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 new= k*1.21 n^2
percent change: 21 percent
m = k (1.10 N)^2
m = 1.21 k N^2 = 1.21 M
100 (m-M)/M = percent change = 21 %
M=k(1.01n)²
M= 1.21 kn² = 1.21m
100 = p. C
= 21%
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!
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.