Solid surface firm estimate form

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Daily exercise b : to place in a relative rank or category c : to fix at a certain amount d : value, rate their promises were set at naught e : to place as an estimate of worth 19 : to place in relation for comparison or balance theory set against practice 20 b : to incite to attack or antagonism war sets brother against brother 21 a : to place by transporting was set ashore on the island c : to put and fix in a direction set our faces toward home once more dof a dog : to point out the position of (game) by holding a fixed attitude 22 : to defeat (an opponent or a contract) in bridge 23 a : to fix firmly : make immobile : give rigid form or condition to set her jaw in determination b : to make unyielding or obstinate 24 : to cause to become firm or solid 25 : to cause (fruit or seed) to develop intransitive verb 2 : to be becoming : be suitable : fit 3 : to cover and warm eggs to hatch them 4 a : to affect one with or as if with weight the pudding sets heavily on my stomach b : to place oneself in position in preparation for an action (such as running) 5 of a plant part : to undergo development usually as a result of pollination 6 a : to pass below the horizon : go

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Values of the index above and below the sigma indicate where to begin the summation and where to end itslicing methoda method of calculating the volume of a solid that involves cutting the solid into pieces, estimating the volume of each piece, then adding these estimates to arrive at an estimate of the total volume; as the number of slices goes to infinity, this estimate becomes an integral that gives the exact value of the volumeslopethe change in [latex]y[/latex] for each unit change in [latex]x[/latex]slope-intercept formequation of a linear function indicating its slope and [latex]y[/latex]-interceptsolid of revolutiona solid generated by revolving a region in a plane around a line in that planespeedis the absolute value of velocity, that is, [latex]|v(t)|[/latex] is the speed of an object at time [latex]t[/latex] whose velocity is given by [latex]v(t)[/latex]standard formequation of a linear function with both variable terms set equal to a constant, [latex]ax+by=c[/latex].sum rulethe derivative of the sum of a function [latex]f[/latex] and a function [latex]g[/latex] is the same as the sum of the derivative of [latex]f[/latex] and the derivative of [latex]g[/latex]: [latex]\frac{d}{dx}(f(x)+g(x))=f^{\prime}(x)+g^{\prime}(x)[/latex]surface areathe surface area of a solid is the total area of the outer layer of the object; for objects such as cubes or bricks, the surface area of the object is the sum of the areas of all of its facessymmetry about the originthe graph of a function [latex]f[/latex] is symmetric about the origin if [latex](−x,−y)[/latex] is on the graph of [latex]f[/latex] whenever [latex](x,y)[/latex] is on the graphsymmetry about the [latex]y[/latex]-axisthe graph of a function [latex]f[/latex] is symmetric about the [latex]y[/latex]-axis if [latex](−x,y)[/latex] is on the graph of [latex]f[/latex] whenever [latex](x,y)[/latex] is on the graphsymmetry principlethe symmetry principle states that if a region R is symmetric about a line [latex]l[/latex], then the centroid of R lies on [latex]l[/latex]table of valuesa table containing a list of inputs and their corresponding outputstangent line approximation (linearization)since the linear approximation of [latex]f[/latex] at [latex]x=a[/latex] is defined using the equation of the tangent line, the linear approximation of [latex]f[/latex] at [latex]x=a[/latex] is also known as the tangent line approximation to [latex]f[/latex] at [latex]x=a[/latex]theorem of Pappus for volumethis theorem states that the volume of a solid of revolution formed by revolving a region around an external axis is equal to the area of the region multiplied by the distance traveled by the centroid of the regiontotal areatotal area between a function and the [latex]x[/latex]-axis is calculated by adding the area above the [latex]x[/latex]-axis and the area below the [latex]x[/latex]-axis; the result is the same as the definite integral of the absolute value of the functiontranscendental functiona function that cannot be expressed by a combination of basic arithmetic operationstransformation of a functiona shift, scaling, or reflection of

The container. The molecule iv) Angle of contact 900 and conditions forexperiences both cohesive as well as adhesive convexity and concavity:forces. In this case also, the net adhesive force( AP ) acting on the molecule A is horizontalsince the wall is vertical. Magnitude ofcohesive force is so large that the net force( AR ) is directed inside the liquid. Fig. 2.19 (d): Acute angle equal to 900. Consider a hypothetical liquid having angle of contact 900 with a given solid container, as shown in the Fig. 2.19 (d). In this case, the net cohesive force AC is exactly at Fig. 2.19 (b): Obtuse angle of contact. 450 with either of the surfaces and the resultant For equilibrium or stability of a liquid force AR is exactly vertical (along the solidsurface, the net force ( AR ) acting on allmolecules similar to molecule A must be surface).normal to the liquid surface at all points. Theliquid near the wall should, therefore, creep For this to occur, AP = AC where, AR isinside against the solid boundary. This makes 2the meniscus convex so that its tangent AT isnormal to AR. Obviously, such liquid does not the magnitude of the net force. From this wewet that solid surface.iii) Zero angle of contact : can write the conditions for acute and obtuse angles of contact: AC 2 For acute angle of contact, AP > , and for obtuse angle of contact, AP 2 Can you tell? How does a water proofing agent work? b) Shape of liquid drops on a solid surface: When a small amount of a liquid is dropped on a plane solid surface, the liquid Fig. 2.19 (c): Angle of contact equal to zero. will either spread on the surface or will form Figure 2.19 (c) shows the angle of droplets on the surface. Which phenomenoncontact between a liquid (e.g. highly purewater) which completely wets a solid will occur depends on the surface tension of(e.g. clean glass) surface. The angleof contact in this case is almost zero (i.e., the liquid and the angle of contact betweenθ → 00). In this case, the liquid molecules nearthe contact region, are so less in number that the liquid and the solid surface. The surfacethe cohesive force is negligible, i.e., AC = 0and the net adhesive force itself is the resultant tension between the liquid and air as well asforce, i.e., AP = AR . Therefore, the tangentAT is along the wall within the liquid and the that between solid and air will also have to beangle of contact is zero. taken in to account. Let θ be the angle of contact for the given solid-liquid pair. T1 = Force due to surface tension at the liquid- solid interface, T2 = Force due to surface tension at the air- solid interface, 38T3 = Force due to surface tension at the air- Table 2.2 – Angle of contact for pair of liquid interface. liquid - solid in contact. As the force due to surface tension is Sr.