2023HSCQ3The diagram shows the direction field of a differential equation. A particular solution to the differential equation passes through (−2,1)(-2,1)(−2,1). Where does the solution that passes through (−2,1)(-2,1)(−2,1) cross the -axis? A. B. C. D.
2023HSCQ4The diagram shows the graphs of the functions f(x)f(x)f(x) and g(x)g(x)g(x). It is known that ∫acf(x) dx=10,∫abg(x) dx=−2,∫bcg(x) dx=3.\begin{aligned} \int_a^c f(x)\,dx&=10,\\ \int_a^b g(x)\,dx&=-2,\\ \int_b^c g(x)\,dx&=3. \end{aligned}∫acf(x)dx∫abg(x) What is the area between the curves y=f(x)y=f(x)y=f(x) and y=g(x)y=g(x)y=g(x) between x=ax=ax=a and ? A. B. C. D. 1 markMultiple choice
2023HSCQ12 (e)The region, RRR, bounded by the hyperbola y=60x+5,y=\frac{60}{x+5},y=x+560, the line x=10x=10x=10 and the coordinate axes is shown. [Diagram of the shaded region and rotation about the yyy-axis.] Find the volume of the solid of revolution formed when the region RRR is rotated about the yyy-axis. Leave your answer in exact form.4 marksShort answer