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IceJOKER
1 month ago
7

(PLEASE HELP ) A falcon flies 800,000 meters in 4 hours. Use the formula d = rt, where d represents distance, r represents rate,

and t represents time, to answer the following questions. Show
your work.

Part A: Rearrange the distance formula, d = rt, to solve for rate.

Part B: Find the falcon's rate in meters per hour.

Part C: Find the falcon's rate in kilometers per hour.

Part D: Which unit, meters, or kilometers, makes more sense to use in this scenario, and why?
Mathematics
1 answer:
zzz [12.3K]1 month ago
6 0

Answer:

r = d/t

r = 200,000 meters/hour

r = 200 kilometers/hour

km/hour is more suitable

Step-by-step explanation:

Given

A falcon travels 800,000 meters in 4 hours.

This means the distance covered is 800,000 meters.

1 km equals 1,000 meters.

Therefore, the distance in kilometers is 800,000 meters divided by 1,000, resulting in 800 km.

t equals 4 hours.

Part A: To find the rate, rearrange the formula for distance, d = rt.

d = rt

By dividing each side by t, we get d/t = r.

Thus, r = d/t

Part B: Calculate the falcon's speed in meters per hour.

d = 800,000 meters

t = 4 hours

r = 800,000 meters divided by 4 hours gives us 200,000 meters/hour.

Therefore, the speed equals 200,000 meters/hour.

Part C: Find the falcon's rate in kilometers per hour.

As established, the distance is 800 km as mentioned earlier.

Hence,

speed = 800 km divided by 4 hours gives us 200 km/hour.

Part D: Which unit, meters or kilometers, is more logical for this situation, and why?

The standard measurement of speed is

km/hour and m/sec.

That is, the choice of units is based on the scale of measurement we need; larger numbers are easier to interpret in kilometers.

Since we are dealing with a large distance, it is advisable to use km/hour.

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Answer:

a) 0.216

b) 0.784

c) 0.288

d) 0.352

e) 0.784

Step-by-step explanation:

The steps for solving this are provided in an image.

8 0
25 days ago
Nik needs to estimate how many books will fit in a bin. Each book is 1 ft tall, 0.5 ft wide, and 0.1 ft thick. The bin is 5 feet
lawyer [12517]

Answer:

600 books

Step-by-step explanation:

The dimensions of the bin are

5 by 2 by 3

The volume of the bin is found by multiplying these three dimensions.

Volume of Bin = 5 * 2 * 3 = 30 cubic feet

To find the volume of each book, we use the same method. The dimensions of one book are:

1 by 0.5 by 0.1

Volume of 1 book = 1 * 0.5 * 0.1 = 0.05 cubic feet

The total number of books fitting into the bin is calculated by:

30/0.05 = 600 books

6 0
1 month ago
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,
Svet_ta [12734]

Answer:

Here’s the response provided

Step-by-step explanation:

Referring to the flask diagram, the diameter of the cylinder measures 1 inch and its height (h) is 3 inches. Thus, the radius of the cylinder (r) = diameter / 2 = 1/2 = 0.5 inch

The volume of the cylinder can be calculated as πr²h = π(0.5)² × 3 = 2.36 in³

As for the sphere, its diameter is 4.5 in. Hence, the radius of the sphere R = diameter / 2 = 4.5/2 = 2.25 in

The volume of the sphere is calculated as 4/3 (πR³) = 4/3 × π × 2.25³ = 47.71 in³

The total volume of the flask = Volume of the cylinder  + Volume of the sphere = 2.36 + 47.71 = 50.07 in³

<pWhen the cylinder and the sphere are expanded by a scale factor of 2, the height (h') of the cylinder becomes 3/2 = 1.5 inches and the radius (r') becomes 0.5/2 = 0.025 inches.

The new volume for the cylinder = πr'²h' = π(0.25)² × 1.5 = 0.29 in³

For the sphere, the new radius is R' = 2.25 / 2 = 1.125 in.

The new volume of the sphere = 4/3 (πR'³) = 4/3 × π × 1.125³ = 5.96 in³

Thus, the new volume of the flask = The new volume of the cylinder  + The new volume of the sphere = 0.29 + 5.96 = 6.25 in³

<pThe ratio of the new volume to the original volume = New Volume of the flask / Volume of the flask = 6.25 / 50.07 = 1/8 = 0.125<pThe resulting volume will thus be 0.125 times the original volume

6 0
1 month ago
A storage pod has a rectangular floor that measures 19 feet by 13 feet and a flat ceiling that is 5 feet above the floor. Find t
Inessa [12570]

Answer:

Area= 247 feet²

Volume= 1235 feet³

Step-by-step explanation:

The storage pod features a rectangular base measuring 19 feet by 13 feet, with a flat ceiling height of 5 feet above.

Calculating the area of the floor yields: length multiplied by width

Length = 19 feet

Width = 13 feet

Area = 19*13

Area = 247 feet²

The volume of the pod can be found by multiplying the area by the height

Height of the pod = 5 feet

Area = 247 feet²

Volume = 247*5

Volume = 1235 feet³

4 0
1 month ago
Penelope has $1,459.75 in her bank account. To pay her bills, she writes 4 checks for $200.25, $359.45, $125, and $299.35. Then
Leona [12618]
1,459.75 - 200.25 - 359.45 - 125.00 - 299.35 = 475.70

475.70 + 375.00 = 850.70

After settling the bills and deposit, her account shows a balance of $850.70
8 0
1 month ago
Read 2 more answers
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