few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
{
  "explanation": "This problem applies trigonometric identities, including the angle addition formula for cosine.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Understand properties of multiplication and the relationship between multiplication and division.

Solve systems of equations.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Add and subtract within 20.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Reason about and solve one-variable equations and inequalities.

Work with equal groups of objects to gain foundations for multiplication.

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Understand solving equations as a process of reasoning and explain the reasoning.

Work with radicals and integer exponents.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand the connections between proportional relationships, lines, and linear equations.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Use properties of operations to generate equivalent expressions.
problem_activity: A bakery sells small cakes for
$${ {{$1}}0}$$
each. At this price, the bakery typically sells
$${100}$$
cakes per week.
The owner of the bakery wants to increase the price of the cake in order to maximize revenue. She determines that for each
$${{$1}}$$
increase in price, she sells
$$5$$
fewer cakes per week.
a.  Which function represents the weekly revenue,
$${R(x)}$$
, the owner of the bakery can expect to earn from the cakes based on
$$x$$
increases in price by
$${{$1}}$$
.
i.
$${R(x)}=(10-x)({100}+5x)$$
ii.
$${R(x)}=(10+x)({100}-5x)$$
iii.
$${R(x)}=(10-5x)({100}+x)$$
iv.
$${R(x)}=(10+5x)({100}-x)$$
b.  At what price will the owner of the bakery earn the maximum weekly revenue from sales of the small cakes?


correct_option_index: 19