Using the method of proof by contradiction, prove that if a product of two positive real numbers is greater than 1,000,000, then at least one of the numbers is greater than 1000.

Step-by-step explanation:

To prove - Using the method of proof by contradiction, prove that if

                  a product of two positive real numbers is greater than

                  1,000,000, then at least one of the numbers is greater

                   than 1000.

Proof -

For a proof of contradiction , firstly we have to assume that the statement is not true.

Here given statement is -  A product of two positive real numbers is greater than 1,000,000.

Let if possible, there does not exist 2 +ve integer real number such that at least one of the numbers is greater than 1000.

⇒both the number are in between 0 to 1000

Let a and b are 2 +ve real numbers.

⇒ab < 1000×1000

⇒ab < 1000000

As given,

ab > 1000000

Contradiction.

Hence proved.

If a product of two positive real numbers is greater than 1,000,000, then at least one of the numbers is greater than 1000.

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral