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Tcecarenko [31]
3 years ago
11

What is the volume of this cube?

Mathematics
2 answers:
Kitty [74]3 years ago
5 0

A cube is a three dimensional figure with all edges equal.

So it length = width = height

The formula to find the volume of a cube is

V = s³.

Here s represents the length of the cube.

In the given question we are given s = 2.1 cm

So the volume of the cube shall be

V = 2.1³

V = 2.1 × 2.1 × 2.1

V = 9.261 cm³

Now this can be rounded off to two decimals as 9.26 cm³

The volume of the required cube is 9.261 cm³ 0r 9.26 cm³


Kruka [31]3 years ago
5 0
The answer is 9.261the answer is 9.261
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In checkers, pieces move diagonally. The board shows a move with two consecutive jumps. Write a composition of translations for
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3 years ago
Find the area of the region bounded by the parabola y = 2x^2, the tangent line to this parabola at (4, 32), and the x-axis.
Anna [14]
I have a solution here that has a slight change in given where instead of <span>(4, 32), it is (3, 18). However, since the solution has provided explanations on each process, step-by-step, I believe that by thoroughly analyzing it, you might just answer this problem on your own!
</span>

f(x) = 2x² ← this is the parabola 

f(3) = 2 * 9 = 18 → the parabola passes through A (3 ; 18), so its tangent line too 


f'(x) = 4x ← this is the derivative 

…and the derivative is the slope of the tangent line to the curve at x 

f'(3) = 4 * 3 = 12 ← this is the slope of the tangent line to the curve at x = 3 


Equation of the tangent line 

The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept 

You know that the slope of the tangent line is 12. 

The equation of the tangent line becomes: y = 12x + b 

The tangent line passes through A (3 ; 18), so these coordinates must verify the equation of the tangent line. 

y = 12x + b 

b = y - 12x → you substitute x and y by the coordinates of the point A (3 ; 18) 

b = 18 - 36 = - 18 

→ The equation of the tangent line is: y = 12x - 18 


Intersection between the tangent line to the curve and the x-axis: → when y = 0 

y = 12x - 18 → when y = 0 

12x - 18 = 0 

12x = 18 

x = 3/2 

→ Point B (3/2 ; 0) 


Intersection between the vertical line passes through the point A and the x-axis: → when x = 3 

→ Point C (3 ; 0) 

The equation of the vertical line is: x = 3 


Area of the region bounded by the parabola y = 2x², the tangent line to this parabola at (3 ; 18), and the x-axis. 

= (area of the region bounded by the parabola y = 2x² and the x-axis) - (area of the triangle ABC) 

= [∫ (from 0 to 3) of the parabola] - [(xC - xB).(yA - yC)/2] 

= [∫ (from 0 to 3) 2x².dx] - [(xC - xB).(yA - yC)/2] 

= { [(2/3).x³] from 0 to 3 } - { [3 - (3/2)].(18 - 0)/2 } 

= [(2/3) * 3³] - { [(6/2) - (3/2)] * 9 } 

= [(2/3) * 27] - { [(3/2) * 9 } 

= 18 - (27/2) 

= (36/2) - (27/2) 

= 9/2 square unit
6 0
2 years ago
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