the ground as a function of the angle from the 3 d clock 38. The height (in ne Per position is given by f(0)=50+45 sin 6 Ca) What are the highest and lowest points on the ride? (b) Describe the dimensions of the Ferris wheet 3L A stunt pilct ties her plane in two complete loops. Al f bottom of the loop (an angle of a meters above the ground, at the rop of the loop (@90) she is s 1200 meters above the ground. Find a fRormula Ar Sketch a graph showing hor height s above ground for-90505630 90) she isym 300 39. The top of a bucket 0.5 meter high is attachhed to a water wheel of diameter 4.5 meters The wheel sits ahove the river so that half of the bucket dips below the surface of the water at its lowest position. Write a function for the height of the center of the hucket (in meters) above the river as a function of the angle 8 as measured counter clockwise from the 3 o'clock position 40. A wind turbine has a tubular steel tower that is 60 mt high. Is has three 30-meter-long blades attached to the ten of the tower, as in Figure 7.63. (a) Blade I starts at the 3 o'clock position and rotates counterciockwise. Find a formula for the heighe h in meters, of the tip of blade 1 as a function of the angle . As usual, we measure 6 counterciokwise from the 3 o'clock position. (b) Two ladsbus land.on the blade the fre A smali frog hops onto the Laxey wheel, a waterwheel in the Isle of Man, the largest in the world Clinging to the wheel, the frog rides from its base, at a height of s 0t. to its top at a height of 725 ft, then back down. It rides the wheel once more before hopping off. Find a formula fors= f(8)the frog's height above ground as a function of 8, the angle (in degrees),-90 Se5630, and sketch its graph. A spy pushes a thumbtack into the bicycle tire of his en- ny The wheel has diameter 740 mm. When the bike be- s to roll, the tack is at an angle of @ 0, at the height e wheel's hub, or s = formula for % = eight above ground for 0< 200 370 mm above the ground. f101 Sketch a graph showing the
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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