Bosco

An ordinary 6-sided die has a number on each face from 1 to 6 (each number appears on one face). How many ways can I paint two faces of a die blue, so that the product of the numbers on the painted faces isn't equal to 6?     

   1 6     2 6     3 6     4 6     5 6        Looks like there are 13 ways.     

   1 5     2 5     3 6     4 5     

   1 4     2 4     3 4     

   1 3     2 3     

   1 2     

   _.     

   The circumference of the inner circle is 6666 ft.     

   The distance between the inner circle and the outer circle is 33 ft.     

   By how many feet is the circumference of outer circle greater than the circumference of the inner​ circle?     

   Use StartFraction 22 Over 7 EndFraction227 for piπ.     

   Diameter_{Inner Circle}  =  (6666) • (7 / 22)  =   2121     

   Diameter_{Outer Circle}  =  (2121) + (33 • 2)  =  2187     

   Circumference_{Outer Circle}  =  (2187) • (22 / 7)  =  6873³/₇     

   Circumference_{Inner Circle}  =                                  6666     

   How much Cricum_OC greater than Circum_IC   =    207³/₇     

   _.     

   A circle is inscribed in a square as shown above.     

   A smaller circle is drawn tangent to two sides of the square and externally tangent to the inscribed circle.     

   Find the area of the blue shaded region.     

   A_square  =  10²  =    100.00     

   A_{big circle}  =  π 5²  =  78.54     

   A_{four corners}  =           21.46     

   A_{one corner}  =  21.46 / 4  =  5.365     

   Diagonal_square  =  10 sqrt(2)  =  14.142     

   Diameter_{small circle}  =  (14.142 / 2) – 5.000  =  2.071     

   Radius_{small circle}  =  2.071 / 2  =  1.0355     

   Area_{one corner} (from above)          =  5.365     

   Area_{small circle}  =  π 1.0355²         =  3.369     

   Area of Interest (by subtraction)  =  1.996  round to  2     

   _.     

    How many gallons of liquid in a 5foot by 6foot by 3.5 foot tank     

    Your tank has a capacity of 5.0' x 6,0' x 3.5' = 105.0 cubic feet.     

    Next, you have to know how many gallons are in a cubic foot.     

    This isn't something you know intuitively, you have to look it up.     

    Here you go:  7.48052 gal / ft³ x 105.0 ft³ = 785.5 gal  (rounded)     

   _.     

How do radicals apply to every day life? They seem to be utterly pointless unless your future career choice is in complicated formulas . . .      

You are completely right.  You will probably never need to calculate the square root of umpteen.  But you don't lift weights in the gym because you expect to find a random heavy barbell lying in the street later.  You lift weights so that when you have to carry heavy groceries, move furniture, or pick up your kid, your body is strong enough to do it without breaking.     

Math is a gym for your mind.  Solving a math problem trains your brain how to take a messy, confusing situation, break it down into smaller parts, and find a logical solution.  Every time you practice math, you are building the mental muscles you need to spot scams, make smart financial decisions, and solve real-life problems.  Math doesn't just teach you equations; it teaches you how to think clearly.     

_.     

     The circumference of a circle is 272.68 m.     

     What is the approximate area of the​ circle?     

     Use 3.14 for pi .     

     272.68 m / 3.14 = 86.84 m  (diameter)     

                                  86.84 m / 2 = 43.42 m  (radius)

     Area  =  π r²  =  (3.14) • (43.42 m)²  =  5920 m²  (rounded)     

     Explain how the area of a circle changes when     

     the circumference of a circle changes.     

     When the circumference of a circle gets larger, that     

     means the circle got larger, and, as a consequence,     

     its area got larger.  The opposite happens when the     

     circumference gets smaller.     

   _.     

   Travelling at 22 miles per hour, how much time does it take to drive 1km . . . .     (the rest is gibberish)     

   1 km  =  0.621371 mile     

   0.621371 mi / 22 mi/hr  =  0.028244 hour      

                                         =  1.694648 minutes        

                                         =  1 minute & 42 secconds    

   _.