Questions in mathematics

Questions in mathematics

📝 Answered - The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, [tex]l[/tex], and the possible width in meters, [tex]w[/tex], of the pool? A. [tex] \begin{aligned} w &\leq 10-1 \\ 21+2 w &\geq 62 \end{aligned} [/tex] B. [tex]w \leq 10-1[/tex] [tex]2 l+2 w>62[/tex] C. [tex]w \leq I-10[/tex] [tex]2 l+2 w \geq 62[/tex] D. [tex]w \leq 1-10[/tex] [tex]2^{\prime}+2 w>62[/tex]

📝 Answered - If [tex]A=\left[\begin{array}{lll}3 & 1 & 5 \\ 2 & 6 & 4 \\ 8 & 7 & 9\end{array}\right][/tex] and [tex]B=\left[\begin{array}{lll}1 & 2 & 4 \\ 1 & 5 & 3 \\ 2 & 4 & 0\end{array}\right][/tex], find [tex]5A[/tex] and [tex]-2A+3B[/tex].

📝 Answered - Which term describes the distance from the center of a circle to any point on the circle? A. Center B. Radius C. Diameter D. Circumference

📝 Answered - Use a graphing utility to graph the polar equations. Find the area of the given region analytically: between the loops of r = 4-8 cos(θ)

📝 Answered - What is the solution to this equation? $5(x-6)+3=-7$ A. $x=4$ B. $x=2$ C. $x=5$ D. $x=3$

📝 Answered - Differentiate. [tex]f(x)=\ln \left[\frac{(2 x+9)(x+7)^6}{(1-6 x)^3}\right][/tex] [tex]\frac{d}{d x}\left[\ln \left[\frac{(2 x+9)(x+7)^6}{(1-6 x)^3}\right]\right]=[/tex]

📝 Answered - Verify that the equation given below is an identity ([tex]\cos 2 x=\cos (x+x)[/tex]) [tex]\cos 2 x=\frac{\cot ^2 x-1}{\cot ^2 x+1}[/tex] [tex]=\frac{\frac{\cos ^2 x-\sin ^2 x}{\sin ^2 x}}{\frac{\cos ^2 x+\sin ^2 x}{\sin ^2 x}} \text { (Do not simplify) }[/tex] Re-enter the numerator, and simplify the denominator of this complex fraction. [tex]=\frac{\frac{\cos ^2 x-\sin ^2 x}{\sin ^2 x}}{\frac{1}{\sin ^2 x}}[/tex] Apply a Pythagorean Identity. Simplify the complex fraction by multiplying the fraction in the numerator by the reciprocal of the fraction in the denominator [tex]=\square \text { (Simplify your answer Do not factor ) }[/tex]

📝 Answered - True or False: The absolute value of ${ }_{10}=10$.

📝 Answered - Submarine $A$ is positioned at -1,100 feet in relation to sea level. Submarine $B$ is positioned at -800 feet in relation to sea level. Each submarine needs to be 200 feet below sea level in 30 minutes. Which compares the speeds at which each submarine needs to travel? A. Submarine A must travel at a rate of $\frac{-200-(-1100)}{30}=30 ft / min$, and Submarine B must travel at a rate of $\frac{-200-(-800)}{30}-20 ftmin$. B. Submarine A must travel at a rate of $\frac{1100+200}{30}=43 \frac{1}{3} ft / min$, and Submarine B must travel at a rate of $\frac{800+200}{30}=33 \frac{1}{3} ft / min$. C. Submarine A must travel at a rate of $\frac{-1100}{30}=-36 \frac{2}{3} ft / min$, and Submarine B must travel at a rate of $\frac{-800}{30}=-26 \frac{2}{3} fv / min$.

📝 Answered - What is the range of the function $y=4 e^x$? A. all real numbers greater than 0 B. all real numbers less than 0 C. all real numbers less than 4 D. all real numbers greater than 4