Let x(t) be the displacement of an object, attached to a vibrating vertical spring with one end fixe from the equilibrium position. Which of the following differential equations allows to model this mass-spring system in which the effect of mechanical resonance occurs? a) z" – 144x = -21sen(12t) b) z" + 144a' = –21sen(12t) c) æ" – 24x' + 144x = -21sen(12t) d) æ" + 144x = -21sen(12t)

Q: An open tank has the shape of a right circular cone (see figure). The tank is 8 meters across the…

A:

Q: Find approximate value of the derivati f(x0)-6f(x,)+3f(x,)+2f(x,) f'(x2) = 6h f(x) = 10 sin(20x²) Ax…

A: Solution :-

Q: Find the inverse transform of the given functions: 5s+3 6s 8 F(s) (5s2+4s+1) s2+7 9.

A:

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2+ 5n, express an in terms of n.

A:

Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

A:

Q: Find the Fourier Series Expansion of the following periodic functions.

A: Given function is f(x)=x3, 0<x<c Let the Fourier series be…

Q: 27. у" — 2у - 2y' 8xe2x. %3D

A:

Q: The standard running track size for track and field events is 400 m. The track consists of two…

A: Given that: Size of the track = 400 m Area enclosed = 9430 m2

Q: What are the points in an elliptic curve y2=x3+ 12345 x + 23456 (mod 23459) at x=1? Use one of those…

A: As per the question we are given the following modular elliptic curve : y2 = x3 + 12345x + 23456…

Q: (a) i) Prove that 1 sin20 1 tane 1+ sin20 1+ tane for 0<0 <- 4 ii) Hence, show that the exact value…

A:

Q: Question 12 Express the area of the given surface as an iterated double integral, and then find the…

A:

Q: Suppose p and q are distinct prime numbers. Find the nor q divide x. number of positive integers r <…

A:

Q: Fit the following data points using Lagrange Interpolating polynomial. Round off values to 4 decimal…

A: The interpolation polynomial for n point can be calculated using the formula:…

Q: Find the inverse transform of the given functions: 3s2+5s+5 1. F(s) = (s3+8s2+19s+12)(s³)

A: According to guidelines I can do 1 question at a time.

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: We have to find the volume of the solid  by Disk Method when the region enclosed by the given curves…

Q: Find: 1 s³ – a 23.

A:

Q: 1 5. L{3e Зе sin? t 2

A:

Q: 1. Set up the following improper integrals by definition. sin(x) xe-x³ dx dx 2? — Зх — 4 а. с. 7 et…

A: Solution b: Given integration is ∫17exx-1dx Here 1 is the only point of infinite discontinuity So we…

Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: 3 b.

A:

Q: Use a triple integral to find the volume of the region bounded by z = 7x + 4y, z = 5, and the planes…

A:

Q: 2e* xy" - (2x + 1)y' + (* + 1)y %3D * ond ex ore linearly indenerndent

A:

Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: Consider the continuous function f: R →R, the graph shown below, if we know that a,b,c x1, x2 , X3…

A:

Q: Which line passing through G is parallel to line IEC? 34 H CGJ BGH AIG O EFG

A: To find the line passing through G is parallel to line IEC .

Q: Evaluate the triple integral. TY sin(yz) dV, where G is the rectangular box defined by the…

A:

Q: 4. Calculate the arc length of the polar curve r = e38 from 0 = 0 to 0 = 2.

A:

Q: Determine the Fourier transform of x(t) = eiu(t) and sketch the following: (a) |X(w)| (b) ZX(@) (c)…

A:

Q: tm 5.39x10 -42 ^ 539 mm a 23x23 mm

A: To do the conversion we use the following: 1 metre = 1000 millimetres  i.e., 1 m = 1000 mm

Q: Use the Midpoint Rule for the triple integral to estimate the value of the intergral, Divide B into…

A:

Q: Which of the following statements is/are a restatement of Euclid's Fifth Postulate? 1. Through a…

A: Given information is I.  Through a point P not on a line l, there exists exactly one line parallel…

Q: 11. 10290° / 402-40° 12. 1/200290°

A:

Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

A:

Q: Use the mixed congruential method to generate a sequence of 32 random numbers with Xo=8, a=9, c=13,…

A: By mixed congruential  (µ) method Xn+1 = (aXn +  c) mod (m) Rn = Xn /32

Q: (9) Let Jo if x2 < y < 2a2, f (x, y) = 1 otherwise. Then, which of the following statements is…

A:

Q: Use the Midpoint Rule for the triple integral to estimate the value of the intergral. Divide B into…

A: We have to use the Midpoint Rule for the triple integral to estimate the value of the integral.…

Q: Perform the change of variables indicated in the problem to obtain the general solution to the…

A:

Q: Find a Maclaurin series expansion for f(x) = e- 2x

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

Q: 15. Let x = (x1, x2). Using the feature mapping show that *(2,3)·¤((4,4) –-(2,3)·(4,4)*

A: Given that for x=x1,x2, the feature mapping is…

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (-3, 3) and (- 3, – 3).

A: This is a problem of locus and analytical geometry.

Q: Solve the differential equation d?y dy 3+2y -t = 0 dt2 dt subject to the initial conditions that…

A: The second-order differential equation given is as follows: d2ydt2-3dydt+2y-t=0 The initial…

Q: The line y= X+2 and the curve y= x contain bounded region between them. Find the volume of the solid…

A: The volume for solid of revolution between curves is the volume of object between a curve f(x) and a…

Q: Compute f(x)dx 2x if x <1 4 if x21 f(x) =

A:

Q: According to building specifications and physical measurements, the maximum weight that foundation…

A: If x is directly proportional to y, then it can be written that x ∝y or x=ky. Here, k is the…

Q: - TT < x < TT; function, f(x) = cos(x/2)

A:

Q: f (t) = v1+ sin t + (8t)15 + t² cos 3t

A:

Q: Use Romberg integration to compute dr correct to three decimal places.

A: Given integration is I=∫01dx1+x Let f(x)=11+x Here a=0, b=1 if we take 1 subinterval, then h=1-01=1…

Q: (5) If z = xf (2) +g (2), then the value of Z. + 2xy- + y?. is Əxdy (а) -1 (b) 0 (c) 2 (d) 3г

A:

Q: Linda bought an 8 foot long piece of framing to frame her 2 college awards. One award is 8.5 inches…

A: Convert 8 foot in inches.

Q: In Holland, 70% of the people own a car. If five adults are randomly selected, what is the…

A: