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If I am guessing correct, the density is the amount of liters divided by the volume. 

So the volume is $7\cdot{4}\cdot{10} = 280$

The density $10690.4\div{280}=\boxed{38.18}$

The first step is to find out how much fabric she has.

We can convert to decimal.

3 1/4 = 3.25

1 1/2 = 1.5

3.25 + 1.5 = 4.75

5 1/2 = 5.5

5.5 - 4.75 = 0.75

She still needs 3/4 yards of fabric. 

I hope this helped.

 3600 * 24 * 365 * (75 - 14 )   =  $ 1,923,696,000

10)The two bases of a right conical frustum have radii 12 and 9. The two bases are 4 units apart. Let the volume of the frustum be V cubic units and the total surface area of the frustum be A square units. Find V + A.

The height  =  4

The volume, V,  is given by

(1/3) * pi * height  ( [radius base 1]^2 +  product of the base radii +[ radius base 2]^2 )  =

pi / 3  *  4  * ( 12^2 +  12*9 + 9^2)

pi / 3 * 4 * ( 144 + 108 + 81 )

pi / 3 * 4  * ( 333)

pi * 4 * 111

444 pi

The surface area A, is given  by :

pi ( sum of radii) * √ [ (difference of radii)^2 + height^2 ] + pi (radius 1)^2 + pi (radius 2)^2

pi ( 21) √ [ 3^2 + 4^2 ] + pi  [ 144 + 81 ]

pi [  21 * 5 + 225 ]

pi [ 105 + 225 ] 

pi [ 330]

330 pi

So

V + A  =

[444 +330 ] pi  =

774 pi

Boy, that is some density of "wood board". By the way, it is equivalent to a density of 1 drop of water in a small pond the size of about 75 Olympic swimming pools!!!.

9)A 288 degree circular sector with radius 15 is rolled to form a cone. Find the height of the cone.

The perimeter of the base of the cone will be :

2 * pi * 15   (288/360)  =  

pi * 30/ 360 * 288

pi *  288/12  = 

24 pi

So....the radius of the cone is given by

24pi  = 2pi * r         divide both sides by 2 pi

12 =  r

The slant height will be the original radius of the sector  = 15

And this forms the hypotenuse  of  a   9 - 12 - 15     right triangle

And the radius forms one of the legs  = 12

So....the height forms the other leg  =  9

2)The radius of a cylinder is 5/6 its height. Find the total surface area of the cylinder if its volume is 150pi.

We have 

150 pi  =  pi [ 5/6 h ] ^2 * h         divide out pi

150  =  (25/36) h^3            multiply both sides by 36/25

150 (36/25)  = h^3

216  = h^3

6  =  h

So...r  = (5/6)h  = (5/6)(6)  = 5

So....the surface area  is

2pi * r  [ r + h ]  =

2pi * (5) [ 5 + 6 ] =

2pi * 55

110 pi  units^2

Thanks for the primer, guest.....I was not familiar with this technique...!!!!

Sorry, Julius....  I meant to say that  x  = 1   is the only critical number  !!!

Correct, Julius  !!!!

For all x > 5,   x - 5 will be positive, thus increasing.....

Also  [ don't worry about how I arrived at this ] ....if  x - 5  is the derivative, then  (1/2)x^2 - 5x + some constant   is the parent function....as shown here, no matter the added constant, this function always increases when x > 5

https://www.desmos.com/calculator/mssfiffnb0

x =1 is a critical number, but how many are there is the question.

Correct

f'(x)  = 7 (x - 1)^6

Set to 0

7 ( x - 1)^6  =  0

(x - 1)^6  = 0

So....x  = 1 is a critical number

Volume of a bucket=10^2 x pi x 25 =~7,850 in^3. You round this next power of 10 =8 x 10^3

Volume of the warehouse =300 x 150 x 10 =450,000 ft^3. First, you convert this to cubic inches:

450,000 x 12^3 =~778,000,000 in^3, which you will round up to next whole integer =800,000,000 =

8 x 10^8. Now, you will divide this by the volume of 1 bucket:

8*10^8 / 8*10^3 - and this would be the Fermi Process of estimatation.

Since the crates are 90 kg measured to the NEAREST 10kg ...I believe to be safe you have to assume that ALL of them can weigh

 94.999...  each.

Forgot the cable part....edited:

Since cable is rated at 6400 to two significant digits......it MIGHT only support   6350 kg   (or as much as 6449.99)

For safety you will have to assume the crates are 94.99 kg each and the cable will only support 6350 kg

Then    6350/94.99 = 66.85 ~~ 66 crates max

Good job Cphill

If x1 > x2     AND  f(x1) > f(x2)     this describes a function with a  POSITIVE slope  (  f' (x)  )

So f'(x) > 0

Assumig you started the second you were born AND 365.25 days/year:

75 x 365.25 x 24 x 3600 = $2,366,820,000.00

Assuming every year is 365 days,

60*60=3600       Seconds to minutes equals an hour

3600*24=86400         Hour to 24 equals day

86400*365=31536000       Day times year equals how much money you make in a year

75 years x 365 days x 24 hours x 60 minutes x 60 seconds =$2,365,200,000

If  f'(x)  = 0  for all x, we just have a horizontal line....so....f(x)  will be the same for all values of x....so...

d) f(x1) = f(x2) for every x1 < x2 

If f'(x) > 0  for all x, then the function must be always increasing from left to right

Thus...if  x1 > x2

Then f(x1) > f(x2)

So...

a) f(x1) > f(x2) for every x1 > x2

well if you started from when you were first born you would make about $1,310,400 a year 

you would get $98,280,000 by 75 years old

7)The lateral surface area of a cylinder is 30% of its surface area. What is the ratio between the base radius and the height of the cylinder

Let S be the surface area....then....

S  =   2pi * r  ( r + h)     (1)

Lateral surface area  =   2pi * r * h  = .30S    ⇒  2pi * r  =  .30S / h    (2)

Sub (2)  into (1)

S  =  (.30S/h) (r + h)   ......  divide through by S

1 = (.30/h) (r + h)

h / .30   =  r + h

h / (3/10)  = r + h

(10/3) h = r + h

(7/3) h  = r

r / h  =  7/3

We will have a vertical asymptote

See an example here:  https://www.desmos.com/calculator/38rlm9mnnw

g (x)  = 2x^2 -1

f(x)  = x^3

g(0)  = 2(0)^2 -  1   =  -1

f(0) = (0)^3  =  0

Note...that at  x  = c  =  0......we have the vertical asymptote  x  =  0