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katrin [286]
2 years ago
15

A truck is 300 miles east of a car and is traveling west at the constant speed of 30 miles/hr meanwhile the car is going north a

t a constant speed of 60 miles/hr. Express the distance between the car and the truck as a function of time

Mathematics
1 answer:
Lerok [7]2 years ago
3 0

Answer:

d(t)=\sqrt{(300+30t)^2+(60t)^2}

Step-by-step explanation:

Let t represents the time in hours,

We know that,

Speed =\frac{Distance}{Time}

\implies Distance = Speed\times time

Since, the speed of truck = 30 miles per hour,

So, the distance covered by the truck in t hours = 30t miles,

Similarly,

Speed of car = 60 miles per hour,

So, the distance covered by car in t hours = 60t miles,

∵ Truck is 300 miles east of the car initially,

Thus, the distance of the truck from the starting point = 30t + 300,

While the distance of the car from the starting point = 60 t,

Now, these two vehicles are going in the directions which are at right angled ( car is going north and truck is going west )

Using the Pythagoras theorem,

Distance between them after t hours,

d(t)=\sqrt{(300+30t)^2+(60t)^2}

Which is the required function.

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If the farmer has 250 feet of fencing to create a rectangular pen, define a function f that expresses the area of the field (mea
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Answer:

Maximum area possible

f(max)  = 3906,25 ft²

Dimensions:

a  = 62,5  ft

w  = 62,5 ft

Step-by-step explanation:

Perimeter of the rectangular fencing    P  =  250 feet

And sides of the rectangle  a  and  w (width of rectangle)

Then

A =  a*w

2a  + 2w  = 250       ⇒  a  =  (250 -2w)/ 2    ⇒  a = 125 - w

f(w)  =  (125  - w ) *w        f(w)  = 125w - w²  

Taking derivatives both sides of the equation

f´(w)   =  125  - 2w              f´(w)   = 0           125  - 2w = 0

w = 125/2

w = 62,5 ft            ⇒  a = 125 - 62,5

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f(max)  = ( 62,5)²

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