva [62]

Answer:

Should be something along the lines of:

3,450 = 326x - 310

Step-by-step explanation:

First, let's start with the number of years. Assume the number of years is x. 3262 greenhouses amounts to about 326 greehouses/year. The other number was the existing greenhouses, but we want just how many greenhouses that were built, per the subtraction sign.

Hope this helps!! : )

Sorry if I am wrong, haven't done equations in a while.

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3 years ago
your family went out to dinner to celebrate your grandmas 100th birthday. The total for the dinner was $208.60, so your parents
Allushta [10]

Answer:

\%Tip = 13.04\%

Step-by-step explanation:

Given

Tip= \$31.29

Bill = \$208.60

Required

Determine the percentage of the tip

First, we calculate the amount paid

Amount = Tip + Bill

Amount = \$31.29 + \$208.60

Amount = \$239.89

The percentage of the tip is then calculated using:

\%Tip = \frac{Tip}{Amount} * 100\%

\%Tip = \frac{31.29}{239.89} * 100\%

\%Tip = \frac{31.29* 100}{239.89} \%

\%Tip = \frac{3129}{239.89} \%

\%Tip = 13.04\%

8 0
2 years ago
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