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The problem describes a trapezoidal flower bed bounded by $y = x + 7$, the x-axis, and the vertical ...

Quadratic EquationsArea CalculationTrapezoidGeometric Application
2025/3/7

The problem asks us to simplify two expressions involving square roots of negative numbers using the...

Complex NumbersImaginary UnitSquare RootsSimplification
2025/3/7

Problem 37: The function $y = -0.024x^2 + 0.55x$ models the height $y$, in feet, of a frog's jump, w...

Quadratic FunctionsVertexParabolaOptimizationWord Problem
2025/3/7

We need to solve three problems: 34. Solve the linear-quadratic system of equations: $y = x^2 + 3x -...

System of EquationsQuadratic EquationsLinear EquationsSolving EquationsPolynomialsFactorization
2025/3/7

We are given three systems of equations and asked to find the solutions using graphing. System 31: $...

Systems of EquationsQuadratic EquationsSolving EquationsGraphingParabolaLinear Equations
2025/3/7

We need to solve the quadratic equations $x^2 - 9x + 20 = 0$ and $3x^2 + 8x + 4 = 0$ by graphing.

Quadratic EquationsFactoringRoots of EquationGraphing
2025/3/7

The problem requires us to solve the quadratic equation $x^2 - 9x + 20 = 0$ by graphing. This means...

Quadratic EquationsGraphingFactoringParabolaRoots of Equation
2025/3/7

We are asked to solve the quadratic equation $x^2 - 9x + 20 = 0$ by graphing. This means we want to ...

Quadratic EquationsRoots of EquationFactoringGraphing
2025/3/7

We have a list of math problems to solve. We will solve problem 24, 25, 26, 29 and 30. Problem 24: S...

Complex NumbersQuadratic EquationsSimplification
2025/3/7

$a > 0$とし、定積分 $S(a) = \int_0^2 |x^3 - ax| dx$ について考える。 (1) $a \geq 4$ のとき、$S(a)$を求める。 (2) $0 < a \le...

定積分絶対値場合分け
2025/3/7