 # Mathematical function problems, Xy - the square of three times y is the minimum. It is known that the square of x plus the square of Y is equal to the square of R. R is a constant value,

## Mathematical function problems, Xy - the square of three times y is the minimum. It is known that the square of x plus the square of Y is equal to the square of R. R is a constant value,

X = cost, y = Sint. Use the double angle formula. When the original formula = R ^ 2 [0.5 * sin2t - (1-2cost) / 2 radical 3] = (R ^ 2 / radical 3) * sin (2t - π / 6) - R ^ 2 / 2 radical 3 > = R ^ 2 (- 1 / radical 3-1 / (2 radical 3)) = - radical 3 * (R ^ 2) / 2. And T = - π / 6, the equal sign can be taken, so the minimum value is - radical 3 * (R ^ 2) / 2

two

### If the root sign X-1 + root sign x + y = 0, the value of the x power of Y is

Root X-1 + root x + y = 0
Root X-1 > = 0
Root x + Y > = 0
x-1=0
x+y=0
x=1
y=-1
X power of y = (- 1) power = - 1

### Two unequal positive numbers satisfy a + B = 2, ab = T-1, let s = (a-b) 2, then the function image of s with respect to t is A-ray (excluding endpoint) B-line segment (excluding endpoint) czhixi

S=(a-b)^2=（a+b）^2-4ab=4-4(t-1)=4t+8
Since a and B are positive numbers, T-1 > 0, t > 1
So s > 12 is a ray
Choose a

### Given the primary function y = (1-3k) x + 2k-1 (k is not equal to 1 / 3), try to answer: (1) What is the value of K when the image passes through the origin? (2) What is the value of K when the image intersects the x-axis at the point (3 / 4,0)? (3) What is the value of K, y increases with x? (4) What is the value of K when the function image is parallel to the line y = - 2x-1? (5) What is the value of K when the image intersects with the Y axis and the negative half axis?

(1) When 2k-1 = 0, k = 1 / 2
(2) 0 = (1-3 * k) 3 / 4 + 2k-1: k = - 1
(3) K < 1 / 3 for 1-3k > 0
(4) K = 1 when 1-3k = - 2
(5) K < 1 / 2 for 2k-1 < 0

### Since the 11th Olympic Games, a grand torch relay ceremony has been held at the opening ceremony. The combustible for the torch is butane (chemical formula C4H10), which burns brightly. The correct one in the following description of butane is () A. Butane is composed of two elements, hydrocarbon B. Butane consists of four carbon atoms and ten hydrogen atoms C. The mass ratio of hydrocarbon elements in butane is 12:5 D. The mass of butane is 58G

A. Butane is composed of two elements of hydrocarbon, so the option is correct;
B. 1 butane molecule consists of 4 carbon atoms and 10 hydrogen atoms, so the option is wrong;
C. The mass ratio of hydrocarbon elements in butane is: (12 × 4）：（1 × 10) = 24:5. Therefore, the option is wrong;
D. The relative molecular weight of butane is 58, not 58 G
So choose a