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andrezito [222]
3 years ago
14

Two freight trucks are traveling to the same destination, and each are traveling at a constant speed. Truck A is 187 miles away

from
its destination at 9 a.m., one hour after leaving from its origin, and is 99 miles away from the destination at 10:36 a.m. Truck B started
traveling to its destination at 6:30 a.m. Truck B is 248 miles away at 8:30 a.m. and 155 miles away at 10 a.m. Analyze each situation
to determine a function that finds the distance to the destination for each truck based on the time in hours after starting the trip from
the origin to the destination. Then use the functions to determine which truck will arrive first to its destination.
Mathematics
1 answer:
Reptile [31]3 years ago
4 0

Step-by-step explanation:

Uhm, try multiplying the destinations of chuck a B and see what they both start a diet and then where they ended at the end if that makes sense

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Find the limit (enter 'DNE' if the limit does not exist)
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Answer:

\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)=2

Step-by-step explanation:

We need to first simplify the expression using rationalization(i.e. if a square root term exists in the denominator, then multiply and divide the whole expression by the denominator(but the change the sign of its middle term))

here, we need to find:

\lim\limits_{(x,y)\rightarrow(0,0)}\left(\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\right)

first we'll rationalize our expression:

\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\left(\dfrac{\sqrt{-2x^2-6y^2+1}+1}{\sqrt{-2x^2-6y^2+1}+1}\right)

\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{(\sqrt{-2x^2-6y^2+1}+1)^2-(1)^2}

\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-2x^2-6y^2+1-1}

\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-(2x^2+6y^2)}

\sqrt{-2x^2-6y^2+1}+1

this is our simplified expression, now we can apply our limits:

\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)

\sqrt{-2(0)^2-6(0)^2+1}+1

1+1

2

the limit does exists and it is 2.

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