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evablogger [386]
3 years ago
10

a long-distance runner passes the 23 km mark of a race in 2 hr 30 min and passes the 44 mark 3 hours later. Assuming a constant

rate, find the speed of the long-distance runner in km/h
Mathematics
1 answer:
Vikentia [17]3 years ago
8 0

Answer:

The speed of the long distance runner is 8km/h

Step-by-step explanation:

In this question, we have a long-distance runner, running at a constant rate and we want to find his speed.

Mathematically,

speed = distance/ Time

From the question, we are told that he passes the 44km mark 3 hours after passing the 23km mark in 2 hours and 30 minutes

what this means is that the total distance he ran was just 44km

Now to the total time, that would be 2 hours 30 minutes + 3 hours = 5hrs 30 minutes or 5.5 hours

The speed is thus = 44km/5.5 hours =

8km/h

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At a candy store, Erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. Meanwhile, Irene bough
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Find the point P on the line yequals=66x that is closest to the point (74 comma 0 )(74,0). What is the least distance between P
tekilochka [14]

Answer:

The point P that is closest to the point (74, 0) is P(7.4, 22.2), and the least distance between P and (74, 0) is 70.2

Step-by-step explanation:

Given

y = 66x

And a point A(74, 0)

We are required to find the point on the line that is closest to A, and then find the distance between these points.

Let the point be P(s, t)

Because it's coordinate satisfies the given equation

y = 3x

Let t = 3s, then we have

p(s, t) = P(s, 3s)

Next, we find the distance between P and A

Let the distance be

D = √[(x1 - y1)² + (x2 - y2)²]

Here x1 = 74, x2 = 0, y1 = s, y2 = 3s.

D = √[(74 - s)² + (0 - 3s)²]

= √(s² - 148s + 5476 + 9s²)

= √(10s² - 148s + 5479)

To maximize the distance, we find the derivative of D with respect to s, and set it to 0.

That is dD/ds = 0

dD/ds =

(20s - 148)/2√(10s² - 148s 5479) = 0

=> 20s - 148 = 0

20s = 148

s = 148/20

s = 7.4

Since t = 3s, we have

t = 22.2

So, the point is P(7.4, 22.2)

Finally, we find the distance D.

D = √[(74 - s)² + (0 - 3s)²]

D = √[(74 - 7.4)² + (0 - 3×7.4)²]

D = √(4435.56 + 492.84)

= √4928.4

D = 70.2

Therefore, the distance is 70.2

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3 years ago
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago
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