Questions in mathematics

Questions in mathematics

📝 Answered - Simplify $3 L: \frac{1}{2} L: \frac{3}{4} L: 1 L$

📝 Answered - Consider the indefinite integral [tex]$\int \frac{-3 e^{-3 x}}{\left(e^{-3 x}+3\right)^2} d x$[/tex]: This can be transformed into a basic integral by letting [tex]$u = \square$[/tex] and [tex]$d u= \square$[/tex] [tex]$d x$[/tex] Performing the substitution yields the integral [tex]$\int \square du$[/tex]

📝 Answered - Match each property with an expression. A. Commutative Property of Addition B. Identity Property of Addition C. Multiplicative Property of Zero D. Distributive Property E. Associative Property of Addition F. Identity Property of Multiplication 1. [tex]$3 x+4=4+3 x$[/tex] 2. [tex]$3+0=3$[/tex] 3. [tex]$3(0)=0$[/tex] 4. [tex]$3(x+4)=3 x+12$[/tex] 5. [tex]$3+(7+9)=(3+7)+9$[/tex] 6. [tex]$3(1)=3$[/tex]

📝 Answered - (b) [tex]log _5(30)=[/tex]

📝 Answered - Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of [tex]$\theta$[/tex] only. [tex]$\sin ^2(-\theta)-\csc ^2(-\theta)+\cos ^2(-\theta)$[/tex]

📝 Answered - $35 \times \frac{\left[1+\frac{7.25 \%}{12} 2^{42}-1\right]}{\frac{7.25 \%}{12}}

📝 Answered - A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time [tex]$t=0$[/tex] seconds. When the weight is released, it oscillates and returns to its original position at [tex]$t=3$[/tex] seconds. Which of the following equations models the distance, [tex]$d$[/tex], of the weight from its equilibrium after [tex]$t$[/tex] seconds? A. [tex]$d=-9 \cos \left(\frac{\pi}{3} t\right)$[/tex] B. [tex]$d=-9 \cos \left(\frac{2 \pi}{3} t\right)$[/tex] C. [tex]$d=-3 \cos \left(\frac{\pi}{9} t\right)$[/tex] D. [tex]$d=-3 \cos \left(\frac{2 \pi}{9} t\right)$[/tex]

📝 Answered - Determine the range of values of [tex]$x$[/tex] for which [tex]$y=\frac{2 x-4}{x^2+5}$[/tex] is a decreasing function.

📝 Answered - What is the additive inverse of the expression below, where $a$ and $b$ are real numbers? $2 a+b$

📝 Answered - Use integration by parts to evaluate the integral: [tex]$\int \cos (\ln (5 x)) d x$[/tex]