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I'm glad it did :)

Hi guest!

To find the volume of the cylinder, we have to multiply the area of the base by the height.

The base has a radius of 10/2=5. 5^2*pi=25pi. 

Now let's find the height. Even though the cylinder is slanted, the height is still the same. So, the height is 11.

25pi*11= 275pi. Rounding this to the nearest hundredth would be \(\boxed{863.94\text{ ft}^3}\)

I hope this helped you, guest!

Please let me know if I did something wrong!

:)

that doesn't seem to be right... but thanks for helping :)

The area of the trapezoid is 4*sqrt(3).

The probability is 6/25.

10*9 = 90 = number of line segments drawn

Hints:

The shaded region is the area of the triangle subtracted from the area of the circle

Area of circle \(=\varpi r^2\)

where r is the radius and it is half the diameter (The straight line that passes the center in the circle) 

I.e. the right triangle you need to find the other side (hypotenuse)

hi geno3141 thanks for responding. I tried your method but it's telling me that your answer is wrong

Solution: 30

Work: The even numbers that are 2-digit are 10, 12, 14, ..., 98.

The even numbers that are multiples of 3 and even are multiples of 6: 12, 18, 24, ..., 96.

There are 5, 6, 7, ..., 49=45 2-digit even numbers and

2, 3, 4, ..., 16= 15 multiples of 6 that are 2 digit.

45-15=30 2-digit numbers that are multiples of 2, but not 3.

I think the Guest that answered got everything correct except for what I corrected.

Hi guest!

To find the area of the shaded region, we can first find the area of the pizza slice looking thing (sorry I forgot what it's called), and then subtract the triangle from it.

Since we know that the radius is 3, the area of the whole circle is 3^2*pi= 9pi. The pizza slice shape thing is 60 degrees, which is 1/6 of the whole circle (360/60=6). So the pizza slice shape thing is \(9\pi*\frac{1}{6}=\frac{3}{2}\pi\). This is equal to \(\approx 4.712\)

Now, let's find the area of the equilateral triangle (we know it's equilateral since the 2 sides are equal to 3, which means the other 2 angles are also 60 degrees). The formula for the area of an equilateral triangle is \(\frac{\sqrt{3}}{4}a^2\). So, the area of the triangle is \(\approx 3.897\)

Now, we just have to subtract \(4.712\) and \(3.987\).

\(4.712-3.987=0.725\) which is closest to \(\boxed{0.8\text{u}^2}\)

I'm not sure this is the correct answer, so please let me know if it's right!

:)

sin(85^o) x 13  =  12.95

Therefore, an opposite side must be at least this long to porduce a triange.

10 is too short  -- there is no triangle.

Solution: 38

Work: The even numbers that are 2-digit are 10, 12, 14, ..., 98.

The even numbers that are multiples of 3 and even are multiples of 6: 12, 18, 24, ..., 96.

There are 5, 6, 7, ..., 49=44 2-digit even numbers and

2, 3, 4, ..., 16= 15 multiples of 6 that are 2 digit.

44-6=38 2-digit numbers that are multiples of 2, but not 3.

Factor everything:  x² - 8x - 20  =  (x - 10)(x + 2)                                 x² + 3x - 4  =  (x + 4)(x - 1)

                                   x² - x - 6  =  (x - 3)(x + 2)                               x² + 10x + 24  =  (x + 4)(x + 6)

Cancelling the like factors:  (x - 10) / (x - 3)  -  (x - 1) / (x + 6)

Getting the common denominator of  (x - 3)(x + 6)

                         [ (x - 10)(x + 6) /  [ (x - 3)(x + 6) ]    -    [ (x - 1)((x - 3) ] /  [ (x - 3)(x + 6) ] 

                        [ (x - 10)(x + 6) - (x - 1)((x - 3) ]   /   [ (x - 3)(x + 6) ] 

                        [ (x² - 4x - 60) - (x² - 4x + 3) ]   /   [ (x - 3)(x + 6) ] 

                        [ -63 ] / [ (x - 3)(x + 6) ] 

One revolution is 2·pi radians.

5.6 revolutions in 8 seconds is 11.2·pi radians in 8 seconds.

Multiplying to get 60 seconds:  11.2·pi·7.5 radians in 60 seconds  =  84·pi radians per minute.

If you find f'(x)  =  ( -3x² - 8x + 3 ) / ( x² + 3x + 5 )²

set it equal to zero and solve, you find the maximum to be 1/3 and the minimum to be -3.

Answer:  [ -3, 1/3 ]

On the right side:  1 Red + 1 Blue balanced 3 Blue

              --->     1 Red + 1 Blue  =  3 Blue

                                       1 Red  =  2 Blue

                                               6  =  2 Blue

                                               3  =  1 Blue

There are 210 such integers, which begin with 3210 , 4210 , 4310 , 4320 , 4321 , 5210 , 5310 , 5320 , 5321...........and end with  9865 , 9870 , 9871 , 9872 , 9873 , 9874 , 9875 , 9876 , Total =  210

The brother currently has 29 dollars.

nevermind guys, I know the answer, its 15:)

The easiest way to find x is to use this proportion:  3 / x  =  x / (3 + 9)

                                                                                 3 / x  =  x / 12

                                   cross-multiply:                          x²  =  36

                         find the square root:                             x  =  6                               (you can ignore the negative value)

You can use the same idea to find y:                       9 / y  =  y / (9 + 3)         

                                                                                 9 / y  =  y / 12

                                                                                     y²  =  108

                                                                                      y  =  sqrt(108)                  

Replace theta with 66 and r with 12 ...   reduce ( 66/360 · 2 · 12 ) to get the proper fraction.

m  =  +/- 2·sqrt(2)

I was going to explain how I got my answer; I used this:  y  =  x²   --->   y'  =  2x   but I forgot what else I did!