On Friday a bowling alley made $842.72 from Lane rentals in $412.38 from the concession stand.

TiliK225 [7]

The thickness of a brand new US penny that hasn't been
worn down is 1.52 millimeters.

If you have a million pennies, there are many ways to arrange them.
You can pile them all in one pile, or shovel them into many piles, or
stack them up in any number of stacks up to a half-million stacks
with two pennies in each stack, or try somehow to stack them all up
in one stack that's a million thicknesses high.

Any stack with 'n' pennies in the stack is 1.52n millimeters high.

If you somehow succeed in stacking all million of them in one stack,
then the height of that stack would be . . .

   (1,000,000) x (1.52 mm) = 1,520,000 millimeters
   152,000 centimeters
   1,520 meters
   1.52 kilometers

(about 59,842.5 inches
4,986.9 feet
   1,662.3 yards
   7.56 furlongs
0.944 mile
      all rounded)

3 0

3 years ago

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago

Patrick has a $1000 bond with a 6% coupon. Howmuch interest will Patrick receive for this bond every 6 months?

alexandr1967 [171]

Its either 300 or 12

3 0

3 years ago

I need to know this answer

Free_Kalibri [48]

Answer:

r = 7

Step-by-step explanation:

Given

r + 15 = 4r - 6 ( subtract 4r from both sides )

- 3r + 15 = - 6 ( subtract 15 from both sides )

- 3r = - 21 ( divide both sides by - 3 )

r = 7

5 0

3 years ago

Read 2 more answers

How many roots, real or complex, does the polynomial 7 + 5x4 – 3x2 have in all?

antiseptic1488 [7]

Answer:

Step-by-step explanation:

it has 4 roots as its degree is 4.

5 0

3 years ago

Read 2 more answers