Cut a cone with a height of 5cm along the height, and the surface area of two objects is increased by 10cm2 compared with that of the original cone I read the answer on the Internet, 10 / 2 * 2 / 5 find out the radius, why is the radius, should be the diameter 10/2*2/5=2cm One third * π * (2 / 1) square * 5 =Five thirds π

Cut a cone with a height of 5cm along the height, and the surface area of two objects is increased by 10cm2 compared with that of the original cone I read the answer on the Internet, 10 / 2 * 2 / 5 find out the radius, why is the radius, should be the diameter 10/2*2/5=2cm One third * π * (2 / 1) square * 5 =Five thirds π

Analysis: the increased surface area is the area of two isosceles triangles with the cone bottom diameter as the bottom and the cone height as the height. (bottom diameter × height △ 2) × 2 = 10 (2R × h △ 2) × 2 = 102R × 5 △ 2 = 52r = 2R = 1cm, cone volume = 3.14 × R & # 178; × h △ 3 = 3.14 × 1 & # 178; × 5 △ 3 ≈ 5.2cm & # 17

It is known that the circumference of the bottom surface of the cylinder is 18.84 cm and the height is 5 cm

(1) 18.84 △ 3.14 △ 2 = 3 (CM); 18.84 × 5 + 3.14 × 32 × 2, = 94.2 + 3.14 × 18, = 94.2 + 56.52, = 150.72 (square cm); (2) 3.14 × 32 × 5, = 3.14 × 45, = 141.3 (cubic cm); a: the surface area of the cylinder is 150.72 square cm, and the volume is 141.3 cubic cm

A conic wood block with a radius of 5cm on the ground is cut in half vertically along the height from the apex, and the indicated surface area is increased by 180cm2. What is the volume of each conic

[interpretation]
The open surface of a cone is a triangle with the diameter of the bottom of the cone as the bottom and the height of the cone as the height. The increased area is twice the area of the triangle. The area of a triangle is 180 △ 2 = 90 (square centimeter)
The diameter D and the area s of the cone bottom can be obtained from the radius r of the cone bottom
D = 5 × 2 = 10 (CM)
S = RR π = 5 × 5 × 3.14 = 78.5 (cm2)
Finding the height h of a cone
H = 90 △ 10 × 2 = 18 (CM)
Finding the volume of cone V
V = SH / 3 = 78.5 × 18 △ 3 = 471 (cm3)
A: the original volume of the cone is 471 cubic centimeters

Given that the quadratic function f (x) satisfies the condition f (0) = 0 and f (x + 1) = f (x) + X + 1, G (x) = 2F (- x) + X, find the expression of F (g (x)) of F (x)
Please be more detailed

Sorry, I didn't copy it wrong

It is known that f (x) is a quadratic function, which satisfies the expression of finding f (x) with 2F (2x) = 12x ^ 2 + 6x + 1
It is also known that if f (x-1) = x ^ 2 + 3x + 1, then the analytic expression of F (x) is?

2F (2x) = 12x ^ 2 + 6x + 1, then f (2x) = 6x ^ 2 + 3x + 1 / 2, let 2x = t, then x = t / 2, then f (T) = 6 * (T / 2) 2 + 3 * t / 2 + 1F (t) = 3 / 2t2 + 3 / 2T + 1 / 2F (x) = 3 / 2x2 + 3 / 2x + 1 / 2; similarly, let X-1 = t, then x = t + 1F (T) = (T + 1) 2 + 3 (T + 1) + 1F (t) = T2 + 5T + 5F (x) = x2 + 5x = 5

If the symmetry axis of quadratic function y = 4x ^ 2-mx + 5 is x = - 2, then when x = 1, the value of Y?
This is how I get it. First I get b = 16 by - B / 2A = - 2, and then I get 4-16 + 5 = - 7
But the answer is 25. What's wrong with me?
The axis of symmetry is not - M / 8. How can you be m / 8

You got the wrong symbol, B = - 16

It is known that the symmetry axis of the image of the quadratic function y = MX + 4x + 2 is a straight line x = 1,

If the axis of symmetry is x = 4 / (- 2m) = - 2 / M = 1, then M = - 2
So

Let the quadratic function f bracket x satisfy that f bracket x + 1 + F bracket X-1 is equal to the square of two x-4x

Let f (x) = ax & # 178; + BX + C, then f (x + 1) + F (x-1) = a [(x + 1) & # 178; + (x-1) & # 178;] + B [(x + 1) + (x-1)] + 2C = 2x & # 178; - 4x;
→ 2ax²+2bx+(2a+2c)=2x²-4x；
Comparing the two ends of the equation, we can see that 2A = 2, 2b = - 4, 2A + 2C = 0; the solution is a = 1, B = - 2, C = - 1;
∴ f(x)=x²-2x-1；

Finding a monotone increasing interval of function f (x) = (cosx) ^ 2-2 (COS (x / 2)) ^ 2

(x) = (cosx) ^ 2-2 (COS (x / 2)) ^ 2 = (cosx) ^ 2 - (1 + cosx) = (cosx) ^ 2-cosx-1 use the substitution, then the element belongs to [- 1,1], and then reverse solve X

What is the increasing interval of the function f (x) = 2x + cosx?

f(x)=2x+cosx
f'(x)=2-sinx
Since SiNx is less than or equal to 1 and f '(x) is greater than zero, it is constant on R, and the increasing interval is r