The circumference of the bottom surface of a cone is 12.56 cm, the height is 9 cm, and the surface area of a cone is (),

The circumference of the bottom surface of a cone is 12.56 cm, the height is 9 cm, and the surface area of a cone is (),

The circumference of the bottom surface of the cone is 12.56 cm = 2 × 3.14 × R, so the radius of the bottom surface is r = 2
Because the height is 9 cm, let the length of generatrix be l, Pythagorean theorem: L & # 178; = 9 & # 178; + 2 & # 178;, l = √ 85
Surface area of cone = bottom area + side area = 3.14 × 2 & # 178; + 3.14 ×√ 85 & # 178; × (12.56 △ 2 × 3.14 ×√ 85) = 22.439 square centimeter

If 3A ^ m + 1b ^ 3 and 4A ^ 2B ^ n-1 are similar, then M-N=
How to write it

In the same category, it shows that the times of two formulas A and B are equal respectively
That is: M + 1 = 2,3 = n-1
m=1,n=4
m-n=1-4=-3

A triangle with an area of 20 square meters and a ratio of bottom to height of 5:2, what is its bottom and height

1： Let the bottom be x and the height be y
2： The equation 1 0.5xy = 20 is established
2 X/Y=5/2
3： The bottom (x) of the equation is 10
The height (y) is 4

Given that a is prime, B is odd, and A2 + B = 2001, then a + B=______ ．

∵ A2 + B = 2001, ∵ a, B must be an odd number, an even number, ∵ B is an odd number, ∵ A is an even number, ∵ A is a prime number, ∵ a = 2, ∵ B = 2001-4 = 1997, ∵ a + B = 2 + 1997 = 1999

The difference between the two right sides of a right triangle is 3 cm, and the area is 9 cm ^ 2

Because the difference between the two right angles is 3, and the area is 9 square centimeters
So the product of two right angles is 18
If the shorter right angle side is set to x, then
x*(x+3)=18
So x = 3
Longer right angle side = 6

The diameter of circle 0 is ab = 4, point P is a point on the extension line, tangent point is C, connecting AC. if point P moves on AB, the angle CPA is flat
The diameter of circle 0 is ab = 4, and point P is a point on the extension line. The tangent line of circle O is made through P, and the tangent point is C, which connects AC. if point P moves on AB, the bisector of angle CPA intersects AC with point m, and the size of angle CMP changes. Explain the reason
The diameter of circle 0 is ab = 4, and point P is a point on the extension line. The tangent line of circle O is made through P, and the tangent point is C, which connects AC. if point P moves on the extension line of AB, the bisector of angle CPA intersects AC with point m, and whether the size of angle CMP changes, explain the reason

The angle CMP is always 45 degrees
The reasons are as follows.
According to the principle that the sum of external angles is equal to the sum of two non adjacent internal angles, angle CMP = angle cap + angle MPa (3)
Triangle ABC is isosceles triangle, so angle cap = angle MCB (5)
Since MP is the bisector of angle CPA, angle MPa = angle MPC (6)
Let's look at the triangle MCP. In this triangle, angle CMP = 180 angle MCP angle MPC (1)
And the angle MCP = angle BCP + angle MCB will be (2), because it is tangent, so the angle BCP = 90 degrees
Substituting (2) into (1), we can get:
Angular CMP = 180 - (90 + angular MCB) - angular MPC = 90 angular MCB angular MPC (4)
Because the former (3) is substituted into (4)
Angle cap + angle MPa = 90 angle MCB angle MPC (7)
Because (5) and (6) angle cap = angle MCB (5) angle MPa = angle MPC (6), substitute (7)
It can be concluded that angular cap + angular MPa = 90 angular cap angular MPa
Finishing, 2 (angle cap + angle MPa) = 90
Angle cap + angle MPa = 45, then according to formula (3), namely angle CMP = 45, is constant, so it will not change
：）

If AB = a, C is any point of AB and Mn is the midpoint of AC and BC respectively, then Mn=
Point B divides the line segment AC into two equal lines, and point B is called the line segment AC? At this time, ab = AC = BC, ab = BC = AC

If AB = a, C is any point of AB and Mn is the midpoint of AC and BC respectively, then Mn = 1 / 2A
Point B divides line AC into two equal lines, and point B is called the midpoint of line AC,
In this case, ab = BC, AC = 2BC, ab = BC = 1 / 2Ac

As shown in the figure, the known point a is a trisection point on the semicircle with Mn as the diameter, point B is the midpoint of an, and point P is the point on the radius on. If the radius of ⊙ o is l, then the minimum value of AP + BP is ()
A. 2B. 2C. 3D. 52

Make a symmetric point a 'of point a about Mn, connect a' B, intersect Mn at point P, then PA + Pb is the smallest, connect OA ', AA', ob, ∵ point a and a 'are symmetric about Mn, point a is a trisection point on semicircle, ∵ a' on = ∠ AON = 60 °, PA = PA ', ∵ point B is the midpoint of arc an ^, ∵ Bon = 30 °, and ∵ a' ob = ∠ a 'on + ∠ Bon = 90 °, and ∵ OA = OA' = 1, ∵ a 'B = 2. ∵ pa + Pb = PA' + P B = a ′ B = 2

If the solution of the equation (2x + a) / (x-1) = 1 of X is positive, then the value range of a is
A.a>-1
B. A > - 1 and a is not equal to 0
C.a>-1
D.a

2x+a=x-1
X = - A-1 is a positive number
x>0
-a-1>0
a

If we know that a hyperbola passes through points a (- 2,4) and B (4,4), one of its focuses is F1 (1,0), we can find the trajectory equation of its other focus F2

The hyperbola crosses points a (- 2, 4) and B (4, 4, 4) and B (4, 4, 4), its focus is F1 (1, 0), 124;af1 ?af1 ?af1 AF1 124124124124124124124 | = | BF2 |, the locus of focus F2 is the middle perpendicular of line AB, and its equation is x = 1 (Y ≠ 0 or 8), (2) when 5 - | af2 | = | BF2 | - 5, That is | af2 | + | BF2 | = 10 ＞ 6, the trajectory of focus F2 is an ellipse with a and B as the focus and the major axis of 10, and its center is (1,4), a = 5, C = 3, B2 = 25-9 = 16, and its equation is (x-1) 225 + (y-4) 216 = 1 (Y ≠ 0). To sum up, the trajectory equation of another focus F2 is: x = 1 (Y ≠ 0 or 8) or (x-1) 225 + (y-4) 216 = 1 (Y ≠ 0)