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algol13
2 years ago
15

The rules for a race require that all runners start at $A$, touch any part of the 1200-meter wall, and stop at $B$. What is the

number of meters in the minimum distance a participant must run
Mathematics
1 answer:
mixer [17]2 years ago
5 0

Let the place that they touch be x meters from the 300 m wall

Then the distance from the 500 m wall will be 1200 - x

Then....the total distance, D, can be expressed asD = sqrt [ x^2 + 300^2 ] + sqrt [ (1200 - x)^2 + 500^2 ]

This can be solved with Calculus, but it's a little messy

The graph shows that the minimum distance is achieved when x = 450m

And the minimum distance  ≈  1442 m

By the way......we can show that this is true if

arctan [ 300 / 450]   =  arctan [ 500 / 750 ]  ......and this is true  !!!!

Learn more about Distance:

brainly.com/question/12356025

#SPJ4

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I have 8 slices of pizza in a box, all 8 are triangle shaped, my perimeter is 43.98 Octagon with each edge 5.49 inches. So, I ne
kondor19780726 [428]

Answer:

1) The area of the circle pizza is approximately 161.64 in.²

2) The area of the octagon shaped pizza is approximately 145.52 square inches

Step-by-step explanation:

The 8 slices of pizza combine to form the composite octagon

The parameters of the pizza are;

The perimeter of the octagon = 43.98 inches

The length of each (outer) edge of the octagon = 5.49 inches

The outer edge of the octagon = The base of the triangle shaped pizza

Let θ represent the vertex angle of the triangle shaped pizza

Therefore, we have;

θ = (The angle at the center point of the pizza)/8 = 360°/8 = 45°

The vertex angle of the triangle shaped pizza, θ = 45°

We note that a triangle shaped pizza is isosceles shaped, therefore, the base angles are given as follows;

The base angles of a piece of pizza = (180° - (angle at vertex))/2

∴ The base angles of a piece of pizza = (180° - 45°)/2 = 67.5°

The length, 'l', of the other sides of the triangle shaped pizza is given by sine rule as follows;

l/(sin 67.5°) = 5.49/(sin(45°)

∴ l = (sin 67.5°) × 5.49/(sin(45°)

l = (sin 67.5°) × 5.49/(sin(45°) ≈ 7.173

The length of the other sides of the triangle shaped pizza, l ≈ 7.173 inches

1) The length of the other sides of the triangle shaped pizza, l = The radius of the circle, r

The area of the circle = π·l²

∴ The area of the circle ≈ π × (7.173 in.)² ≈ 161.64 in.²

2) The area of each triangle piece of pizza is given as follows;

The area of a triangle, A = 1/2×l·b·sin(C)

∴ A = 1/2× 5.49 × 7.173 × sin(67.5°) ≈ 18.19

The area of each triangle piece of pizza, A ≈ 18.19 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 8 × A

∴ TA ≈ 8 × 18.19 inches² ≈ 145.52 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 145.52 inches²

4 0
2 years ago
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ICE Princess25 [194]

Answer: middle one = 4/4 + 1 + 2 =3

Step-by-step explanation:

4/4 also equals one so x=4    1+2=3

4/4=1  

7 0
3 years ago
Solve the following inequality for x.
Alexus [3.1K]

Answer:

X < -1

Step-by-step explanation:

4x - 5 + X < -10

5x < -5

× < -1

8 0
3 years ago
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Use the menu provided to answer the following question. If a student purchased 1 can of juice, 2 slices of pizza, 1 bag of peanu
pochemuha

Answer:

$8.25

Step-by-step explanation:

1.25+(2.25x2)+1.00+(1.25x2)=8.25

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2 years ago
A film student wants to capture a shot of a satellite dish placed at the top of a building. The line of sight between the ground
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Answer:

34.78 feet

Step-by-step explanation:

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This is because cosine is equal to adjacent over hypotnuse

Once I found x, I used the pythagorean theorem to get 34.78 feet

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