Question

Please fill in the blank

Answer 1

Answer:

The independent variable is h

The dependent variable is P

Domain of h: 3<h<23

Range of h: 26<P<46

Step-by-step explanation:

Domain and Range of Functions

A function that is explicitly defined can have restrictions on its variables that guarantee its existence. For example, a function with a variable denominator must restrict the domain (values of the dependent variable) so, the denominator is never zero. Once determined the domain of the function, the range is made of all values the function can take.

We have a triangle with sides h,13, and 10. The perimeter of the triangle, called P is the sum of its sides

P=h+13+10=23+h

h is the independent variable, whose value modify the value of P, so P is the dependent value

Since h is the third side of the triangle, some restrictions apply. First, h cannot be less than the difference between 13 and 10, because it will produce an incomplete triangle. For example, if h=2, it won't be enough to bond the other vertices of the triangle with a line. So the minimum value of h is 3.

On the other hand, h cannot exceed the sum of the other sides, because in that case, they won't be long enough to reach the last vertex of the triangle. So h must be less than 23. It forms the restriction of the domain

3<h<23

As a consequence, the range will be restricted also.

Since P=23+h, we get h=P-23. Replacing in the above domain:

3<P-23<23

Adding 23, the range is revealed:

26<P<46

Answer 2

Answer:

a. P = 23 + h

b. Independent - h

   Dependent - P

c. Domain: $3$

   Range: $26$

Step-by-step explanation:

a. The perimeter is the sum of lengths of all sides, so,

$P=10+13+h\\ \\P=23+h$

b. The independent variable is h and the dependent variable (its value depends on value of h) is variable P.

c. Use triangle's rule:

$h+10>13\\ \\h+13>10\\ \\10+13>h$

So,

$h>3\\ \\h$

Hence, the domain of the function is

$3$

Thus,

$P(3)=23+3=26\\ \\P(23)=23+23=46,$

and the range of rhe function is

$26$