### A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.

The rope is pulled by a winch at 4 feet per second. When 14 feet of rope is out, what will be the speed of the boat? As the boat inches closer to the dock, what happens to its speed? 4 feet per second is a constant speed at which the boat is moving. When […]

### Determine the missing coordinates of the points on the graph of the function. y=arctan

$(x,y)=(-sqrt 3,a)$ $(x,y)=(b,-dfrac{pi}{6})$ $(x,y)=(c,dfrac{pi}{4})$ The question aims to determine the missing coordinates of the points on the graph of the function y= arctan x. Read moreChoose the point on the terminal side of -210°.A pair of numbers that shows the exact position of a point in a cartesian plane using horizontal and vertical lines called coordinates. […]

### Find the volume of the solid generated by revolving the shaded region about the y-axis.

This article aims to find the volume of the solid formed by rotating the shaded region about the y-axis. The article uses the concept of volume of the solid. The volume of the solid generated by a region under $f(x)$ bounded by the y-axis and vertical lines $y=a$ and $y=b$, which is […]

### Show that the equation has exactly one real root.

$2x+cos x = 0$ This article aims to find the roots of the given function. The article uses the concept of the mean value theorem and Rolle’s theorem. The readers should know the definition of the mean value theorem and Rolle’s theorem. Expert Answer Read moreChoose the point on the terminal side of -210°.First, remember the mean value theorem, which states that given […]

### Find the exact value of each of the remaining trigonometric functions of theta.

[costheta=frac{24}{25} , {270} ^circ<theta<{360} ^circ] – Part (a) – $sintheta=?$ Read moreChoose the point on the terminal side of -210°.– Part (b) – $tantheta=?$ – Part (c) – $sectheta=?$ – Part (d) – $csctheta=?$ Read moreFind the area of the region that lies inside both curves.– Part (e) – $cottheta=?$ The aim of the article […]