Answer to Question #108351 in Algebra for Anu

Question

Which of the following statements are true or false? Give reasons for your answer. (10)
i) In the process of learning a concept, what should be noticed and given recognition
is the end product.
ii) Capacity and volume of 3D-objects are different concepts.
iii) The sum of the interior angles of a pentagon is 450 degree
iv) All rational numbers are integers but all integers are not rational numbers.
v) (− 4 )− (− 7) = − 3

Answer 1

i) Is not a statement, and therefore cannot be defined (this is a question).

However, based on the definition of this concept, this is true.

ii)Truth.

Let's look at two examples.

The first will be a balloon.

After we inflate it, its volume is equal to the volume of rubber and the volume of air in it.

The capacity here is just the volume of air we inflated the balloon with.

This illustrates the limited capacity of the Volume.

Another example is not a hollow cube, but Archimedes ' law.

Its capacity is obviously not the same as the volume that displaces an equal volume of liquid.

Adding voids to it with the help of waving magic wands, voids - "bubbles", we will increase its possible capacity, but the volume of water displaced by it will not change.

iii) False. The sum of the angles of a Pentagon is the sum of the angels of three triangles (draw two diagonals).sum up the angle of one 180-degree triangle. 180*3=540 degrees.

iv) False. Rational numbers are a relation, n/m, where n, m are integers.

All integers are rational because n / 1=n.

v) False. (-4)-(-7)=(-4)+(-(-7))=(-4)+7=7-4=3