4. a bird left its post and
flew in a triangular path. it
flew 21 yards south, 72
yards east and 75 yards
diagonally to end back at
the post. is it a right triangle?

It is a right triangle

Explanation:

We are given the directions in which a bird flew to make a triangle.

We are required to determine whether the triangle is right angle.

What is a right triangle?

Then, a² + b² = c²

In this case;

Taking the legs as a= 21 yards and b = 72 yards and the hypotenuse, c = 75 yards.

Then we can determine whether it is a right triangle;

a² = 21² = 441

b²= 72² = 5184

c² = 75² = 5625

a² + b² = 5625

Therefore; a² + b² = c²

Hence, the triangle is right triangle.

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml