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Elenna [48]
3 years ago
6

Given the speeds of each runner below, determine who runs the fastest.

Mathematics
1 answer:
Tju [1.3M]3 years ago
7 0

Answer:

Stephanie  

Step-by-step explanation:

To compare each runner's speed, we must convert them all to the same units.

Let's convert then all to feet per second.

1. Stephanie

Speed = 13 ft/s

2. Emily

\text{Speed} = \dfrac{\text{538 ft}}{\text{45 s}} = \text{12.0 ft/s}

3. Brooke

\text{Speed} = \dfrac{\text{1 mi}}{\text{560 s}} \times \dfrac{\text{5280 ft}}{\text{1 mi}} = \text{9.4 ft/s}

4. Katie

\text{ speed} = \dfrac{\text{747 ft}}{\text{1 min}} \times \dfrac{\text{1 min}}{\text{60 s}} = \textbf{12.4 ft/s}

Stephanie is the fastest runner.

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A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?
Luden [163]

Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

V=\dfrac{1}{3}\pi r^2h

where, r is radius of the base and h is vertical height of the cone.

Putting r=6 and h=9, we get

V=\dfrac{1}{3}\pi (6)^2(9)

V=\pi (36)(3)

V=108\pi

Therefore, the volume of the figure is 108\pi sq. units.

7 0
3 years ago
Which of the following statements are true of the
Anuta_ua [19.1K]

Answer:

B, D, and E.

Step-by-step explanation:

A) The system has infinitely many solutions. This is wrong because according to the graph, there is only one solution- where the lines intersect. This would only be true if the lines never intersected.

B) A solution to the system is (-1, -2). This is true because this is the only point where the lines intersect.

C) A solution to the system is (0, -1). Since these aren't parabolas and the one above is true, we can say this is false. Also, the lines don't intersect at (0, -1).

D) One of the equations is y=x-1. This is true because the y-intercept for the red line is -1 and the slope of the equation is 1. You can also find this out by directly solving for the equation.

E) One of the equations is 3x+y=-5. If you put this into slope-intercept form, you will find out that the equation is y=-3x-5. This is true because the y-intercept of this is -5 and the slope of this is -3.

8 0
3 years ago
Read 2 more answers
Can someone help me with this problem?
Tatiana [17]

Answer:

C

Step-by-step explanation:

if not c it's B

8 0
3 years ago
Taylor dropped a rubber ball from a height of 8 feet.The ball hit the ground after 1 second,bounced up to 5 feet in the next sec
Rzqust [24]

Answer:

The graph is constant in the interval [4,6]

Step-by-step explanation:

We are given that,

Taylor dropped a rubber ball from a height of 8 feet.

So, at time t= 0 sec, the ball is being thrown.

Now, the next events follows as below:

1. After a second, the ball hits the ground.

2. It bounces up to 5 feet in the next second.

3. The ball again hits the ground in the next second.

4. Now, the ball again jumps up to height 2.5 feet, when Taylor holds the ball for 2 seconds more.

So, we get the figure given below, we see that,

The graph is constant in the interval [4,6].

3 0
3 years ago
If someone sleeps 8 hours a day for 75 years how many hours did that person sleep in his lifetime?
ra1l [238]
The person sleeps 8 hours a day.

There are 365 days in a year and 366 days in a leap year.

A leap year occurs every 4 years.

If we divide 75 by 4, we get 18.75. This number represents how many leap years occurred in 75 years. So, the person experienced approximately 19 leap years.

19 leap years has 6954 days.

The other 56 years, which have 365 days each year, have a total of 20,440 days.

That's a total of 27,394 days.

27,394 × 8 = 219,152 hours

This is approximately 24 years or 9,131 days.
7 0
3 years ago
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