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3 years ago

A bicyclist travels at a constant rate of 11miles in 1/4hour. Find the unit rate of the hikers in miles per hour

1 answer:

7 0

11 miles in 1/4 hour
1/4 of an hour is 15 minutes
so 11 in 15 minutes
x /60 = 11/15
cross multiply
x*15 = 60 * 11
15x = 660
divide both sides by 15
x = 44

the unit rate of the hikers in miles per hour is 44 mph.

You can also solve like this
1/4 of hour is 15 minutes
to get to the whole hour you would multiply by four
so you'd (11miles in 1/4 hour) * 4
44 miles in 1 hour

Hope this helps :)

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Zepler [3.9K]

Answer:

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Step-by-step explanation:

Diameter = 19 cm

Radius = 19/2 = 9.5 cm

Volume = $\frac{4}{3} (3.14)(9.5)^3$

V = $\frac{4}{3}(3.14)(857.375)$

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3 years ago

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A cube-shaped gift box has a volume of 8 cubic inches what is the side length of the box

Pani-rosa [81]

Answer:

Each side is 2 inches long.

Step-by-step explanation:

Volume is Length x Width x Height

For a cube, all sides are the same so you need to figure out what number you can cube (multiply by it self 3 times) to get it to 8.

2 x 2 x 2 = 8

So, each side is 2 inches long.

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3 years ago

Woody is five years older than Buzz. If x represents Buzz's age, what is the y-intercept of the line that represents this additi

ZanzabumX [31]

Answer:

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Step-by-step explanation:

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3 years ago

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:

brainly.com/question/8242520

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2 years ago

Ben also bought a package of 3 T-shirts for $14.25. What is the unit price, per T-shirt

Harrizon [31]

Answer:

4.75 per T-shirt

Step-by-step explanation:

Divide 14.25 by 3

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3 years ago