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

How many litres of water will have to be added to $1125$ litres of the $45 \%$ solution of acid so that the resulting mixture will contain more than $25 \%$ but less than $30 \%$ acid content?

The values of $x$ for which the inequality $\frac{8x^2+16x-51}{(2x-3)(x+4)} > 3$ holds,are

If $\frac{2x}{2x^2 + 5x + 2} > \frac{1}{x + 1}$,then

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module