To prove: A2 + B2 + C2 + 200 = 12a + 16C + 20b is what triangle? (A2 refers to the square of a, similarly to B2, C2)

To prove: A2 + B2 + C2 + 200 = 12a + 16C + 20b is what triangle? (A2 refers to the square of a, similarly to B2, C2)

A2 + B2 + C2 + 200 = 12a + 16b + 20c a2-12a + 36 + b2-16b + 64 + c2-20c + 100 = 0 (a-6) 2 + (B-8) 2 + (C-10) 2 = 0 a = 6 B = 8 c = 10 A2 + B2 = C2 right triangle

Let F 1 and F 2 be the left and right focal points of the hyperbola respectively. If there is a point a on the hyperbola, let ∠ f 1af 2 = 90 & # 186;, and | AF 1 | = 3 | AF 2 |, calculate the eccentricity

It is defined by hyperbola as: pf1-pf2 = 2A, Pf1 = 3 PF2, PF2 = 2A,
∴a＝｜PF2｜.
∵∠F1PF2＝90°,∴｜PF1｜^2＋｜PF2｜^2＝｜F1F2｜^2＝4c^2,∴10｜PF2｜^2＝4c^2,
∴c＝√10｜PF2｜/2.
∴e＝c/a＝（√10｜PF2｜/2）/｜PF2｜＝√10/2.

|2-radical 5 | + radical 5 × radical 20

|2-radical 5 | + radical 5 × radical 20
=Root 5-2 + root 5 × 2 root 5 root 5 > 2
=Root 5-2 + 10
=Root 5 + 8

How to do the x power differential of y = (1 + SiNx)

Logarithm on both sides: lgY = x * LG (1 + SiNx)
Then take the differential on both sides: 1 / YDY = [LG (1 + SiNx) + X * cosx / (1 + SiNx)] DX
∴dy=（1+sinx）^x*【lg（1+sinx）+x*cosx/（1+sinx）】dx

Set up equation to solve word problem: a number is 6.9 more than 3.5, find the number

Let xx-3.5 = 6.9
x=6.9+3.5
x=10.4

How to calculate that 10 1 is equal to 24 by addition, subtraction, multiplication and division

Add, subtract, multiply and divide, and you will be God and man
There is this (log10 + log10 + log10 + 1)! = 4! = 24
That's factorial

Given the first-order function Y1 = 1 / 3x + 4 / 3, y2 = 1 / 2x-7 / 4, and 2Y2 ≤ 5 / 2 ≤ Y1, the value range of X is obtained

y1=1/3x+4/3
y2=1/2x-7/4
2y2≤5/2≤y1
X-7 / 2 ≤ 5 / 2 and 1 / 3x + 4 / 3 ≥ 5 / 2
X ≤ 6 and X ≥ 7 / 2
So the value range of X is [7 / 2,6]

There is a circular fountain in front of the gate of a park, with a circumference of 42 meters. What is the radius and area of the circular fountain
((keep integer)))
There must be a formula

R = 42 / 2 π = 21 / π M
S = π R ^ 2 = π * (21 / π) ^ 2 = 441 / π M2

11, 12, 13 and 14 are 24 points

11-(13-12)+14=24

Mathematical method of curvature radius at any point of curve
RT

R = ((1 + y '^ 2) ^ 3 / 2) / y' ` note: y 'is the first derivative, y' ` is the second derivative, and ^ is the sign of power