最新の問題
The problem requires us to solve for $b$ in the equation $\frac{a}{bc} = \frac{d}{e}$.
Equation SolvingAlgebraic ManipulationVariables
2025/5/2
We are given the equation $\frac{c}{d} = \frac{b}{a}$ and asked to solve for $d$.
Algebraic ManipulationSolving EquationsVariables
2025/5/2
The problem consists of two parts. Part 1: Given the function $f(x) = \frac{6x - 3}{5}$, find $f(1.2...
FunctionsLinear EquationsSlopeY-intercept
2025/5/2
与えられた行列が直交行列となるように、$a, b, c$の値を定める問題です。直交行列とは、転置行列が逆行列と一致する行列のことです。つまり、$A^T A = I$ (ここで$A^T$は$A$の転置行...
行列線形代数直交行列ベクトルの内積
2025/5/2
We are asked to find the principal amount that needs to be invested to obtain a future value of $17,...
Simple InterestFinancial MathematicsAlgebra
2025/5/2
The problem provides a total cost function $C(x) = 850 \ln(x + 10) + 1700$, where $x$ is the number ...
Cost FunctionLogarithmsOptimizationCalculus
2025/5/2
The problem provides a demand function $p = 100e^{-q/2}$, where $p$ is the price per unit and $q$ is...
Exponential FunctionsDemand FunctionModelingCalculus (Implicit)
2025/5/2
与えられた2つの行列が直交行列であることを示す問題です。行列が直交行列であるとは、その行列の転置行列が逆行列と等しい、つまり $A^T A = A A^T = I$ (Iは単位行列) が成り立つことを...
線形代数行列直交行列行列の計算転置行列
2025/5/2
The problem describes the sales decay of a product using the formula $S = 80000e^{-0.9x}$, where $S$...
Exponential DecayModelingLogarithmsSalesApplications of Calculus
2025/5/2
We are asked to solve the equation $\ln(x+4) + \ln(x) = \ln(x+18)$.
LogarithmsEquationsQuadratic EquationsSolution Verification
2025/5/2