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kolbaska11 [484]
3 years ago
10

Please help me ineed it now ​

Mathematics
1 answer:
yanalaym [24]3 years ago
3 0

Answer:

look at explanation

Step-by-step explanation:

To solve all of these questions you just need to scale. While scaling you can divide or multiply.

1. \frac{180 km}{4 hrs} (divide by 4 to get unit rate)

     unit rate = \frac{45km}{1hr}

2. If it takes one hour to travel 40 miles, then we don't have to scale or anything. We know \frac{40 miles}{1 hr}, the answer is...

"It'll only take one hour to travel 40 miles. This is correct because the unit rate is \frac{40 miles}{1 hr}. "

3. Knowing that the constant speed of the plane is \frac{800 km}{1 hour\\}, we can scale then add half of the unit rate to get our answer.

\frac{800 km}{1 hour\\} x 3 = \frac{2400 km}{3 hrs}   800 x 3 = 2400

then add half of unit rate which is \frac{400 km}{30 mins}  \sqrt[2]{800} = 400

so, our answer is \frac{2800 km}{3.5 hours}

4.  \frac{3km}{30 mins} <--- ( divided by 2) \frac{6 km}{1 hr} ( multiplied x 2.5) ---> \frac{15 km}{2.5 hrs}

To get an easier way to find the answer, if possible you can scale back farther than the 1 hour mark.

Elmer would take 2 and a half hours to ride 15 km.

5. The boys speed is \frac{4 km}{1 hr}. All we need to do is divide by 2. \sqrt[2]{8} = 4

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Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

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you replace t1 from the first equation in the second equation:

(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}

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t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths  intersect are:

r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)

B) You have the following two trajectories of two independent particles:

r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t

From the first equation you have:

t=1+2t\\\\t=-1

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

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