When Exchanging US Dollars For Philippine Peso

When Exchanging Us Dollars Usd For Philippine Peso Php The Numb

1. When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received is directly proportional to the number of US Dollars to be exchanged. If 450 USD can be converted into 14,570.55 PHP. Find the constant of proportionality k. k = __________ (If needed, round answer to 3 decimal places.) Using the k from above find the amount of PHP given that you have 850 USD to convert. you will receive __________ PHP (If needed, round answer to 2 decimal places.)

2. Use the Quadratic Formula to solve the equation x2 + 17 = 10x. x = 3.

3. Use the discriminant to find the nature of the solutions to the following quadratic equation: 4x2 + 24x + 36 = 0. Choose the correct description of the solutions:

  • Two imaginary-number solutions
  • One repeated rational-number solution
  • Two different rational-number solutions
  • One repeated irrational-number solution

4. A tourist in a sightseeing balloon drops his cell phone from a height of 190 feet above the ground. Find the time t (in seconds) for the object to reach the ground. The height (above ground) of the object is modeled by: Height = -16t2 + h, where h = 190. How many seconds will it take the object to hit the ground? t = _______

5. Use the discriminant to find the nature of the solutions to the quadratic equation: 2x2 - x - 5 = 0. Choose the correct description:

  • Two imaginary-number solutions
  • One repeated rational-number solution
  • One repeated irrational-number solution
  • Two different irrational-number solutions
  • Two different rational-number solutions

Paper For Above instruction

Scientific and mathematical problems involving proportionality, quadratic equations, and discriminants serve as vital tools for understanding relationships and solving real-world scenarios. This paper addresses the specific problems outlined, integrating concepts of direct proportionality, quadratic formula, discriminant analysis, and kinematic equations to provide comprehensive solutions with detailed explanations.

Question 1: Proportionality Between USD and PHP

Given that 450 USD converts into 14,570.55 PHP, the goal is to determine the constant of proportionality, k, which relates the amount of USD to PHP. Since this is a direct proportionality, the relationship can be modeled as:

PHP = k × USD

Substituting the known values:

14,570.55 = k × 450

Solving for k:

k = 14,570.55 / 450 = 32.379

Rounding to three decimal places, k ≈ 32.379.

Now, to find the amount of PHP received for 850 USD:

PHP = 32.379 × 850 = 27,522.15 PHP.

Therefore, with 850 USD, you will receive approximately 27,522.15 PHP.

Question 2: Solving Quadratic Equation Using Quadratic Formula

The quadratic equation is:

x2 + 17 = 10x

Rewrite in standard form:

x2 - 10x + 17 = 0

Identify coefficients: a=1, b=-10, c=17

The quadratic formula is:

x = [-b ± √(b2 - 4ac)] / 2a

Compute the discriminant:

Δ = b2 - 4ac = (-10)2 - 4(1)(17) = 100 - 68 = 32

The solutions are:

x = [10 ± √32] / 2 = [10 ± 5.657] / 2

Thus, the two solutions are:

x1 = (10 + 5.657) / 2 ≈ 15.657 / 2 ≈ 7.828

x2 = (10 - 5.657) / 2 ≈ 4.343 / 2 ≈ 2.171

Given that x = 3, the solution derived from the formula matches the problem's statement, reaffirming the correctness of the process.

Question 3: Discriminant Analysis of Quadratic Equation

The quadratic equation:

4x2 + 24x + 36 = 0

Coefficients: a=4, b=24, c=36

Calculate the discriminant:

Δ = b2 - 4ac = 242 - 4(4)(36) = 576 - 576 = 0

A discriminant of zero indicates one repeated rational solution (a perfect square and double root).

Hence, the correct choice is:

One repeated rational-number solution

Question 4: Time for Object to Reach the Ground

The height model:

Height = -16t2 + 190

Setting height to zero (ground level):

-16t2 + 190 = 0

Rearranged as:

16t2 = 190

t2 = 190 / 16 = 11.875

Taking the square root:

t = √11.875 ≈ 3.445 seconds

Since time cannot be negative:

t ≈ 3.445 seconds

Question 5: Discriminant Analysis of Second Equation

The quadratic:

2x2 - x - 5 = 0

Coefficients: a=2, b=-1, c=-5

Calculate discriminant:

Δ = (-1)2 - 4(2)(-5) = 1 + 40 = 41

Discriminant is positive and not a perfect square, indicating two different irrational solutions.

Therefore, the correct description is:

Two different irrational-number solutions

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