A cuboid wood is 5.2 meters long. If it is sawn 10 cm short, its volume will be reduced by 1000 cubic centimeters. What is the original volume of this wood?

A cuboid wood is 5.2 meters long. If it is sawn 10 cm short, its volume will be reduced by 1000 cubic centimeters. What is the original volume of this wood?

The volume is reduced by 1000 cm ^ 3 because the saw is shortened by 10 cm
So the bottom area is 100cm ^ 2
So the original volume is 520cm * 100cm = 52000cm ^ 3
Because 1dm ^ 3 = 1000cm ^ 3
So the original volume is 52dm ^ 3
DM is decimeter
DM ^ 3 is the cubic decimeter

A cuboid wood is 5.2 meters long. If it is cut 10 cm, its volume will be reduced by 1000 cubic cm,
What is the original volume of wood?

Bottom area = 1000 cubic cm △ 10 cm = 100 square cm = 0.01 square meter
The volume is 5.2x0.01 = 0.052 cubic meters

Sawing a 2-meter-long rectangular timber into two sections increases its surface area by 8 square decimeters. How many cubic meters is the original volume of this rectangular timber?
The correct answer is 0.08 cubic meters,

8 / 2 = 4 square decimeter = 0.04 square meter
0.04 * 2 = 0.08 M3

Use two 8 cm long and 4 cm wide rectangles to make a square. What is the area and perimeter of the square?

Area = 8 × 8 = 64 square centimeter
Perimeter = 4 × 8 = 32 cm
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Known a = 0.00 025 b=0.00…… 01 (there are 1000 zeros in a and 1000 zeros in B)
Known a = 0.00 025 b=0.00…… 01 (there are 1000 zeros in a and 1000 zeros in B) a * b = () a / b = ()

A = 2.5 * [10 ^ (- 1001)], B = 1 * [10 ^ (- 1001)]
∴a*b=2.5*[10^(-2002)]=0.00…… 025 (2001 zeros after decimal point)
a/b=2.5

The known function f (x) = cos & # 178; (x - π / 6) - 1 / 2cos2x
(1) find the minimum positive period and symmetry axis of F (x)
(2) find the range of F (x) in the interval [- π / 12, π / 2]

When f (x) = cos & # 178; (x - π / 6) - 1 / 2cos2x = [1 + Cos2 (x - π / 6)] / 2 - (cos2x) / 2 = 1 / 2 + [cos (2x - π / 3) - cos2x] / 2 = 1 / 2 + sin [(2x - π / 3 + 2x) / 2] sin [(2x - π / 3-2x) / 2] = 1 / 2 - 1 / 2 * sin (2x - π / 6) minimum t = 2 π / 2 = π, symmetry axis is 2x - π / 6 = n π

The circumference of the rectangle is 22 decimeters, and the length is 7 decimeters. How many parts of the length is the width? How many parts of the circumference is the width?

Width is 4, so width is 4 / 7 of length and 2 / 11 of perimeter

How to calculate the circumference, area, surface area and volume of a circle?
Because I haven't touched some mathematical formulas for a long time,

Circumference of circle = 2 π r area of circle = π R ^ 2 surface area of cylinder = upper bottom area + lower bottom area + side area volume of cylinder = bottom area × height

Simplified radical (1 / 3-2 * tan30 + 1)

√(1/3-2*tan30°+1)
=√1/3-2√3/3+1)
=√[(4-2√3)/3]
=√[(3-2√3+1)/3]
=√[(√3-1)²/3]
=(√3-1)√3/3
=1-√3/3

How to find the derivative of implicit function x = ln (XY)

x=ln(xy)
x=lnx+lny
1=1/x+(1/y)*y'
(-1/y)y'=1/x-1
y'=-y/x+y