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Q: Find the laplare transfurmution of the followsng 3X+3y +5X = 25 Cost , X(0) =2 %3D 2x'- 3y' = 5 Sint…

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Q: dy Given y= cos3x, at r = 1.5 is approximately: da Select one: A. 2.933 В. 2.933

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Q: n Ix]a Ex Sxt] Lb ee calcalate the expuliond faz s in Dimear geggelkion hion ee and. b. analys

A: Given,  the linear regression analysis matrix equationn∑X∑X∑X2ab=∑Y∑XYWe need to calculate the…

Q: дz əs дz at || 11 z = e cos(8), r = st, 8 8 = √ S6 + 56

A: Solution is done in step 2,3

Q: dw given w = ² – 2y + z² and a = cos (st), Use Chain Rule to find ds -2s Int and z = 8 - - Vi.

A: Given,             w=x2-2y+z2 , x=cosst , y=-2slnt , z=s-tTo find : Use chain rule to find ∂w∂s.

Q: 2 cos Ø sinotos"0 csc0 Reuorite the expresson as a single triganometrie function whose anqument is…

A: Given: The expression 2cosϕsinϕ+cos2ϕcscϕ, To simplify: The given expression in term of one…

Q: HIf y-cos Bt, find the freauency tw)and Thke fundamental Pekied la)

A: We have to find the frequency and fundamental period for y=cos8t.

Q: find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the…

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Q: Find the area of the region shared by the cardioids r= 12(1+ cos 0) and r= 12(1- cos 0). The area…

A: General equation of the cardioids is r=a(1+cosθ) and Area of the cardioids is 6πa2

Q: Use there solue the IVP 2. of xZ dn - 24y cO g (6) = -4 y'Co) = t 4 y Cx) =

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Q: Is y c + 2 xe Colution to y" + 2y' +y=0. A Verify y= 4 cos (2x) + 6sin (2x) is a solotion to y "44y

A: We will find actual derivatives and checking by substituting in differential equation that, if it is…

Q: of the hghset of cheryt the t y temthe 2M percetaof the tres aea dy tn than ees hae ate your

A: Given that  The histogram data of heights of cherry trees. We write the given data in frequency…

Q: [AFE] Given, y = V1+ cos (x²) Find by using chain rule.

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: dx, Simpiny the dls ver using nyper ons. Select the corr oice. 2x 1 +C O None of these. 2+1 + C 2 O-…

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Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Find : b e R such that 81 / sin(b)y dS 10' whereSis the part of y? + z² 4 which is between x = 3 - z…

A: ∫∫Ssin(b)y dS=8110where S is the part of y2+z2=4 which is between x=0 and x=3-z in the first…

Q: Use at least 6 decimal places of accuracy 1. C sin (z² + 2) dx using n = 6 2. √ √² +6dz √² +6 dz…

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Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: az az Use the chain rule to find and as at sin(8) = r = st, 0 = s + t4 az %3D ds az %3D at Submit…

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Q: de B: Evaluate the 2m a-cos20 when z = et and Iz| = 1. %3D

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Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: D. Use the Wronskian to detcrminc whether or not the vcctors arc independent or not (the answer for…

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Q: const at Verify 4=(e~x-I is the gereral solticn

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Q: H.w Evaluate;- Cos TT lt-1)idt

A: To evaluate:  1) ∫-∞∞δt-2e-tcosπt-1dt2) ∫03∫-∞∞t2+4δt-τdτ dt

Q: The coefficient of sin(2x) t F(x) =(cos() is Blank 1 (use fraction form not decimal no space) in the…

A: To determine the coefficient of sin2x in the antiderivative of Fx=cosx26.

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: Determine the value of k which will make h' (7/4) = 6 when h(r) = ln (cos z) + kr. %3D O 5

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Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: The antiderivative of Cos(3x) is Blank 1 (use small letter no space)

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Q: @lProve f A=3i+ rotating an ang

A: we have to prove that the length of the vector 3i+2j+k does not change when rotating the axes around…

Q: 2- FIND f (t) or fis) AS APPRO PRIATE A) L}Je costdt COS ) y+2メ=8(t-)0)00)=イ

A: Here we use basic definition of Laplace transform

Q: a) (dx pcG) V ZxqG))3x (pG) V96), Pore this bis the converse of t he implication above correct!

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Q: The general Solulion of diffentional eguatun (D² + 20 +5)y= Cos he

A: given differential equation can be writen as:(D2+2D+5)y=coshxy''+2y'+5y = coshx

Q: Exercise: Answer the following by finding dy/dx. 5sin-lr cosh x (a) y = Vsect x + In 7 4 (b) + In y…

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Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: Given f(x, y) = 7æ° cos (y*), find .9 COS fzy(x, y) = fyy (x, y) = %3D

A: Given  f(x, y) = 7x9 cos(y8) To find fxy, fyy

Q: UCe the Vmit de fi miおもn of rhc aefrile へとgral, im ; fcxi)x - 5fしょsdx」 to prove hat ハう fex) dx= -…

A: Prove ∫abf(x)dx=-∫baf(x)dx using the limit definition of the definite integral as follows. By limit…

Q: Find of y So that the -2.४) ०९५ the vame A (3,4); B co, 4) Collinegr 9nd

A: The detailed solution is given below Thank you

Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…

Q: 3. m y(t) + k y(t) = Fo cos ot, while o # wo; y(0) = yo, y(0)= 0 [ y(t) = (yo - A) cos oot + A cos…

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Q: dz az Use the chain rule to find and as sin(8) r = st, 6 = s + t3 = az %3D as az %3D

A: Given:- z=sinθrr=stθ=s3+t3 To find:- ∂z∂s and ∂z∂t