6.6millimeters of rain fall into a rectangular roof. 8meters long and 6 meters wide. The rainwater drains into a cylindrical barrel of diameter 60centimeters. How far does the water level rise in the barrel​

1.12 meters

Step-by-step explanation:

this is the same as filing a box with the same ground area 6.6 millimeters high and then drain it at once into the barrel.

so, the volume of the box filling is (1 m = 1000 mm)

Vb = 8000 × 6000 × 6.6

now, this is then also the volume of the cylinder when filling it up with everything inside the box.

and the general volume of a cylinder is (as for the box) ground area times height.

just here the ground area is a circle with the diameter of 60 cm and therefore the radius of 60/2 = 30 cm.

1 cm = 10 mm => r = 300 mm

the area of a circle is

Ac = pi×r²

=>

Vc = pi×r²×h(eight) = pi×300²×h

and that is also the value of Vb.

Vc = Vb = pi×90000×h

h = Vb / (pi×90000) = 8000×6000×6.6/(pi×90000) =

= 800×6×6.6/(pi×9) = 800×2×2.2/pi = 800×4.4/pi =

= 1120.45 mm = 1.12 m

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)