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lutik1710 [3]
2 years ago
10

A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.

Mathematics
1 answer:
yan [13]2 years ago
6 0
Using the given values from the problem and the illustration, three points are known which are (0,0), (6.5,-31), (-6.5,-31). The first step in solving this problem is to determine the equation of the parabola.
y = ax²
-31 = a(6.5)²
-31 = 42.25a 
a = -31/42.25 
a = -124/169 

Therefore, the equation of the parabola is y = (-124/169)x². The value 4.5 is then substituted in the equation as x to get the answer which is 16.14 meters.
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Nookie1986 [14]

Answer:

-15x + 39 = -3(5x - 13)

Step-by-step explanation:

a. -3(5x - 13) = -15x + 39

b. -3(5x + 13) = -15x - 39

c. 3(5x - 13) = 15x - 39

d. 3(5x + 13) = 15x + 39

7 0
2 years ago
Which of the below descriptions shows a possible HAMILTON PATH?
ra1l [238]

Option B: FECBAD represents the Hamilton path

Explanation:

The vertices in the given graph are A,B,C,D,E and F

We need to determine the Hamilton path of the given graph.

By definition, we know that a Hamilton path touches each and every vertex in a graph exactly once.

Hence, we need to connect the vertices in such a way that the graph touches each and every vertex exactly once.

Option A: EFADECBA

From this description, we can see that the path starts from the vertex E and connects all the vertices but some of the vertices are repeated twice.

Hence, the path EFADECBA is not a Hamilton path.

Therefore, Option A is not the correct answer.

Option B: FECBAD

From this description, we can see that the path starts from the vertex F and connects all the vertices exactly once.

Hence, the path FECBAD is the Hamilton path.

Therefore, Option B is the correct answer.

Option C: ADEFBC

From this description, we can see that the path starts from the vertex A and connects all the vertices but the path from F to B has to touch the vertex A. Thus, the vertices are repeated twice.

Hence, the path ADEFBC is not a Hamilton path.

Therefore, Option C is not the correct answer.

Option D: ADECBAFE

From this description, we can see that the path starts from the vertex A and connects all the vertices but some of the vertices are repeated twice.

Hence, the path ADECBAFE is not a Hamilton path.

Therefore, Option D is not the correct answer.

6 0
3 years ago
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Ghella [55]

Answer:

1.(b)

2.(b)

3. (d) 4cm

4.(a)

Explanation :

The polygons will have the same shape and size, but one may be a rotated, or be the mirror image of the other.Polygons are congruent when they have the same number of sides, and all corresponding sides and interior angles are congruent.

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Answer:

12.

Step-by-step explanation:

b - 4a

Substitute this equation with a=3 and b=24:

24 - 4(3)

24 - 12

12

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nataly862011 [7]

Answer:

The estimate is greater then.

Step-by-step explanation:

143*2=286

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2 years ago
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