geno3141

24 000 000 000 / 60 000 000

Cancelling multiples of ten in the numerator with corresponding multiples of ten in the denominator:

--->   24 000 / 60  =  2400 / 6  =  <your answer>

r  =  √[x² + y²]   --->   r  =  √[5² + 6²]   --->   √[61] 

θ  =  tan^-1(y/x)   --->   θ  =  tan^-1(6/5)   

(r, θ)  =  ( √(61), tan^-1(6/5) )

u'(t) + u(t) =  k

--->   u'(t)  =  k - u(t)

--->   ∫u'(t)dt  =  ∫[k - u(t)]dt

--->   u(t) + C₁  =  ∫kdt - ∫u(t)dt

--->   u(t) + C₁  =  kt + C₂ - ∫u(t)dt

--->   u(t)  =  kt - ∫u(t)dt + C

It is the side that is opposite the right angle in a right triangle.

Divide the mass of an average blue whale by the mass of an average giraffe.

cos(π/2) = 0   --->   cos²(π/2) = 0   --->   -3cos²(π/2) = 0

A formula for the volume of a cone is:  V  =  (1/3) · π · r² · h

Since you know the values for V and h, can you solve this formula for r?

If so, multiply that answer by 2 to get the diameter; if not, post back and we can help you.

Assuming that the problem is:  3^{n + 2} + 3^{n + 3} - 3^{n + 1}  =  3ⁿ·3² + 3ⁿ·3³ + 3ⁿ·3  =  9· 3ⁿ + 27· 3ⁿ + 3· 3ⁿ

   =  (9 + 27 + 3)· 3ⁿ   =  39· 3ⁿ 

A rational number is a number that can be written as an integer divided by an integer (but, it can't be divided by zero).

Integers are numbers from this set:  { ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }

Since both 11 and 29 are integers, the fraction 11/29 is a rational number, not an irrational number.

To be a perpendicular bisector it must be both perpendicular and a bisector.

To be a bisector, it must pass through the midpoint of the line segment AB.

A formula for finding the midpoint of A(x₁, y₁) and B(x₂, y₂) is  Midpoint  =  ( (x₁ + x₂)/2, (y₁ + y₂)/2 ).

--->   Midpoint  =  ( (2 + 8)/2, (-1 + 3)/2 )  =  (5, 1)

To be perpendicular, the slope of the line must be the negative reciprocal of the original line.

A formula for slope is:  m  =  (y₂ - y₁) / (x₂ - x₁)

--->   Slope  =  (3 - -1) / (8 - 2)  =  4/6  =  2/3

--->  Negative reciprocal of that slope:  m  =  -3/2

Point-slope equation of a line:  y - y₁  =  m(x - x₁)

--->   Point  =  (5, 1)         Slope  =  -3/2

--->   y - 1  =  -3/2(x - 5)

--->   2y - 2  =  -3(x - 5)

--->   2y - 2  =  -3x + 15

--->   2y  =  -3x + 17

--->   3x + 2y  =  17