Question

Question 19 5 pts A trough vertical ends have the shape of the parabola is filled with water. The width of top is 3.2 maters and the depth from top to the vertex is 2.1 maters. Find the hydrostatic force on one end of the trough. (Keep two decimal places.) Question 20 5 pts The hyperbola has foci (3,2) and (3,6) and one of vertices is (3,3). Find the equation for it and y- ___ when x = 8.19.(Keep three decimal places.) Question 21 Ente

Answer 1

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Question 19) gever, coretto of the pooroboli, brough is 3.27 f her depth from top to the vertex is 2.1m (-1.62.14 yr 3.2m (+1.6, 2.1 2.1 dys Etib 1.6 The equation of the curve is: X² (ally hay The parabole passes through poenta (+ 1.6, 2.1) (1,6) 2 4Q (2.1) = añ 0.305 ,ه २२ 1.22 equation of parabreda levomes: y. Ty = 0.82x² o bc=(1,1045) vg

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Dende de parabeli seumunsko horizontal stoups each of old Ag, hongth by faith with dy & Length along x-adis Wi 2. The width of the ith strup at distance y from verter 2 (1.1045 y ) & depth of that strup from surface is is d = 2.1-4 The area of the sectangulas ith steup is Ai = w; by wi ay = 261.1045) Jy dy Pressure on the itheadangular stsip Pi=862) where 8 = unit weight of water 9.807 kN/m3 => Pi - (9,807) (2.1-4) The hydrostati pove on one end of the toroughis: PiAir (9807) (2.1-y) (2) (1.1045)vý dy of Piti- ficas o On using celulator, F=37156.10 N

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verteiol hyperbolo Question 20 from the question, we observe that both the focilie on a line parallel to y oxis, as theis 2-6000dinate w constant (ie - 3) , Terme the hypoedola is a Let the equation of the westial hypoalde bere, bei (x-b²_1 where Chik) is centre b² whose, vertues are chikta) fou are ch, ktc) distance between foc is ac & c² - 0²+6² (9 – k)2 a2 give's one wertoe = 3,3) & fou are (3,2)£13,6) let bot Chik+c) = (3,6) Ch, K-c) = (3,2) 7 h = 3, k+c=6 & K-c=2 ak=8 = K = } " Chik)=(3, 3) Hence Chik-a)=(3,3) =) K-a-8-7 Q=K-3=4-3=1 also distance between (3,2) f 0,6 s 2c

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pion - 26=4=) c=2 62 c²-0² 4-1 as c ² = Q² + b ²7 bz 3 here, the equation is: G-4² (x-3) - 1 3 For x=8.19, the value ofy is (8.19-3 2 + 3 (9-4) ² 9.9787 y-4 = 3.1589 7.1589) (02 (y=7.159

SUMMARY:

1. The hydrostatic force on one end of the trough is 37156.10 N

2.The equation of the hyperbola is (y-4)²-((x-3)²/3) = 1. The value of y for x=8.19 is y = 7.159 .