Describe a situation you’re familiar with where one quantity changes constantly in relation to another

Mathematics

1 answer:

Crank3 years ago

8 0

Answer:

One such situation is the amount of money in excess you paid for an item and the amount of change you will get. Another such scenario would be the total numbers of hours with respect to the total number of days. With more days, there will be more time hence more hours.

Step-by-step explanation:

You might be interested in

Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.