The number of functions f, from the set
\(A = {x∈N: x^2-10x+9≤0} \)to the set \(B = {n62:n∈N}\)
such that
\(f(x)≤(x-3)^2+1\), for every \(x∈A,\)
is ______.
The number of functions f, from the set
\(A = {x∈N: x^2-10x+9≤0} \)to the set \(B = {n62:n∈N}\)
such that
\(f(x)≤(x-3)^2+1\), for every \(x∈A,\)
is ______.
Correct Answer: 1440
Solution and Explanation
A = {x∈N, x2-10x+9≤0}
= {1,2,3,...,9}
B = {1,4,9,16,....}
f(x)≤(x-3)2+1
f(1)≤5, f(2)≤2,....f(9)≤37
x = 1 has 2 choices
x = 2 has 1 choice
x = 3 has 1 choice
x = 4 has 1 choice
x = 5 has 2 choices
x = 6 has 3 choices
x = 7 has 4 choices
x = 8 has 5 choices
x = 9 has 6 choices
∴ Total functions = 2 × 1 × 1 × 1 × 2 × 3 × 4 × 5 × 6 = 1440
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Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations