Part 1: Measure the distance of the diagonal (from one corner to the opposite corner) of the screen on your computer monitor to the nearest tenth of a centimeter or sixteenth of an inch. Measure the height of the screen along the vertical as well. Use the Pythagorean theorem to find the width along the horizontal

In your post, include the length of the diagonal, the width, and the calculations needed to determine the horizontal length of your computer monitor. After you have calculated the approximate length using Pythagorean theorem, use a measuring device to measure the horizontal length of your monitor. Was your measurement close? Why might the measurements not be exactly the same?

Typing hint: Type Pythagorean theorem as a^2 + b^2 = c^2. Do not use special graphs or symbols because they will not appear when pasted to the discussion board.

Part 2: Using the Library, web resources, and/or other materials, find a real-life application of a quadratic function. State the application, give the equation of the quadratic function, and state what the x and y in the application represent. Choose at least two values of x to input into your function and find the corresponding y for each. State, in words, what each x and y means in terms of your real-life application. Please see the following example. Do not use any version of this example in your own post. You may use other variables besides x and y, such as t and S depicted in the following example. Be sure to reference all sources using APA style.

Part 1: To measure the distance of the diagonal of your computer monitor, you can follow these steps:

1. Measure the vertical height of your computer monitor using a measuring tape or ruler, rounding to the nearest tenth of a centimeter or sixteenth of an inch. Let's assume the measured height is 30 centimeters.

2. Measure the horizontal width of your computer monitor, again rounding to the nearest tenth of a centimeter or sixteenth of an inch. Let's assume the measured width is 50 centimeters.

3. Apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Let a represent the height of the screen, b represent the width of the screen, and c represent the diagonal.

The Pythagorean theorem equation for this scenario can be written as:
a^2 + b^2 = c^2

4. Substitute the measured values for a and b into the equation and solve for c:

30^2 + 50^2 = c^2
900 + 2500 = c^2
3400 = c^2
c ≈ √3400
c ≈ 58.31 centimeters

So, the measured length of the diagonal of your computer monitor is approximately 58.31 centimeters. Now, you can use a measuring device to measure the actual horizontal length of your monitor.

After measuring the horizontal length of your monitor, compare it to the calculated approximate length using Pythagorean theorem. The measurements might not be exactly the same due to measurement errors, inaccuracies in the measuring tool, or slight variations in the monitor's actual dimensions. However, if the difference is small, it indicates that the calculated length is relatively close to the actual length, validating the accuracy of the Pythagorean theorem.

Part 2: A real-life application of a quadratic function is projectile motion. When an object is launched into the air, its vertical position can be modeled using a quadratic function. Let's consider the example of a basketball being thrown upward:

Application: Projectile Motion of a Basketball

Equation of the Quadratic Function:
h(t) = -16t^2 + v0t + h0

Where:
h(t) represents the height of the basketball at time t,
t represents time (in seconds),
v0 represents the initial upward velocity of the basketball,
h0 represents the initial height from which the basketball is thrown.

Assuming the basketball is thrown with an initial velocity of 15 m/s and from a height of 1.5 meters, we can find the corresponding height for different values of time.

1. For t = 2 seconds:
h(2) = -16(2)^2 + 15(2) + 1.5
h(2) ≈ 6.5 meters

This means that after 2 seconds, the basketball is approximately 6.5 meters above its initial height.

2. For t = 4 seconds:
h(4) = -16(4)^2 + 15(4) + 1.5
h(4) ≈ 4.5 meters

This means that after 4 seconds, the basketball is approximately 4.5 meters above its initial height.

In this real-life application, x (or t) represents time, and y (or h) represents the height of the basketball. The quadratic function allows us to determine the height of the basketball at any given time during its projectile motion. The values of x and y provide information about the height of the basketball at different instances of time.