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WARRIOR [948]
3 years ago
13

2) Bobby makes model train sets. Each set requires 1,998 pieces of track. At the Hobby store, there are 37 pieces in each box. a

.How many boxes does Bobby have to buy to make a model train set? Show all your work.
Mathematics
1 answer:
eimsori [14]3 years ago
5 0

Answer:

You never gave the speed of the blue train. The path to collision is equal to 1½ circles. 1.5 x 210 meters = 315 meters I'm going to arbitrarily guess the speed of the blue train is 15 meters per minute. They are therefore approaching each other at a combined rate of 35 meters per minute. 315 / 35 = 9 minutes Answer: 9 minutes

Step-by-step explanation:

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The diameter of a wheel of a car is 0.75 m. if the car travels at an average speed of 14 m/s, find the
raketka [301]

Step-by-step explanation:

Circumference of wheel = πd = 0.75πm.

How far the car travels per minute

= 60s * (14m/s) = 840m.

Hence number of revolutions per minute

= 840m / 0.75πm

= 356.507....

= 357. (nearest whole number)

6 0
3 years ago
Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360
Natasha2012 [34]

\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]

\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

   \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]

5 0
3 years ago
Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.
-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

4^n+17 is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so 4^k+17 is divisible by 3

and we check what happens for k+1

4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17

3\cdot 4^k is divisible by 3 and

4^k+17 is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that 4^n+17 is divisible by 3 for all positive integers n.

Thanks

4 0
3 years ago
The current rates for an 80/20 mortgage are 4.25% for the first mortgage and
LUCKY_DIMON [66]

Answer:

5.35%

Step-by-step explanation:

8 0
3 years ago
Write a real-world
ArbitrLikvidat [17]

Answer:

<u>Problem:</u>  Jamie was driving for 24 miles in the first hour and 36 miles is the second hour.  But, she stopped at a gas station 1/4 of the total drive.  Find how far the gas station is from her start.

<u>Answer:</u>  

24 + 36 = 50

50 * 1/4 = 50/4

50/4 = 12.5

<u>Explanation:</u>  The gas station is 12.5 miles from her start to a 50 mile journey.  The gas station was 1/4 of the total drive which was 50 miles.  1/4 of 50 is 12.5

4 0
3 years ago
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