Hie Apply Heun's methad with N=10, h=02, t,= 021, and wo=0.5 to appnmote the Sola tin d I:v.p y=y-t+\, ostsz, ylo) = 0.5

Q: Find the length s of the spiral c(t) = (t cos(t), t sin(t)) for 0 < t < 7n. Hint: Use the formula 1…

A: step:-1 Formula of length of curve say s(t)=x(t), y(t) on [a, b] is L=∫abdxdt2+dydt2dt Given that…

Q: O Find the arc leng tnof fe curre the at 6 t on the intenel OLAL3 1/4

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Q: carth quate intesly This Scole of earthquate intesity ramges fram This scole I to t ll

A: Modified Mercalli intensity scale

Q: HW #25 Geomety SL. what additional in formation is needed t Prore that these 2 A's are by SAS…

A: Consider the following figure: TD¯≅SG¯MD¯≅SL¯

Q: Not yet answered 3 Jl dy let y = In(csc a – cot z), then is dr :Select one 1 .a CSC a - cot æ sec a…

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Q: ds Q. Find Jc 2 + y² + z?" where C is the helix x = a cos t, y = a sin t, z = bt, 0 <t < 1.

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Q: The common area between the cardioid r = 1+ cose and the circle r = 3cose is: Select one: (1+ cose)?…

A: For cardioid  θ=0,   r=1+1=2 θ=π2,    r=1+0=1

Q: The bending moment, M, varies with distance, x, from one end of a beam according to: 1 M = - zwx? +…

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Q: Find the length of the spiral c(t) = (t cos t, t sin t) for 0 <t < 2n to three decimal places. Hint:…

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Q: Using the convolution theorem, to find 1 LT+1)(s²+1) +sin t-cos t O e'+sin t-cos t 2 e-sin t-cos t…

A: The given function is                      L-11(s+1)(s2+1)

Q: A tann ,intially connista of fure water, A solution into the tann at a rate cf 3'gal/ng uxtyre flóws…

A: Let y(t) is the amount of salt in the tank at any time t.

Q: EX: Show that o dz =2TL whcre CIS a unit Circle. Sal: Z= re. io dz = ire do ig ir e de %3D = 2i Note…

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Q: Given R(t) = 4 cos ti + (1+ 3cost)j +5sintk. Find the arc length of the portion of R(T) from t=0 to…

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Q: The area A of a triangle with sides of lengths a and benclosing an angle of measure u isA = 1/2 ab…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: VPu × (1 – Pu) (0.50) ( ) d.f. 117 (116) (о.03) 322 ( ) ( ) ( ) denom. tobtained AUC (0.65) (O ( )…

A: The table provided in the question is The necessary calculations are given below.

Q: Which of the following is(are) true? (Choose all applicable answers.) O cosh z = e +e* 2. O coth a e…

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Q: O with n=4, 20timaste S°(ax-)dx using the Trapezeidal -3 Approxi a i mation and Simpsen's Ru le .…

A: Answer

Q: Is AB a tangent to OC? 29 C 10 A Your answer: nt o Yes, AB is a tangent. No, AB is not a tangent.…

A: We have to check

Q: Find T N ¢B for the carve at the indlicated pont Carレe posnt r(t) = at

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Q: If the area enclosed by the curve z = 5 cos t and y = 5 sin' t (where te R) is A- then what is A?…

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Q: We have e+y dA = n(e-2) where B is the interior of t radius 2 and centered at the origin. Select…

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Q: Given: R(t) = (cos t + t sin t) î + (sin t – t cos t) ĵ + t²k^ , t 2 o What is the total distance…

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Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

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Q: While evaluating the approximate value of 20 x² dx, using Trapezoidal rule, taking 3 h = 0.5, the…

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Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: 2. In 00, AE is tangent to 00 at E, mZBCF = 112 and mBE:mDE = 3:7. Find: (а) тBЕ (b) mZA E A В C (c)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: The þaramehc equalion of the unde x+ =9 is ☺ x = 9 cost, y=9 sint X = 3 cost, y= 3sint X = 3 cost,…

A: A circle is a two dimensional  shape an it is  a closed curve . A set of all the point are at the…

Q: Find T(t) and N(t) at the given poi: x = e cos t, y=e' sin t, z = %3D %3D T(0) = N(0) = %3D

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Q: 4) By Diskuethod Detremin the volup Hiw Dx=1 and lnes y=1 aboat x=0 2) fex) = x? and line y:1 in the…

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Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: 3. Given that g(r, y) = x² + y? subject to ry = 1, show that g(x, y) has no maxi- mum points. (Hint:…

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Q: Given R(t) =4 cos ti + (1 + 3cost)j + 5sintk. Find the arc length of the portion of R(T) from t = 0…

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Q: 4) Given: AB is an external tangent to Q0 and 0Q at points A and B, radi for O0 nd OQ are and 12,…

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Q: Find the length and the cuur vature of the Smooth eurve rCt) = (snt)i t(5 cost); + (sint)K from o to…

A: Given curve is rt→=sinti+2costj+sintk and given t from 0 to 2π We have to find the length and…

Q: Calculate the angle of twist for the solid steel shaft in the Figure below. Let torque be T 11.3 x…

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Q: Blid E8ne thất iš čut up into 2 section 4 and B, such that section A is a cone similar to the…

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Q: the back if necessary. 1. Given: OB AC at G a) If m/BOC = m LACO and CG = 35 cm, what is OC ?

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Q: 3. a) Show that the length of the arc of the curve y=f(x) where f(x) = Insecx 0sxs is 4 In(1 + vz)…

A: L= integration of [1+{f'(x)}2] from a to b f(x) = ln sec x  f'(x) = tanx   Putting the value of…

Q: Find the length of one arch of the cycloid x = 9(t – sin(t), y = 9(1 – cos(t)).

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Q: 5 From the given diagram, find (a) the length of PR, 24 cm (b) sinZQPR = 7 cm R. wol bas sups a mo n…

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Q: a cosece, y = b cot0, then %3D x? , y? A) ? b? 可 x? y? = 1 ? b? 1 B - a a If x = a sec0,y= b tan 0,…

A: Given:6. x=a cosecθ, y=b cotθ7.x=a secθ,   y= b tanθ

Q: Given z= f(x, y) is differentiable and x= e' sint and y = e' cos t ôz a) Show that + + ду ôs b) Find…

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Q: The area of the region inside the circle r = 6 cos 0 and outside the cardioid r = 2(1 + cos), a > 0…

A: Given: the circle r =6 cos θ and the cardioid r=2(1+cosθ )

Q: The position of a baseball (in ft) is represented by r(t) = 45 2ti + (2 + 45/2t - 16t2)j. Find the…

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Q: If the area enclosed by the curve x = 5 cos³ t and y = 5 sin° t (where t E R) is A, then what is A?…

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Q: E(X is called the second moment about orgin ylgn İhi

A: In this question we have to verify about the second moment about origin in the concept of mean and…

Q: Find dyldy and xz4 Sint, y² Scost, OCtca24 For which vakes Of t is Hhe cure concave puars? anguer n…

A: x=4sint  , y=5cost

Q: If the area enclosed by the curve r = 2 cos t and y = 2 sin t (where t E R) is A- then what is A? 8.…

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.