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3 hr 2s / (12*4 km² )     *   2*12 km²/ 10s =  .3 hr        or       18 minutes 

Neat! 

Correct!

It won't reach 180ft!

2 snowplows can clear a road 12km x 4 m in 3 hours. How long will take for 10 snowplows to clear a road 2km x 12m.

My solution is 18 minutes but in book answer is 9 minutes. Am I wrong or there is error in book?

2 snowplows can clear a road 12km x 4 m in 3 hours. How long will take for 10 snowplows to clear a road 2km x 12m.

 Hello Guest!

\(N=W/t\)

\(N_{sp}=\dfrac{12km\cdot 4m}{2\cdot3h}\cdot \dfrac{1000m}{km}=8000m^2/h\)

\(t=\dfrac{W}{N_{sp}}\)

\(t=\dfrac{2km\cdot 12m}{10\cdot 8000m^2/h}\cdot \dfrac{1000m}{km} \)

\(t=0.3h\cdot\dfrac{60min}{h}=\color{blue}\ 18min\)

10 snowplows clear a road of 2km x 12m in 18min.

You're right.

  !

You are right answer is 18 I also got 18

In first case area is 12000*4=48000m

2 person clear road at 3 hour so one person can do at 2*3 = 6 hour 

Than 10 person can do this same work at 6/10= .6hour =36 minutes

In second case area is 2000*12=24000

So by logic time to do this work is 18 min

50mi - 60mi/h*0.5h - 35mi/h*0.5h = 2.5mi              30min = 0.5h

2.5mi : 0.5h = 5mi/h

Since they are both on the unit circle, a and b differ only in angle.  Without loss of generality we can set the angle of b to be zero, so that b = 1.

Then \(|\frac{a-b}{1-\bar{a} b}|=|\frac{a-1}{1-\bar{a}}|\)  

If we let  \(a=e^{i\theta}\)  then \(|\frac{a-1}{1-\bar{a}}|=|\frac{e^{i\theta}-1}{1-e^{-i\theta}}|=|e^{i\theta}|=1\)

So, as long as \(\theta \ne 0\)  the ratio is 1

For his art project, Julian wanted to make a pixel art by completely covering the 2-feet-by-3-feet poster board with colored stickers that measure 1.5-inches-by-1.5-inches without any overlap.How many stickers would Julian need?

Hello Potatobird!

\(2ft\cdot 3ft\cdot \frac{12^2\cdot inch^2}{ ft^2}:(1.5^2\cdot inch^2)=\color{blue}384\)

Julian needs 384 stickers.

  !

315m  +  131

When m = 3, [315 * 3 + 131] ==1,076 - Smallest 4-digit value of N

idk,

but if  a=1 and b=-1 than it would be     2/2 = 1

I suspect that is the biggest but I do not really know.  I am just guessing.

The answer is A. :)

sqrt (45)  = 3sqrt (5)

sqrt  (360) / sqrt (2)  =  sqrt(360/2)  = sqrt (180) =  sqrt (36 * 5)  =  6sqrt (5)

Combining  all of these    =      3sqrt (5)  +2sqrt (5)   + 6sqrt (5)  =  11sqrt(5) =  sqrt ( 121 * 5)  =

sqrt (605) 

N  =  605

The percents  of the  mixture  don't matter.......the same mixture percents will  be  used  no matter  what  their cost

If P  was  the price  before the increases

After the increases  the price  is   P (1.2)(1.25)   = 1.5P

So   the  price  has  increased   by 50%

N is a four-digit positive integer. Dividing N by 9 , the remainder is 5. Dividing N by 7, the remainder is 5. Dividing N by 5, the remainder is 1. What is the smallest possible value of  N?

\(1000 \le N \le9999\)

All the pronumerals I use here are positive integers.

N=9k+5

N=7m+5

so

N=63T+5

(N-5)/63=T

\((1000-5)/63=15.7\\ (9999-5)/63=158.6\\\)

So T must be between 16 and 158    

N=5g+1

So

the last digit of N must be 1 or 6

N=63T+5

N - 5=63T

***1-5=***6        ***6-5=***1

 So the last digit of 63T must also be 6 or 1         

3 times what single digit ends in 6 or 1?     3*2=6,  3*7=21

So T must end in a 2 or a 7

So T is a number between 16 and 158 that ends in 2 or 7. 

We want the smallest one.

Try T=22       

 Edit:

Silly me, T=17 is the smallest that fits these restrictions and it will give N=63*17+5=1076. 

Just as our guest has already determined with his/her computer program.

N=63*22+5 = 1391

does this really work?

check:

1391 does equal 1 mod 5

1391 does equal 5 mod 9

1391 does equal 5 mod 7

So I believe the answer to be  N=1391

Let the time Jennifer walks =  J

4 hrs * 12mph   = 48 miles

The total distance  she travels =  48 + 2J

So  the total hrs  she travels =  4 + J

The time it took   Thomas to reach the bike  is     48/ 4   = 12 hours

Let his time on the  bike =  T

So  the   distance  he travels  is    48 +  12T

And the  time he travels =  12 + T

The time they  travel is equal    and  so is the  distance  ....so...

4 + J  =  12  + T          (1)

48 + 12T  =  48 + 2J      ⇒     12 T  = 2J    ⇒   6T   = J      (2)

Sub (2)  into (1)

4 + 6T =   12 + T

5T  = 8

T  =  8/5   =   1. 6 hrs

The total time to catch  up to Jennofer  =      12 + 1.6  =  13.6  hrs

Check

Distance  Jennifer travels =   48 + J  =   48 + 2*6(1.6)  = 67.2 miles

Distance  Thomas  travels  =  48 + 12 (1.6)  =   67.2 miles

OOPS....small error....now corrected  !!!

The sum  = 48 ....   so.....

P + Q  =   44

P + R  =   38

P + S =    32

Q + S  =   26

Q + R   =  32

R + S   =  20

Subtract the first two  equations ⇒

Q - R  =  6

Q + R  =  32       add these

2Q =  38

Q =  19

S  =  7

P  =  25

R  =   13

P +   Q  +  R  +  S   =      25  +  19 +  13   +  7    =      64

Very nice! thanks!

We can convert complex numbers x + yi to the point (x,y).  This gives us the answer ab = 18.