Boost Your Math Modeling Skills

A system of equations modeling the given conditions. Then solve the system by addition method and find two numbers.
The system of equations is given by
${\displaystyle \frac{x}{2}=\frac{y+8}{3}}$
${\displaystyle \frac{x+2}{2}=\frac{y+11}{3}}$

A bouy floating in the ocean is bobbing in simple harmonic motion with period 6 seconds and amplitude 3ft. Its dispfacement d from sea level at time ${\displaystyle t=0}$ seconds is 0 ft, and initially it moves downward. (Note that downward is the negative direction.)
Give the equation modeling the displacement d as a function of time t.

The dimensions of a rectangle whose perimeter is 22 feet and area is 24 square feet.

To calculate: The equations modeling the word problem that states that subtraction of the second number from three times the first number gives 1 and addition of the first number with twice the second number gives 12 and the solution to the system of equations.

To find: The points where the comet might intersect the orbiting planet.
It is given that the planet's orbit follows a path described by ${\displaystyle 16x^2+4y^2=64}$.
Given that a comet follows the parabolic path ${\displaystyle y=x^2-4}$.

To find the measure of diversity H for the following proportions of each:
hemlock, 0.521. beech, 0.324. birch, 0.081. maple, 0.074.

To find:
The total sales T(x) of Northwest Creations, to the nearest dollar using the model where the distribution of x thousand catalogues is approximated by ${\displaystyle T\left(x\right)=5000\log (x+1)}$.

To solve:
The equation ${\displaystyle E=IZ}$ for given ${\displaystyle E=57+67i,Z=9+5i}$

This homework question has to do with modeling with functions.
1.) A rectangle has a perimeter of 80 ft. Find a function that models its area A in terms of the length x of one of its sides.
Can you please explain exactly what you did and what you used to find the formula.

The speed of each of the runners by modeling the system of linear equations.

To find:
a) The speed of the sprinter while he running as crossed the finish line
b) After how many seconds was he running at the rate of 10 m per sec
Using the model function ${\displaystyle f\left(t\right)=11.65(1-e^{-\frac{t}{1.27}})}$ where f(t) is the speed of the sprinter per second after t seconds.

To find: The exact location of the ship tracked by the tracking system.

Twelve gallons of a salt solution consists of ${\displaystyle 35\mathrm{\%}}$ salt. It is the result of mixing a ${\displaystyle 55\mathrm{\%}}$ solution with a ${\displaystyle 25\mathrm{\%}}$ solution. How many gallons of each of the solutions was used? Let ${\displaystyle x=}$ the number of gallons of the ${\displaystyle 55\mathrm{\%}}$ solution and ${\displaystyle y=}$ the number of gallons of the ${\displaystyle 25\mathrm{\%}}$ solution. The corresponding modeling system is $\{\begin{array}{l}x+y=12\\ 0.55x+0.25y=0.35(12)\end{array}$ Solve the system by using the method of substitution and what is the ordered pair?

To find: The number of students took at least one online college course in 2012, using the given model, Number of students ${\displaystyle =0.0112x^2+0.4663x+1.513.}$

To find: The approximated thereshold (in dollars) in 2012, using the given model.
The given model is Number of students ${\displaystyle =y=2.719x^2+196.1x+8718}$

Whether the given function is an appropriate model for extended years and explain the reason.
Given: The polynomial function is ${\displaystyle f\left(x\right)=-0.87x^3+0.35x^2+81.62x+7684.94}$
Here, x represents the number of years after 1987 and f(x) represents the number of thefts in that respective year.

To calculate: Percentage of gene combinations that result in albino coloring, further model a polynomial representing possible gene combinations.

The equations modeling the word problem and the numbers that satisfy the equations.
Subtraction of the second number from two times the first number gives 3. Addition of three times the first number with twice the second number gives 8.

To find:
The number of mini-marshmallows in one serving of Swiss Miss Chocolate box using the expression ${\displaystyle 3+2\times 4÷2-3\times 7-4+47.}$

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. ${\displaystyle (1,3),(2,6),(3,12),(4,24)}$
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work.
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.