Remember that multiplication is <em>commutative</em>, which means the order in which we multiply things doesn't matter.
The order of u × q × v × p (which we can abbreviate uqvp) isn't as important as the fact that <em>we're multiplying all four values together</em>. We could just as easily rewrite the expression as pquv, and it'd represent the same value.
To find this value then, we can simply multiply pq and uv - the values we already know - together.
If we start with the expression pq = 23, we can multiply either side by uv (taking advantage of the <em>multiplication property of equality) </em>to get
pquv = 23uv
And since we know that uv = 1/23, we can use the <em>substitution property of equality</em> to replace the uv on the right side with 1/23:
pquv = 23(1/23)
The <em>inverse property of multiplication </em>states that any number multiplied by its inverse (its reciprocal) gives us 1. 23 and 1/23 are reciprocals of each other, so 23(1/23) = 1, which means
pquv = 1
Finally, going back to the second paragraph, we can use the <em>commutative property of multiplication </em>to rearrange the left side of the equation, giving us the solution
uqvp = 1
The area of the blanket is 4.05 sq. meters.
First aquarium dimensions:
Length = 6 m.
Width = 4 m and
Height = 2 meter.
Second aquarium dimensions:
Length = 8 m.
Width = 9 m and
Height = 3 meter.
We know formula for volume of a cuboidal box = Length*Width*Height.
Plugging values of length, width and height of first aquarium in formula of volume. We get
V1 = 6*4*2 = 48 m^3.
Plugging values of length, width and height of second aquarium in formula of volume. We get
V2 = 8*9*3 = 216 m^3.
In order to find the total cubic meters of space do the sea turtles have in their habitat, we need to add both volumes.
Therefore, Total voulme of both aquarium = V1 +V2 = 48+216 = 264 m^3.
Therefore, total 264 m^3 cubic meters of space the sea turtles have in their habitat.
9x^2 - y^2 = 1
a.) 18x - 2y dy/dx = 0
2y dy/dx = 18x
dy/dx = 9x/y
b.) y^2 = 9x^2 - 1
y = √(9x^2 - 1)
y' = 9x / √(9x^2 - 1)
c.) substituting y = √(9x^2 - 1) into solution for part a gives
dy/dx = 9x / √(9x^2 - 1)
Thus the two solutions are consistent.
