A car travels 56.7 miles in a hour. If it continues at the same speed, how far will the car travel in 12 hours?
2 answers:
You might be interested in
Theoretically, the number of the vertex comes at the top must be equal for infinitely many numbers of trials, but it's a tedious job to roll the dice for a large number of times. Rolling the tetrahedron only 10 times will not predict the correct result.
Han suspects that this tetrahedron is weighted in some way to make 1 appear more often than the other numbers.
So, check his suspect experimentally with the help of the concept of center of mass. A fair tetrahedron must have the center of mass at the center of the body.
The given tetrahedron has 4 equilateral triangular faces, so at first, measure all the sides of triangular faces and make sure that all are having the same length.
Then, conduct an experiment to check the location of the center of mass.
Hang the tetrahedron by attaching a thin string at the vertex 1 as shown in the figure and observe the base surface ( triangle 234) whether it is parallel to the ground or not.
Now, repeat the same by hanging it with vertices 2, 3, and 4 and observe the base surface.
For the center of mass to be located at the center of the tetrahedron, the base must be parallel to the ground (flat ground).i.e the hanging string must be perpendicular to the base for all the four cases.
If this is so, then the tetrahedron is a fair tetrahedron otherwise not.
Given:
The expression is:
It leaves the same remainder when divided by x -2 or by x+1.
To prove:
Solution:
Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).
Let the given polynomial is:
It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that
...(i)
Substituting in the given polynomial.
Substituting in the given polynomial.
Now, substitute the values of P(2) and P(-1) in (i), we get
Divide both sides by 3.
Hence proved.