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Angelina_Jolie [31]
2 years ago
6

A local movie theater sells two bag sizes of popcorn. Both bags are in the shape of a rectangular prism. Bag A measures 4" long,

3.5" wide and 6" tall. Bag B holds twice as much popcorn as Bag A. If Bag B is 8" long and 3" wide, how tall is Bag B?
Mathematics
1 answer:
Natali5045456 [20]2 years ago
8 0

Answer:

the height of bag b is 7

Step-by-step explanation:

first, find the volume of bag a.

volume formula:

length * width * height = volume

length = 4

width = 3.5

height = 6

substitute the values into the formula

4 * 3.5 * 6 = volume

84 = volume

the volume of bag A is 84

next, find the height of bag b

volume formula:

length * width * height.

length = 8

width = 3

volume = 168 (84 * 2)

8 * 3 * h = 168

24h = 168

24h/24 = 168/24

h = 168/24

h = 7

the height of bag B is 7

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A boat sails 285 miles south and then 132 miles west. What is the magnitude of the boats resultant vector?
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The magnitude of the boats resultant vector is 314.1 mi

<h3>What is a vector?</h3>

A vector is a physical quantity that has both magnitude and direction.

<h3>What is a resultant vector?</h3>

A resultant vector is the sum of two or more vectors.

<h3>How to find the boats resultant vector?</h3>

Since the boat sails 285 miles south and then 132 miles west, we have that its first direction vector is r = (285 mi)j. Also, its direction vector west is r' = -(132 mi)i

So, the resultant vector R = r + r'

=  (285 mi)j + (132 mi)i

=  (132 mi)i + (285 mi)j

So, the magnitude of the resultant vector is R = √(r² + r'²)

So, substituting thevalues of the variables into the equation, we have

R = √(r² + r'²)

R = √((285 mi)² + (132 mi)²)

R = √(81225 mi² + 17424 mi²)

R = √(98649 mi²)

R = 314.08 mi

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So, the resultant vector is 314.1 mi

Learn more about magnitude of resultant vector here:

brainly.com/question/28047791

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Step-by-step explanation:

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Step-by-step explanation:

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x = 180 - 66 = 114°

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