They didn't multiply 8 "throughout the equation." This is an expression, and they are using the distributive property like this: a(b + c) = ab + ac.KTiaam said:Homework Statement
I know this isn't exactly calculus related but it is from working out a calculus problem
I was wondering how:
(8/27) * [103/2 - (13/4)3/2]
equals
(1/27) * [80 * sqrt(10) - 13 * sqrt(13)]
The Attempt at a Solution
All i can conclude from this answer is that they multiplied 8 throughout the equation but i don't understand the rest of it, it doesn't make sense
Mark44 said:They didn't multiply 8 "throughout the equation." This is an expression, and they are using the distributive property like this: a(b + c) = ab + ac.
(8/27) * [103/2 - (13/4)3/2]
= 1/27 * [8 * 10 √10 - 8 * (13/4) * √(13/4)]
Can you continue from here?
103/2 = 101 + 1/2 = 10 * √10ktiaam said:i understand that part but where did the power of 3 go?
Mark44 said:103/2 = 101 + 1/2 = 10 * √10
KTiaam said:wow am i really that dumb?
103/2 was equal to (√10)3
The concept of equality in an equation means that whatever is done to one side must also be done to the other side in order to maintain balance. This is similar to a scale, where the weights on each side must be equal in order for the scale to be balanced.
The purpose of equality in an equation is to solve for an unknown quantity. By performing the same operations on both sides, we can isolate the unknown variable and determine its value.
Yes, in some cases, both sides of an equation may contain only numbers and still be equal. This means that the equation is already balanced and no further actions need to be taken.
Yes, in some cases, an equation may have multiple solutions where both sides are equal. This means that there are multiple values that can satisfy the equation and make it balanced.
To determine if an equation is balanced, we can perform the same operations on both sides and see if they result in the same value. If they do, then the equation is balanced and both sides are equal.