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Novosadov [1.4K]
3 years ago
12

A runner runs around a circular track. He completes one lap at a time of t = 269 s at a constant speed of v = 4.6 m/s. What is t

he radius, r in meters, of the track?
Mathematics
1 answer:
AURORKA [14]3 years ago
5 0

Answer:

\boxed{\text{197 m}}

Step-by-step explanation:

The formula relating distance (d), speed (s), and time (t) is

d = st

1. Calculate the distance

d = 269 s × 4.6 m·s⁻¹ = 1240 m

2.Calculate the track radius

The distance travelled is the circumference of a circle

\begin{array}{rcl}C & = & 2 \pi r\\1240 & = & 2 \pi r\\\\r & = & \dfrac{1240}{2 \pi }\\\\& = & 197\\\end{array}\\\text{The radius of the track is }\boxed{\textbf{197 m}}

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Alligators lay between 20 and 50 eggs in a nest. A park ranger in Everglades national park counted the number of eggs in 28 nest
zlopas [31]
40×28= the answer is 1,120 eggs that he counted
5 0
2 years ago
There are no universally accepted definitions of the ages of Millennials and Generation Xers; the consensus is that the former a
nadya68 [22]

Answer:

<u>A. The probability that a Millennial is married is 0.089 or 8.9%.</u>

<u>B. The probability that a Baby Boomer is single, never married is 0.03 or 3%.</u>

<u>C. The probability that one person selected randomly (female or male) is married is 0.513 or 51.3% </u>

<u>D. The probability that someone who is living with a partner, but not married is a Generation X is 0.025 or 2.5%.</u>

Step-by-step explanation:

According to the information provided on the analysis table, we can answer the questions:

A. The probability that a Millennial is married is 0.089 or 8.9%.

B. The probability that a Baby Boomer is single, never married is 0.03 or 3%.

C. The probability that one person selected randomly (female or male) is married is 0.513 or 51.3% (Millennial 0.089 + Generation X 0.223 + Baby boomer 0.201)

D. The probability that someone who is living with a partner, but not married is a Generation X is 0.025 or 2.5%.

7 0
2 years ago
Y = x² – 4 y = 2r + 4​<br><br>Solve algebraicallu for the solutions of equations below.
oksano4ka [1.4K]

Step-by-step explanation:

Okay, the first step is to rewrite this equation in "vertex form." You can search that up but it's basically just (h/k).

y = ( x − 1) 2 + 3

Now, we are going to use the vertex form, "y = a (x - h)2 + k, to get the values of a, h, and k.

By using the form we get 1 for the value a, 1 for the value h, and 3 for the value k.

1 = a

1 = h

3 = k

Becuse the value of a is positive, the parabola opens up!  (A parabola is the U shaped line in a graph, so that opens up.)

Now, we find the vertex (h,k)

which is (1,3)

Now we find the p from the vertex to the focus.  (vertext the top, focus one of the points.)

Follow this formula to find the distance from the vertex to a focus by using this formula

1/4a.

Now we just gonna substitue 1 for a, since we know that 1 equals a above ^

1/4 * 1

Solving that, we got a nice little 1/4.

Next we find the focus

"Find the focus.

The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

(h,k+p)

Substitute the known values of h, p, and k into the formula and simplify.

(1,134)

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

x=1

Find the directrix.

y=114

Use the properties of the parabola to analyze and graph the parabola.

Direction: Opens Up

Vertex: (1,3)

Focus: (1,134)

Axis of Symmetry: x=1

Directrix: y=114

Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.

xy−1704132437

Graph the parabola using its properties and the selected points.

Direction: Opens Up

Vertex: (1,3)

Focus: (1,134)

Axis of Symmetry: x=1

Directrix: y=114

xy−17041324"

(Sorry if this is long! But I hope you understand it better now! Thanks for the points!)

3 0
2 years ago
Find the area of the triangle <br> 19cm<br> 15cm<br> 12cm
777dan777 [17]

Answer:

Step-by-step explanation:

4 0
2 years ago
It would mean a lot.
LUCKY_DIMON [66]
First, subtract y2 - y1 to find the vertical distance. Then, subtract x2 - x1 to find the horizontal distance.

Formula to find distance given two points.

Square root (X2 - X1)^2 + (Y2 - Y1)^2

Xa Ya Xb Yb
A = (3, -4) B = (-1, 3)

Xa goes into X2 and Xb goes into X1

(3 - (-1))^2

Ya goes into Y2 and Yb goes into Y1

(-4 - 3)^2

Square root (3 - (-1))^2 + (-4 - 3)^2

Square root (4)^2 + (-7)^2

Square root 16 + 49

Square root 65

= 8.06

The error was Drako had (3 - 4)^2 when it should have been (3 - (-4))^2 because a positive is subtracting a negative.
6 0
2 years ago
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