A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree at the rate of 2 ft/sec, how fast is the bottom of the ladder being pulled away from the tree when the bottom of the ladder is 9 ft away from the mango tree? Oft/sec ft/sec ft/sec Oft/sec

Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

A:

Q: Question 9 Evaluate: lim1 (3-2x)tan (37) O e O None of the choices 01 e 3r O ∞

A:

Q: An open-top box is to be made from a 12-inch by 18-inch piece of plastic by removing a square from…

A: We can find the value of x by using the second derivative test.

Q: xdx √2x-1

A: This question is related to indefinite integration, we will solve it using given information.

Q: A graphing calculator is recommended. (a) Find the vertical asymptotes of the function y = x² + 2…

A:

Q: √4x²(x³-5) dx = x³ (x¹2 - 25x² + 250x6 - 1250x³ +6250) + c O 16(x³ - 5)4 + c O(³-5)5+c O (2³-5) 5+ c

A: See the details solution in below

Q: implicit

A:

Q: H.W: show that the equations are homogeneous and solve: 20 2. x² dy + (y² - xy)dx = 0

A:

Q: əz дz Find and ax if z is defined implicitly as a function of x and y by the equation ay + +z6+…

A:

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized? |

A:

Q: What is the exponential growth rate change of an investment that has a b=1.92?

A:

Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

A:

Q: 5- Evaluate: f Sin (2x7 - 3) dx x6

A:

Q: g(x)=x5bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: Given a=15, b=12 & c= 15

Q: Find dy/dx for: y cosy = xy Y O -y sin y+cos y-x Y cos y-x Y -y sin y-x 1 cos y-x O O O

A: Given :y cosy= xy

Q: 7. Thirty two teams join a beach volleyball league. The league is split into four divisions where…

A: How many games should be scheduled in total for the league??

Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for -5≤x≤5 f(x)= 2x…

A:

Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: 300 150 Find lim f(t) and t-4- lim f(t) = t-4- lim f(t) = t-4+ 4 lim f(t). t-4+ mg mg 8 12 16 t

A: Follow next step

Q: If the first-quadrant area bounded by the parabola y = 4 - x² will revolve about the x-axis, the…

A: Given curve, y=4-x2 Portion of given graph rotate around X axis in first quadrant, Therefore Put x=0…

Q: analyze and sketch the curve y=x² / (x-1)

A:

Q: Determine if the function f(x) is continuous and/or differentiable at x = 2? x+10 for 2≤x≤2 f(x) =…

A:

Q: g(x)=x-bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: We have to solve given Questions.

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Concept: Exact differential equation: For the differential equation of the form Mdx+Ndy=0 If ∂M∂y=…

Q: 18.f √25-4x² X -dx

A:

Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

A:

Q: dy 1+x²)²e³ = -2x dx

A: Topic:- differential equations

Q: Verify that the indicated function y p(x) is an explicit solution of the given first-order…

A:

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A:

Q: Determine whether or not the following limits exist (explain why or why not): x² - y² a) lim…

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: 1- Calculate the area of the region which is bounded by: y = (x - 1)², y = (x-4)2, and y = 0.

A:

Q: (10. a = [-1, 5,2], b = [3, 2,-6], and c = [1, -4,-2]. Calculate the following: a) axb b) a b × c c)…

A:

Q: (D³ - 2D³ – 2D² – 3D − 2) y = 0 - - -

A:

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A:

Q: Let h(x) = tan(3x + 4). Then h' (2) is and h'' (2) is

A: The function is given by hx = tan3x+4 To evaluate: The values of h'2 and h''(2)

Q: + 75 3-4x Evaluate lim x-4 1 -4x-6 + Enter an exact answer. Provide your answer below: 13

A:

Q: 4. Let v = (v1, v2, v3), w = (wi, w2, w3) be two non-zero vectors not on the same line in R Suppose…

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

Q: 28 Suppose cos(x) = and csc(x) < 0. Give all answers as exact values (no decimals 35 a. The terminal…

A: Use Trigonometric identities

Q: Find F(s). ℒ{e−8t cos(6t)}

A: To find the laplace transform of the given function.

Q: Solve cos(x) = - 0.73 on 0x < 2π There are two solutions, A and B, with A B A: B = ||

A:

Q: Evaluate • 622 dV where G is bounded by r+ 2y + 4z = 8 in the first octam

A: Given problem:- Evaluate ∫∫∫G 6z2 dv where G bounded by x+2y+4z=8 In the first octant

Q: A farmer finds that if she plants 100 trees per acre, each tree will yield 45 bushels of fruit. She…

A: Here we will find the number of trees per acre to maximise harvest,

Q: Evaluate O √x(1+x²) dx 2 x1/2 1 2x¹/2 O O 2,2/3 3 O 3x²/3 2 + 2x¹/2 + C x1/2 + +C 2 2x5/2 5 5x5/2 -…

A: Note: Every options given by the question are incorrect. I am 100% sure about it.  The correct…

Q: Find all solutions to 2 sin(0) 0 = = - 1 on the interval 0 ≤ 0 < 2π

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: (Use symbolic notation and fractions where needed.) side of base: 6 height: 6 minimal surface area:…

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Prove that if i and k are relatively prime positive integers, for every positive integer l the…

A: Concept: Number theory: Number theory is an area of mathematics that aids in the study of the set of…

Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…