Questions in mathematics

Questions in mathematics

📝 Answered - A water tank is being filled, and the water level [tex]f(t)[/tex] in liters depends on time [tex]t[/tex] in minutes. At minute [tex]t=10[/tex], is the water level changing smoothly without interruption? To confirm, we check: * Is [tex]f(10)[/tex] defined? This question implies, was the water level recorded at minute 10? * Does [tex]\lim _{t \rightarrow 10} f(t)[/tex] exist? This question implies, does the water level approach a specific value as time nears 10? * Does [tex]\lim _{t \rightarrow 10} f(t)=f(10)[/tex]? Is the water level changing at [tex]t =10[/tex] seconds discontinuous, continuous and discontinuous, neither continuous nor discontinuous, or continuous?

📝 Answered - Solve for x. 3x = 6x - 2

📝 Answered - $\begin{array}{l} 2 x)^2=4 x^2(-3)^2=9 \ (2 x-\underbrace{3(2 x-3)}_{2(-3)(2 x)}}=-12 x \end{array}$ 1) $(x+6)(x+6) \quad x^2+12 x+36$ 2) $(2 x+5)(2 x+5) 4 x^2+20 x+25$ 3) $(3 x-4)(3 x-4) 9 x^2-24 x+16$ 4) $(x+8)^2 \quad x^2+16 x+64$ 5) $(4 x-3)^2 \quad 16 x^2-24 x+9$

📝 Answered - Use matrices and elementary row operations to solve the following system of equations: [tex] \begin{aligned} -x+2 y+3 z & =11 \ 2 x-3 y & =-6 \ 3 x-3 y+3 z & =3 \end{aligned} [/tex]

📝 Answered - Solve for $x$: $x^2+17 x+72=0$ Box1 (Larger Solution): $\square$ Box2 (Smaller Solution): $\square$

📝 Answered - Part C Rewrite $\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2}$ as an exponential expression with a base of 2.

📝 Answered - Suppose the graph of f(x)=\sqrt{x} is shifted down 4 units and to the left 5 units. What is the equation of the new graph? Verify the result graphically. The equation of the new graph is g(x)=\sqrt{x+5}-4 Verify the result graphically. Choose the graph showing f(x)=\sqrt{x} as a dashed blue curve and the transformed curve as a solid red curve below. A. B. C. D.

📝 Answered - Select the correct answer. The monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $55. If there are 461 households in the community, about how many of them have electric bills less than $200? A. 81 B. 45 C. 21 D. 95

📝 Answered - Consider the quadratic function [tex]$f(x)=\frac{1}{5} x^2-5 x+12$[/tex]. Which statements are true about the function and its graph? Select three options. A. The value of [tex]$f(-10)=82$[/tex] B. The graph of the function is a parabola. C. The graph of the function opens down. D. The graph contains the point [tex]$(20,-8)$[/tex]. E. The graph contains the point [tex]$(0,0)$[/tex].

📝 Answered - A vitamin degrades in the body according to the function represented in the table, where [tex]$x$[/tex] is the time in hours and [tex]$f(x)$[/tex] is the dosage in milligrams. What was the original dose? A. 0.50 milligrams B. 8 milligrams C. 24 milligrams D. 500 milligrams