The number of points P(x, y) with natural num | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The quadrilateral is bounded by the lines $x = 0$ ($y$-axis),$y = 0$ ($x$-axis),$2x + y = 2$,and $x + y = 5$.For a point $(x, y)$ to be inside the

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) The quadrilateral is bounded by the lines $x = 0$ ($y$-axis),$y = 0$ ($x$-axis),$2x + y = 2$,and $x + y = 5$.For a point $(x, y)$ to be inside the quadrilateral with natural number coordinates $(x, y \in \{1, 2, 3, \dots\})$,it must satisfy the inequalities:$1) \ x > 0$$2) \ y > 0$$3) \ 2x + y > 2$$4) \ x + y Testing integer values for $x$:If $x = 1$: $2(1) + y > 2 \implies 2 + y > 2 \implies y > 0$. Also $1 + y If $x = 2$: $2(2) + y > 2 \implies 4 + y > 2 \implies y > -2$. Also $2 + y If $x = 3$: $2(3) + y > 2 \implies 6 + y > 2 \implies y > -4$. Also $3 + y If $x \ge 4$: $x + y The total number of such points is $3 + 2 + 1 = 6$.

The number of points $P(x, y)$ with natural numbers as coordinates that lie inside the quadrilateral formed by the lines $2x + y = 2$,$x = 0$,$y = 0$,and $x + y = 5$ is

Similar Questions

If $x$ is real and satisfies $x + 2 > \sqrt{x + 4}$,then

The solution set contained in $R$ of the inequation $3^x+3^{1-x}-4 < 0$ is:

The solution set for the system of linear inequations $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,and $y \geq 0$ is represented graphically. Which of the following figures represents the correct solution set?

Solve for $x$ in the following inequality: $\frac{4}{x+1} \leq 3 \leq \frac{6}{x+1}$ where $x > 0$.

The feasible region represented by the inequations $2x + 3y \leq 18$,$x + y \geq 10$,$x \geq 0$,$y \geq 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module