Area of Region X = 16pi
Area of Region Y = 20pi
Area of Region Z = 13pi
Difference of greatest region and smallest region = 7pi
The probability of landing on any number = (1/ 8)....so.....the number of times the spinner [theoretically] lands on a "6" =
1112 * (1/8 ) = 139 times
Volume of the smaller box = 11 * 10.5 * 13.5 = 1559.25 cm^3
The volume of the larger box will be the volume of the smaller box times the cube of the scale factor = 1559.25 * (5/3)^3 = 7218.75 cm^3
Here you go : https://www.desmos.com/calculator/9gjsaammjd
The solution is given by the coordinates of the orange dot.....
d/dx (sqrt(3) x^5 - 6 x^4 + 54 sqrt(7) x^3 + 2 x^2 - (5 x)/7 + 34.16) =
5 sqrt(3) x^4 - 24 x^3 + 162 sqrt(7) x^2 + 4 x - 5/7
√ [18b^5 ] * √[2ab] =
√[ 36 a b^6] =
6 * l b^3 l*√a we need the absolute value bars in case b might be negative
sin (a + b) = sinacosb + sinbcosa = .86
sin (a - b) = sinacosb - sinbcosa = .34 add these
2sinacosb = 1.20 divide by 2
sinacosb = .60
Sub this into either of the first two equations
.60 + sinbcosa = .86 subtract .60 from each side
sinbcosa = .26
[1 + 2/3] + [ 1 + 1/3] = 3
Here's a graph : https://www.desmos.com/calculator/vemib55ov3
x represents hours and y represents distance in miles
For example......the point (1, 10) is on the graph.....it represents x = 1 hour traveled = y = 10 miles
The side will be 40/√2 cm
So......the area = side^2 = ( 40/√2)^2 = 1600/ 2 = 800 cm^2
