How do the graphs of the functions f(x) = (Three-halves)x and g(x) = (Two-thirds)x compare?

Answer:

7 years

Step-by-step explanation:

Since a graph isn’t provided, I will indicate how many years are involved, and you should be able to deduce it from this. First, let’s [use a calculator] to find 2% of 250, which equals 5. Adding 5 to the total only slightly impacts 2% of the original amount, changing it by 0.1 or 5/50. We can continue adding 5 until we exceed 282, which occurs after 7 increments, calculated as (285 minus 250) divided by 5. Thus, the answer is indeed 7 years. A quick calculation will confirm this.

Response:

100 percent increase

Detailed explanation:

1st garden

Length = 6 ft

Width = 4 ft

Perimeter = 2 (l+w)

                 = 2 (6+4) = 2(10) = 20

2nd garden

The length and width of this garden are double those of the first

Length = 2 *6 = 12

Width = 2 *4 = 8

Perimeter = 2 (l+w)

                 = 2 (12+8) = 2(20) = 40

Percent change = (new - old )/old * 100 percent

The first garden represents the old garden = 20  and the second refers to the new garden = 40

Substituting values in

Percent change = (40-20)/20 = 20/20 =100 *100 percent

                            = 100 percent increase

The domain refers to all potential input values, specifically represented by the x-axis on a graph. Conversely, the range includes all possible output values, depicted along the y-axis.

The graph clearly extends horizontally from (-∞,∞) on the x-axis, indicating that its domain is (-∞,∞).

Similarly, it can be seen that the graph stretches vertically from (-∞,∞) on the y-axis, denoting that the range is also (-∞,∞).

This indicates the function includes an infinite array of values. Therefore, there are no limitations on either the domain or the range for this function.

Response:

Step-by-step breakdown:

When you sketch that diagram (great description, by the way!), what you essentially have is a right triangle with a base of 32 and a hypotenuse of 45. The right angle resides at one of the base's ends, and x represents the vertex angle. We must find this vertex angle first to determine the angle of depression from the second bird to the watcher. The side measuring 32 is opposite to angle x, with 45 being the hypotenuse; hence, the trigonometric relation we need is sine:

and

sin(x) =.711111111

Go to your calculator, press the 2nd key followed by the sin key, and your display will show:

then, enter in your decimal.711111111 and hit equals. You should arrive at an angle of 45.325. That angle is x. However, that's not the angle of depression. The angle of depression is the complementary angle to x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325, resulting in

Angle of depression = 44.67 or 44.7 degrees.