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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

複素数 $z$ に関する方程式 $z\bar{z} + (3-3i)z + (3+3i)\bar{z} + 2 = 0$ を解く問題です。

複素数方程式絶対値
2025/3/7

複素数 $z$ に対して、式 $z\bar{z} + (3-3i)z + (3+3i)\bar{z} + 2$ の値を求めます。

複素数共役複素数平方完成
2025/3/7

The problem asks to find the y-intercept of the equation $5x + 2y = 12$. We are given that the slope...

Linear EquationsSlope-Intercept FormY-intercept
2025/3/7

We are given the equation $5x + 2y = 12$ and asked to find the slope of the line.

Linear EquationsSlope-Intercept FormSlope
2025/3/7

The problem requires us to find the slope and y-intercept of the line shown in the graph, and then w...

Linear EquationsSlopeY-interceptGraphing
2025/3/7

The problem is to determine the equation of the line shown in the graph.

Linear EquationsSlope-intercept formCoordinate Geometry
2025/3/7

The problem is to find the equation of the line shown in the graph. We need to identify two points o...

Linear EquationsSlope-intercept FormCoordinate Geometry
2025/3/7

The problem asks to find the $y$-intercept of a line, given that the slope of the line is $2$. The s...

Linear EquationsY-interceptSlope
2025/3/7