A bullet fired from a gun follows the trajectory x = at, y = bt – 16t2 (a, b > 0) Show that the bullet leaves the gun at an angle 0 = tan- (). ab from the origin. 16 and lands at a distance

Q: Find the length of the curve. The cardioid r= 3(1- sin 0)

A:

Q: The curve y = tan x crosses the line y = 2x between x = 0 and x = pai/2. Use Newton’s method to find…

A:

Q: Use the trapezoidal rule with n = 5 to approximate 3 cos(x) -dx Keep at least 2 decimal places…

A:

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

A:

Q: Let A be a curve defined by the equations 3 x = 3t2 – 4 and y = sin (-nt). Set up (do not evaluate)…

A: Here, the given parametric curve A is: x=3t2-4, y=sin-32πt Now, to find the arc length of A from…

Q: tan 44.1°

A:

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

A:

Q: Suppose a particle has velocity given by v(t)=sin(t). What is the net displacement of the particle…

A:

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

A:

Q: The angle between tangent and the radius vector of the curve r 5(1- sin@) at 0= is %3D

A:

Q: Approximate (a) arctan 0.95 and (b) arctan(−1.2) using the linear approximationtechnique

A: Use the following steps shown below to find by using linear approximation technique. First see the…

Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

A:

Q: Find the length of arc from (0,0) to (4,4) of the curve x = 2/y.

A: given curve     x=2y            we have to   find the arch length fro (0,0)  to  (4,4)now  x=2y ⇒…

Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

Q: Determine the second moment of X about origin

A:

Q: The roots of Characteristic equetion of a thrrd oreler, lineor homapeneous-equation with constaut…

A: Consider homogenous differential equation with constant coefficient:…

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

A:

Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),…

A: We have to find dsdtt0=π4

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: The force on a particle is described by 4x +1 at a point x along the -axis. Find the work done in…

A: Given  Force F = 4x3+1

Q: Sketch the graph of two functions g(x) = cos x and h(x) = on the same plane. Choose [a, b] that…

A: Given g(x)=cosx and h(x)=x/2

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: Find the angle between the radius vector to the curve r = 2a sin 30 and its tangent when 0 = /6.

A: The given curve is r and differentiate with respect to theta:

Q: Sketch the graph of two functions g(x) = cos x and h(x) : plane. Choose [a, b] that satisfied |b –…

A: Given function is g(x)=cosx and h(x)=x/2

Q: Compute the point of intersection of the curve sinx and x-1 with the help of Bisection method. Ans.…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Use Newton's method to estimate the solution to sin(theta) = 1- theta/2 up to four iterations.

A: Given function is: f(θ)=sinθ+θ2-1 Rewriting function in other variable: f(x)=sin x+x2-1 Newton…

Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Find an approximation using linearization techniques. Please do not use the table of values.…

A: Given, Using the linearization technique to find the  approximate value of sin (3.19)

Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Jz sin 0 do 2

A:

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

A:

Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

A:

Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

Q: Differentiate: arctan(cosh(x)) Show all working out.

A: to find the derivative of arctan(cosh(x)) proceed as follows we know that ddxtanx=11+x2  apply chain…

Q: Find the points on the givern curve where the tangent pairs.) 7= 6 cos(0) horizontal tangent (r, 8)…

A: Consider the given Curve, r=6cosθ Find the points on the given curve where the tangent line is…

Q: Determine the speed (in meters per second) of a particle with a trajectory (2 sin (3t), 9 cos (3t)),…

A: Consider the given parametric equation of the trajectory of the particle, 2sin3t,9cos3t so we can…

Q: Find generul solution ý +y tan (x) = see (X) - sec %3D

A:

Q: Use a linear approximation to estimate sin 29°

A:

Q: Let C be the curve which uses straight line segments to travel from (0, 0) to (0,1) to (2,0) and…

A: The curve C is the line segments travels from 0, 0 to 0, 1 to 2, 0 and then back to 0, 0. Draw the…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

A:

Q: Use an appropriate local linear approximation to estimate the value of sin(31°).

A:

Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,