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kvasek [131]
3 years ago
5

A gazebo is located at the center of a large, circular lawn with a diameter of 100 feet. Straight paths extend from the gazebo t

o a sidewalk around the lawn. If two of the paths for a 60 degree angle, how far would you have to travel around the sidewalk to get from one path to the other?
52ft
105ft
26ft
50ft
Mathematics
2 answers:
zzz [600]3 years ago
7 0

Answer: The first option, 52 ft.

Step-by-step explanation:

The data we have is:

The diameter of the lawn is 100ft.

Between the two pats, we have a 60° angle, so we want to calculate the distance between both paths, walking around the circle, this would be the length of the arc of 60°.

Now, first, we know that the perimeter of the circle is equal to 2*pi*radius.

So a section of the perimeter can be calculated as:

L = Angle*radius.

But we need to write the angle in radians.

We know that 180° = pi = 3.14

then (60°/180°)*3.14 = 1.04

60° is equivalent to 1.04 radians.

Now, we have the diameter of our circle, and we know that the radius is equal to half the diameter, so if d = 100ft, r = 100ft/2 = 50ft.

Then the length of the arc is:

L = 1.04*50ft = 52.3 ft

Then the correct answer is the first one (where the result is rounded to the next whole number, 52 ft.)

ludmilkaskok [199]3 years ago
6 0
It is 52 ft that the anwser
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Answer:

1\frac{7}{20}

Step-by-step explanation:

Step one

Given data

On  Monday, Jesse drank 3/4 of liter of water before jogging

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the lcm is 20

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in mixed numbers(i.e a whole and a fraction together we have) we have

1\frac{7}{20}

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Please help ASAP. PRE ALGEBRA
telo118 [61]

Answer:

x=35

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35,40,105

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The sum of the angles of a triangle is 180 degrees.

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First step is to combine the like  terms on the left hand side:

40+4x=180

Second step is to subtract 40 on both sides.

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2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3
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Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29

The associated matrix to the system is

\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]

3.

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]

Using backward substitution we have that

0x_5=-140, then 0=-140 and this is absurd. Then The system is inconsistent.

4 0
4 years ago
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