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3 years ago

5. During the eruption of Mount St. Helens in 1980. debris was ejected at a speed of over 440 feet per second

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

7 0

Answer:

3500 ft

Step-by-step explanation:

We assume you intend the equations to be ...

$y(t)=-16t^2+425t+8200\\x(t)=113t$

Then we can solve the second equation for t and use that in the first equation. We can solve the first equation for y=6000.

x = 113t

t = x/113

y(t) = y(x/113) = -16(x/113)² +425(x/113) +8200 = 6000

(16/12769)x² -(425/113)x -2200 = 0 . . . . . . subtract 6000, multiply by -1

Using the quadratic formula, the positive solution is ...

x = ((425/113) +√((-425/113)² -4(16/12769)(-2200))/(2(16/12769))

The fraction in the denominator can be inverted and used as a multiplier. We also use a√b = √(a²b) to simplify the radical.

x = (48025 +√4104275825)/32

x ≈ 3502.8

Rock was thrown about 3500 feet horizontally.

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3 years ago

The Carousel at Carowinds has 4 rings of horses. Fred is riding on the inner ring, which has a radius of 7 feet. Juan is riding

nikdorinn [45]

Answer:

Juan travel 31.4 feet farther than Fred in one rotation.

Step-by-step explanation:

In this problem we need to determine the change in linear position of Fred and Juan, whose formula is:

$s=\theta \cdot r$ (Eq. 1)

Where:

$r$ - Radius, measured in feet.

$\theta$ - Angular arch, measured in radians.

$s$ - Change in linear position, measured in feet.

If both makes one rotation in the carousel, we obtain the change in linear position of each player:

Fred ( $r = 7\,ft$ , $\theta = 2\pi$ )

$s= 2\pi\cdot (7\,ft)$

$s = (3.14)\cdot (7\,ft)$

$s = 21.98\,ft$

Juan ( $r = 17\,ft$ , $\theta = 2\pi$ )

$s= 2\pi\cdot (17\,ft)$

$s = (3.14)\cdot (17\,ft)$

$s = 53.38\,ft$

And the difference between both travelled distances is:

$\Delta s = 53.38\,ft-21.98\,ft$

$\Delta s = 31.4\,ft$

Juan travel 31.4 feet farther than Fred in one rotation.

4 0

3 years ago

Eileen and her brother Andrew had a bicycle race. Eileen Rode at a speed of 20 ft per second while Andrew Rode at a speed of 15

Julli [10]

Eileen was 600 feet away from the finish line before the race began.

Step-by-step explanation:

Step 1; Eileen rode at a speed of 20 feet per second whereas Andrew rode at a speed of 15 feet per second. So for every second that passes the distance in between decreases by 5 seconds. Assume x is the number of seconds at which the distance in between is 0. The distance in between at the beginning of the race is 150 feet due to the headstart.

Distance between them = Decreasing distance every second × x

150 feet = 5 feet/ second × x

x = 150 feet / 5 feet/second = 30 seconds.

So it takes Eileen 30 seconds to cover the distance between her and Andrew and cross the finishing line at the same time.

Step 2; The race lasted for 30 seconds so we can find the distance Andrew and Eileen traveled by multiplying their speed per second with the total number of seconds.

Distance Andrew traveled = speed per second × total number of seconds

= 15 feet per second × 30 seconds = 450 feet

Distance Eileen traveled = speed per second × total number of seconds

= 20 feet per second × 30 seconds = 600 feet

Graph plot;

The X-axis is time with 5 seconds for each cm

the y-axis is distance with 100 feet for each cm.

Eileen's plot (0,0), (5,100), (10,200), (15,300), (20,400), (25,500), (30,600).

Andrew's plot (0,150), (5,225), (10,300), (15,375), (20,450), (25,525), (30,600).

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3 years ago

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Andrej [43]

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3 years ago

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Alla [95]

99*76=7524
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3 years ago

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