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BaLLatris [955]
2 years ago
12

A traveler is trying to determine the fastest way to travel from city A to city Z. The possible travel routes, with the time req

uired for each segment, is shown below.
What is the shortest path and what is the shortest possible time to travel from A to Z? (Round your answer to the nearest whole number.)


Shortest Path Choices: A-B, B-E, E-Z ; A-C, C-Z ; A-B, B-D, D-Z
Mathematics
1 answer:
Vlad1618 [11]2 years ago
8 0

Answer:

Shortest Path : A-C, C-Z

Shortest possible time = 143

Step-by-step explanation:

P.S - The exact question is -

Given -

T1 = 38

T2 = 52

T3 = 63

T4 = 67

T5 = 91

T6 = 62

T7 = 64

To find - What is the shortest path and what is the shortest possible time to travel from A to Z ?

Proof -

Choices for shortest path is -

Choice 1 : A-B, B-E, E-Z ;

Choice 2 : A-C, C-Z ;

Choice 3 : A-B, B-D, D-Z

Now,

For Choice 1 : A-B, B-E, E-Z

Distance between A-B = T1 = 38

Distance between B-E = T4 = 67

Distance between E-Z = T7 = 64

So,

The distance = 38 + 67 + 64 = 169

Now,

For Choice 2 : A-C, C-Z

Distance between A-C = T2 = 52

Distance between C-Z = T5 = 91

So,

The distance = 52 + 91 = 143

Now,

For Choice 3 : A-B, B-D, D-Z

Distance between A-B = T1 = 38

Distance between B-D = T3 = 63

Distance between D-Z = T6 = 62

So,

The distance = 38 + 63 + 62 = 163

∴ By comparing we get

Shortest Path = A-C, C-Z

Shortest possible time = 143

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Aaron creates a stacked cake comprised of three cylindrical sections and plans to cover the top of each section with a different
spin [16.1K]

Answer:

Option C

Step-by-step explanation:

Complete question is

Each lower section is a total of two inches wider than the section above it. If the yellow top of the upper section has an area of 12.56 square inches, what is the approximate area of the green visible portion of the bottom section which he will need to cover with icing?

A. 13 square inches

B. 88 square inches

C. 49 square inches

D. 22 square inches

Solution -

Given

Top of each cylindrical section is covered with a different color icing

Radius of each color icing is two inches less than the section below it.

Let the radius of the icing be "r"

Then the surface area of the icing will be  \pi r^2

Now area of the yellow icing is equal to 12.56 square inches

Thus,

\pi r^{2}  = 12.56

On solving the above equation for r, we get -

r^2 = \frac{12.56}{3.14} \\r^2 = 4\\r = \sqrt{4} \\

r = 2 inches

Now radius of the section below the icing is equal to

r + 2\\= 2+ 2\\

= 4 inches

Area of the section below the icing

= \pi r^2\\= 3.14 * 4^2\\= 50.24

Thus, option C is correct

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