1. A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 1.5 m/s, determine the differential equation which describes the motion. Assume that positive displacement is downward.

Q: x Q3: Show that csch-¹ (²7) = coth-¹(x+¹) x-1,

A:

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: 24) Find dy /dx for the following functions : a) y². cotx= [sin(x,y)]-¹ b) y = (lnx + x) tan x

A: Given: a)y2·cotx=sinxy-1b)y=lnx+xtanx

Q: Find the intervals where the function 1 f(x) = 2cosx + sin2x, 0 ≤ x ≤ 2π is concave up.

A:

Q: T 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

A:

Q: Q2// Find the resulting volume of the curve y = sin x cos x rotation about the x-axis if x=0, x=/?

A:

Q: 3 -6 -4 -3 4 Let y = V1 = 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁ and…

A: Let, W be the subspace spanned by v1 & v2 . Now, calculate the distance:…

Q: Consider the function below. (If an answer does not exist, enter DNE.) C(x) = x¹/5(x + 6) (a) Find…

A: Let's solve.

Q: 6. If q p² p³ - 1 9² p2 µ³ – 1 1 = 0, show that pqr = 1. - 22

A:

Q: Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of…

A:

Q: given the following equation: 36y^2-4x^2=144.  a) determine if the function is an ellipses or a…

A: This question can be solved using the concept of conic section.

Q: Determine if the following operation on the two given matrices is defined, and if it is, determine…

A: We have to determine if the following operation on the two given matrices is defined, and if it is ,…

Q: In(y) = −3x² + ln(7)

A:

Q: If we have a valuable F(x) find: fro f(x) dx = −cscx + c

A:

Q: 6. Find the general solution of the PDE. The solution u is a function of x and y. Ux=x-yz +y³

A:

Q: Evalvate 5x-12 X (x²+4) dx

A:

Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

A:

Q: Consider the function below. ex f(x): 8 + ex (a) Find the vertical asymptote(s). (Enter your answers…

A:

Q: Find the derivatives of the following functions as specified: f(x) = sin(cos r), f"(x)

A: Given: so,       f'(x)=sincosx'         =coscosxcosx'          =coscosx-sinx         =-coscosxsinx

Q: on with a nonremovable discontinuity at x=4 on with a removable discontinuity at x=-4 on that has…

A: Answer is in next step . please give a like !!

Q: By using the differential operator D and it's inverse, solve this equation: y"+y=sin(x)

A: Follow the procedure given below.

Q: find the area of the region bounded by the curve y = x^3 and the line y = 8 using   a. vertical…

A:

Q: Evaluate the following integral by using Odd and Even Powers Method: y = cos(x) dx =

A: If power of cos(x) is odd then put sin(x) = t and reduce the integrand in terms of 't' and then…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: We have to determine the value of initial amount

Q: 0=yج - - لا

A: Follow the procedure given below.

Q: Simón wants to build a rectangular pen for his animals. One side of the pen will be against the…

A:

Q: x-8 7 Consider the lines 1₁: x = 1 + 3t, y = 2 + 3t, z = 3 - 10t and 1₂: a) Find the point of…

A: Given problem:- Consider the lines l1 : x = 1+3t, y = 2+3t, z=3-10 and l2: (x-8)/7 =(y+1)…

Q: Solve for x: |x+5| < |X-71

A: Follow the procedure given below.

Q: dx 4 sin x 3 cos x

A:

Q: R: y = 2x +1,x+y=7,x = 8

A:

Q: A baker sells cupcakes and bases her prices on the number of cupcakes purchased. 72Total Cost 66 60…

A:

Q: II. Use the differentiation rules to solve for the derivative of each function. Show your complete…

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

Q: Determine whether the statement is true or false. If it is true, explain why it is true. If it is…

A: Here we have to choose the correct option.

Q: // لاح - لا - لا -4

A:

Q: The value of the following limit Lim (cos(x) cot(x) is: AL

A:

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t².

A: Given: Now,        z=2xy-x2y2  =22tt2-2t2t22  =4t3-4t6

Q: By using the unlimited coefficients method, choose the correct answer for this equation…

A:

Q: 2. In π 2 π ln - 4 e* cos(ex) dx

A:

Q: In a random check on an assembly line, the probability of finding a defective item is 0.005.…

A: This question can be solved using binomial probability distribution.

Q: det Evaluate +4 in 3 -α a. 1.107 O a O b O C Od O e b. 1.249 c. 0.491 d. 0.393 e. none of the…

A: To solve the following integral using substitution

Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

A:

Q: ²²1559 1≤ y ≤9 Find the length of the curve_x==y 3

A: If if x is a function of y then  the length of the curve is L=∫ab1+dxdy2dy   over the inetrval a≤y≤b…

Q: (a) Given functions f(x) = 3x+2 and g(x) = x³ - 1, find fog and the inverse of fog. 4. (b) Use the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: Suppose that the polynomial function fis defined as follows. f(x)=(x-13)²(x-8)³(x+4)³ List each zero…

A:

Q: Write an augmented matrix and use elementary row operations in order to solve the following system…

A:

Q: dy 1. Determine for each of the following. Do not factor but simplify where appropriate. dx a) y =…

A:

Q: i/ - y - y - 6y = ex - الا و

A: Given

Q: m 1 Let x be a continuous random variable over [a,b] with probability density function f. Then the…

A:

Q: 1. The function shown A. is continuous at x = 2 B. has a limit that exists at x = 2 C. is…

A: solution is given below

Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

A: