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The sum of two numbers is 208 One third of the greater number equals the smallest number what are the numbers?
The sum of two numbers is 208.x + y = 208One third of the greater number equals the smallest number.x / 3 = ySubstitute the value for "y" in the first equation:x + (x/3) = 208Multiply everything by 3:3x + x = 624Combine the values of x:4x = 624Divide by 4:x = 156Solve for y:156 + y = 208y = 208 - 156y = 52
What is the smallest positive integer n such that 2n is a perfect square and 3n is a perfect cube?
n=72 satisfies the relation. 2*72 = 12**2, and 3*72 = 6**3. The only question is whether or not that is the smallest integer that will do so. All perfect squares of which 2n is a factor are of form (2x)**2 = 4x**2, with n= 2x**2. Similarly all perfect cubes of which 3n is a factor are of form (3y)**3 = 27y**3 with n = 9y**3. So, we need integers x and y such that 2x**2 = 9y**3. If the integers x and y are the smallest that satisfy the equation, then we have the smallest n. It doesn't work for y = 1, or any other odd number. If y = 2, n = 72. There is a number x =6 which satisfies the relation. Since y is smallest possible, then n=72 is the smallest positive integer that satisfies the relation.
How do you find the period of tangent function?
You find the smallest positive value y such that tan(x + y) = tan(x) for all x.
What is half of a number y?
Y/2
What is the difference of a number y cubed and 4 is less than the product of 8 and the number y?
abs(y^3 - 4) < 8*y
