A 16ft. ladder leans against a wall. The bottom of the ladder slides away from the wall at a rate of 2ft./sec.. How fast is ladder sliding down the wall when the base of the ladder is 6ft. away from the wall? ft./sec.. Round your answer to three decimal places.

Q: Compute the gradient of the following function, evaluate it at the given point P, and evaluate the…

A:

Q: Find the slope passing through the two given points. 1.) (-4,-3) and (-7,-7)

A:

Q: Apply the Second-Derivative Test to find all relative extrema of the function  f(x)=cosx-x ,…

A:

Q: Consider the function below. x + 4 f(x) +4 (a) Find the exact value of the maximum of f. f(x): = X =…

A:

Q: Let y = 3x². Find the change in y, Ay when x = 3 and Ax = 0.3 Find the differential dy when x = 3…

A: The given function y=3x2 We have to find ∆y and dy.

Q: (d) Give one example to illustrate that vectors satisfy the triangle inequality. Justify your…

A:

Q: 5. Set up a triple integral to find the volume of the tetrahedron that has vertices (0,0,0),…

A: Given vertices ( 0,0,0 ) ( 0,0,4 ) ( 3,0,0 ) ( 0,4,0 )

Q: Given the following graph a. Evaluate f (3). f(3) = Number b. Solve for f(x) = 3. n ril H Submit…

A:

Q: Find an appropriate change of variables (and then use it) to evaluate 1/₁₂ (x + y)² ex²-y² dx dy R…

A:

Q: (c) Let F(x, y, z) = x^3i + y^3j + z^3 k i) ∇ · F (ii) ∇ × F

A:

Q: Calculate the gradient of f(x, y) = cos(x² + 3y) Vf= A

A: To calculate the gradient of the function.

Q: Use the Newton's method to find the positive root of equation x² -2=0 to three decimal points.

A: we need to find out the positive root of equation using Newton's method.

Q: Find the absolute maximum and minimum values (show final answer as an exact value): f(x) = 2-sin r…

A:

Q: Using Rolle's theorem for the following function, find all values c in the given interval where…

A: Given query is to apply rolle's theorem.

Q: Consider two nonnegative numbers x and y where x + y = 2. What is the maximum value of 11x²y? Enter…

A: Let's find maximum value of function.

Q: sin (=) functions of u and v. If z = sin( дz du дz Əv and x = In(u) and Y v4, find the following…

A:

Q: Consider the function f(x) below. At what value(s) of x are the inflection points? Enter answer…

A: for inflrction points  put   f''(x)=0d dx(xn)=nxn-1d dx(constant)=0

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) J- sin(2x) 14 + cos²(x)…

A:

Q: Question One (a) Let U = 3i-j-4k and V = -2i+4j-3k. Show that U-V is commutative but U x V is not.…

A: “Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Find the most general antiderivative F(x) given the function below. f(x) = -10 sec² (x) - 6 csc² (x)…

A: ∫sec2dx=tanx+c∫csc2dx=-cotx+cwhere c is constant of integration

Q: SHOW COMPLETE SOLUTION Find the points of intersection between the circle (x-2)²+(y-6)² = 40 and…

A:

Q: Identify which of the following formulas applies to the future value of a series of payments, with…

A:

Q: Given z = = f(x,y), x= x(u, v), y = y(u, v), with x(3, 3) = 5 and y(3, 3) = 4, calculate zu(3, 3) in…

A:

Q: "roblem 9. True or False. Explain your choice carefully. is convergent. nv2, n = 1, 2, 3, ... is…

A:

Q: n = 1 10" 4 +97

A: To determine the convergence or divergence of the given series.∑n=1∞ 10n4+9n

Q: Suppose that you have open a saving account with initial deposit of $ 5000, you continue to deposit…

A:

Q: +00 2 e. Se Sexx²dx 0

A:

Q: Given A [3] find the determinant

A: To find the determinant of given matrix.

Q: Ive the trigonometric equation A. B. C. D. 36.5°, 83.5°, 156.5° and 203.5, only 70.5°, 190.5° and…

A:

Q: Use a geometric series or the nth-Term Test to determine the convergence or divergence of the…

A:

Q: = 4x + 5 At what point (x, y) is the function f(x) closest to the point (4, -8)? Enter an exact…

A: Topic-  Application of derivatives We are given a function f(x)=4x+5 And a point (4,-8)

Q: Estimate the area under the graph of f(x) = x² + 4x + 1 over the interval [ – 3, 0] using five…

A: Here we have given a functionf(x)=x2+4x+1. Now plotting the graph of the given function we get.

Q: A non-native species of fish is introduced into a lake and is attacking a certain type of native…

A: Given Native: x(t) = −447.94t3 − 5250t2 + 44992t + 150000 Non-native: y(t) = −589.14t3 − 0.7t2 +…

Q: 2. Obtain the general solution by the indicated technique: separation of variables 2.1…

A: 2. According to question,2.1 Given Differential equation,2a2-r2dr =r3 sin θ dθ,We have to solve this…

Q: Use completing the square in order to put the followingation into te of the standard quadratic…

A:

Q: have found the minimum distance using the second derivative and write a thorough conclusion. to a…

A: Given:    Curve      y=lnx2   Let x,y be point on curve             Another point is 52,0 We know…

Q: Use the graph of the function to estimate the interval on which the function is increasing. y -SA-…

A: Increasing Function:  If f(x) is a function, and x1 and x2 are any points in the domain such that x1…

Q: (b) You are given the point (-2, π/4) in polar coordinates. (i) Find another pair of polar…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Evaluate sin (945°) without using the calculator. 1. 2. INGNINGS- 3. 4. 5. None of these 1 6. 2

A:

Q: Determine whether the integral is convergent or divergent. 3 36 √3-x O convergent O divergent dx If…

A: Given integral:- ∫23363-xdx

Q: (9) Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 3. Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the given…

A:

Q: 21-22 Find y' and y". 21. y = x² ln(2x)

A:

Q: Find the critical points of the function x3 ² + 2x² - + 2x² - 12x. 3 Use a comma to separate…

A: for critical points  f'(x)=0d dx(xn)=nxn-1

Q: If I cut a Pizza into 2 equal pieces, How long is the crust(circum.) is each piece??? Smidget Radius…

A:

Q: 2. 3 (D-9)³y=0

A: Let's solve given diffential equation.

Q: When coughing, the windpipes contract to increase the velocity of air passing through the windpipe…

A: We need to find out the v'(r), value of r that maximizes the velocity of air and v(rmax).

Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A: To find the exact surface area.

Q: In step 3, how did you know to use yp = ( 1 / (D^2 + 9) ) 4sin(2x)?

A: The given initial value problem y''+9y=4sin(2x), y0=1, y'0=1. We have to find the solution of the…

Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: lim (cos(9x))(+2)…

A: d dx(lnx=1xd dx(cosx)=-sinxd dx(xn)=nxn-1sinxcosx=tanx