What is the number of elements in a union b when a is a subset of b?
The number of elements in a union b is equal to the number of elements in b.
What is the value of cos^2(45) - sin^2(15)?
The value of cos^2(45) - sin^2(15) is (sqrt(3)-1)/(2sqrt(2)).
What is the sum of the series 3+5+7+...+n?
The sum of the series 3+5+7+...+n is n(2+n)/2.
What is the value of n if 12 choose n is equal to 8 choose n?
The value of n is 4.
What is the total number of terms in the expansion of (x+a)^47 - (x-a)^47?
The total number of terms in the expansion of (x+a)^47 - (x-a)^47 is 24.
What is the equation of the line that is perpendicular to y=3x-1 and passes through (1,2)?
The equation of the line that is perpendicular to y=3x-1 and passes through (1,2) is x+3y-7=0.
What is the eccentricity of the ellipse x^2/36 + y^2/16 = 1?
The eccentricity of the ellipse x^2/36 + y^2/16 = 1 is sqrt(5).
What is the perpendicular distance of the point (6,7,8) from the xy plane?
The perpendicular distance of the point (6,7,8) from the xy plane is 7.
What is the limit of (1-cos(4θ))/(1-cos(6θ)) as θ approaches 0?
, The limit of (1-cos(4θ))/(1-cos(6θ)) as θ approaches 0 is 2/3.
1. What is the value of 3(1-2sin23θ) / (1+2sin22θ) * (1-1+2sin23θ)?
The value is sin22θ / sin23θ.
2. What is the arithmetic mean if the coefficient of variation is 60 and the standard deviation is 24?
The arithmetic mean is 40.
3. When is f(x1) ≠ f(x2) for f(x) = x4?
f(x1) ≠ f(x2) when x14 ≠ x24.
4. Is there a defined range for secant inverse x?
No, the range of secant inverse x is not defined.
5. If x + tan-1y = 4π/5, what is cot-1x + cot-1y?
cot-1x + cot-1y = 90°.
6. What is g(f(x)) if f(x) = x1/3 and g(x) = 8x3?
g(f(x)) = 8x.
7. What are the values of x and y for the equation 2+y=5x, 6+0=y and 1+2x=8?
x=3 and y=3.
8. Is the binary operation * on R-{-1} defined by a*b=a+b+1 associative?
No, the binary operation * on R-{-1} defined by a*b=a+b+1 is not associative.
The number of elements in a union b is equal to the number of elements in b.
What is the value of cos^2(45) - sin^2(15)?
The value of cos^2(45) - sin^2(15) is (sqrt(3)-1)/(2sqrt(2)).
What is the sum of the series 3+5+7+...+n?
The sum of the series 3+5+7+...+n is n(2+n)/2.
What is the value of n if 12 choose n is equal to 8 choose n?
The value of n is 4.
What is the total number of terms in the expansion of (x+a)^47 - (x-a)^47?
The total number of terms in the expansion of (x+a)^47 - (x-a)^47 is 24.
What is the equation of the line that is perpendicular to y=3x-1 and passes through (1,2)?
The equation of the line that is perpendicular to y=3x-1 and passes through (1,2) is x+3y-7=0.
What is the eccentricity of the ellipse x^2/36 + y^2/16 = 1?
The eccentricity of the ellipse x^2/36 + y^2/16 = 1 is sqrt(5).
What is the perpendicular distance of the point (6,7,8) from the xy plane?
The perpendicular distance of the point (6,7,8) from the xy plane is 7.
What is the limit of (1-cos(4θ))/(1-cos(6θ)) as θ approaches 0?
, The limit of (1-cos(4θ))/(1-cos(6θ)) as θ approaches 0 is 2/3.
1. What is the value of 3(1-2sin23θ) / (1+2sin22θ) * (1-1+2sin23θ)?
The value is sin22θ / sin23θ.
2. What is the arithmetic mean if the coefficient of variation is 60 and the standard deviation is 24?
The arithmetic mean is 40.
3. When is f(x1) ≠ f(x2) for f(x) = x4?
f(x1) ≠ f(x2) when x14 ≠ x24.
4. Is there a defined range for secant inverse x?
No, the range of secant inverse x is not defined.
5. If x + tan-1y = 4π/5, what is cot-1x + cot-1y?
cot-1x + cot-1y = 90°.
6. What is g(f(x)) if f(x) = x1/3 and g(x) = 8x3?
g(f(x)) = 8x.
7. What are the values of x and y for the equation 2+y=5x, 6+0=y and 1+2x=8?
x=3 and y=3.
8. Is the binary operation * on R-{-1} defined by a*b=a+b+1 associative?
No, the binary operation * on R-{-1} defined by a*b=a+b+1 is not associative.
