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mihalych1998 [28]
2 years ago
14

You are saving money for a new bicycle, which costs $85.99. So far you have saved $47.52. How much mor do you need before you ca

n purchase the new bicycle? ​
Mathematics
1 answer:
Ede4ka [16]2 years ago
8 0

Answer:

$38.47

Step-by-step explanation:

amount of money required

=$(85.99-47.52)

=$38.47

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Katen [24]
4. 6/8, 5. 3 5/8, 6. 7 7/8, 7. 72 months and 2,190 days
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Identify the property used in each step of solving the inequality 7x+4<46
meriva
7x+4<46

7x+4(-4)<46(-4) <- Subtraction Property of Equality

7x<42

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A ship leaves port at 10 miles per hour, with a heading of N 35° W. There is a warning buoy located 5 miles directly north of th
Leno4ka [110]

The value of the angle subtended by the distance of the buoy from the

port is given by sine and cosine rule.

  • The bearing of the buoy from the is approximately <u>307.35°</u>

Reasons:

Location from which the ship sails = Port

The speed of the ship = 10 mph

Direction of the ship = N35°W

Location of the warning buoy = 5 miles north of the port

Required: The bearing of the warning buoy from the ship after 7.5 hours.

Solution:

The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Where;

a = The distance between the ship and the buoy

b = The distance between the ship and the port = 75 miles

c = The distance between the buoy and the port = 5 miles

Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°

Which gives;

a = √(75² + 5² - 2 × 75 × 5 × cos(35°))

By sine rule, we have;

\displaystyle \frac{a}{sin(A)} = \mathbf{ \frac{b}{sin(B)}}

Therefore;

\displaystyle sin(B)= \frac{b \cdot sin(A)}{a}

Which gives;

\displaystyle sin(B) = \mathbf{\frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }}

\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx 37.32^{\circ}

Similarly, we can get;

\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx \mathbf{ 142.68^{\circ}}

The angle subtended by the distance of the buoy from the port, <em>C</em> is therefore;

C ≈ 180° - 142.68° - 35° ≈ 2.32°

By alternate interior angles, we have;

The bearing of the warning buoy as seen from the ship is therefore;

Bearing of buoy ≈ 270° + 35° + 2.32° ≈ <u>307.35°</u>

Learn more about bearing in mathematics here:

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2 years ago
86 -5 + 22 - 42 - 7 =
WITCHER [35]

Answer:

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Step-by-step explanation:

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In ΔUVW, u = 8.1 cm, v = 8.4 cm and ∠W=102°. Find the length of w, to the nearest 10th of a centimeter.
zvonat [6]

Answer:12.8

Step-by-step explanation:

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