M varies directly as the square of N. If N increases by 10%, find the percentage change in M
M = k N^2
m = k (1.10 N)^2
m = 1.21 k N^2 = 1.21 M
100 (m-M)/M = percent change = 21 %
m=k*n^2
m=k(n+.1)^2
m new= k*1.21 n^2
percent change: 21 percent
M = k(n+1)²
M=k(1.01n)²
M= 1.21 kn² = 1.21m
100 = p. C
= 21%
I need better explanation
Well, well, well, if M varies directly as the square of N, then we have a quadratic relationship going on. Now, if N increases by 10%, we need to find out the percentage change in M.
Let's visualize it like this:
If N increases by 10%, that means it becomes N + 0.1N, which simplifies to 1.1N. Now, if M varies directly as the square of N, that means M becomes (1.1N)^2.
To find the percentage change, we need to compare M with its original value. So we do (1.1N)^2 / N^2.
Simplifying that expression, we get (1.1)^2, which is equal to 1.21.
So, the percentage change in M is 21%. Ta-da!
To find the percentage change in M when N increases by 10%, we need to understand the concept of direct variation and how it relates to percentage change.
When two variables are directly proportional, it means that they change in the same direction according to a fixed ratio. In this case, M varies directly as the square of N, which can be written as M = kN^2, where k is the constant of proportionality.
Let's say we have an initial value for N, denoted as N₀, and the corresponding value for M, denoted as M₀. When N increases by 10%, its new value can be found by multiplying N₀ by 1.10 (since 10% can be expressed as 0.10). Therefore, the new value for N is N₁ = 1.10N₀.
Now, to determine the change in M, we substitute the values of N into the equation:
M₁ = kN₁^2 = k(1.10N₀)^2 = 1.21kN₀^2
The new value for M, denoted as M₁, is 1.21 times the original value of M₀.
To find the percentage change in M, we calculate the difference between M₁ and M₀, divide it by M₀, and then multiply by 100 to express it as a percentage:
Percentage change in M = [(M₁ - M₀) / M₀] * 100
Substituting the values, we have:
Percentage change in M = [(1.21kN₀^2 - kN₀^2) / kN₀^2] * 100
Simplifying further:
Percentage change in M = (0.21kN₀^2 / kN₀^2) * 100
The kN₀^2 terms cancel out, leaving us with:
Percentage change in M = 0.21 * 100 = 21%
Therefore, when N increases by 10%, the corresponding change in M is a 21% increase.