A right triangle has legs of 15 inches and 20 inches whose sides are changing. The short leg is decreasing by 4 in/sec and the long leg is shrinking at 8 in/sec. What is the rate of change of the hypotenuse?

Q: (5.) Let u(x, y) = ln(x² + y²) (a. (c. State the domain of u: Determine lim f(x, y) (x,y) →(1,0)…

A:

Q: what does f'(m) = ?

A: We need to provide meaning of f'(m).

Q: Which of the following limits does not yield an indeterminate form? 4x3 x0 cos(x)-1 (A) lim (B) lim-…

A: The indeterminate form:

Q: Find the velocity and acceleration vectors for the motion described by x=8+ t², y = 4-4t², z=4+3t².…

A:

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Question explained below:Explanation:ANSWER :​​

Q: The area of a circle is increasing at a constant rate of 88 square meters per second. At the instant…

A: The area of a circle is increasing at a constant rate of 88 square meters per second.dAdt=88 square…

Q: Please solve this vector calculus practice problem showing all the steps. Thanks!

A: Solution is done.Explanation:Approach to solving the question: Detailed explanation: Examples: Key…

Q: Suppose that the marginal propensity to consume is dC dy = 0.2 - e-0.5y (in billions of dollars) and…

A:

Q: Use the rectangular approximation with 4 rectangles, using the right endpoint for the height, to…

A: The right Riemann sum∫abf(x)dx≈Δx(f(x1)+f(x2)+f(x3)+⋯+f(xn−1)+f(xn))Δx=b−an

Q: Please don't provide handwritten solution ....

A: The correct answer is approximately D). 10,232 units. Explanation:The supply function of a commodity…

Q: pls answer using calculus

A: The pressure, P, is also changing at -2.1 Pa/s or -2.1 N/m2s (decreasing).Explanation:

Q: Write out the form of the partial fraction decomposition of the function. Do not determine the…

A:

Q: pls solve

A: Answer is in the below box. If you have any doubts at anywhere in the explanation or answer please…

Q: 1) Use the second derivative test to classify any critical points and determine whether each…

A:

Q: Please use Differential equation or intergral equation to solve thanks

A: Done.Explanation:Done

Q: i-2j +3k Find the equation of the plane that passes through the points (-3, 1, -2), (2,1,-1), and…

A: Hence Complete the solution.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: No hand written responses. I need help with a step-by-step breakdown in laymen terms for the below…

A: The estimated change in area is 515.22 mm2 (rounded to two decimal places).Explanation:We find the…

Q: Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product…

A: Cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product…

Q: Let ā= −i − 2j + 3k, b = i - 2j + 3k, c = −i +2j - 3k.

A: The given vectors .The objective is to find the vector that is perpendicular to both  and .

Q: 6. The quadratic Taylor approximation of f(x, y) near (x, y) = (a, b) is given by f(x,y) ≈ Q(x, y) =…

A: Given: To Find: To  find the quadratic Taylor approximation of .

Q: 78. Apparent discrepancy Resolve the apparent discrepancy 1 (x − 1)²|x + 2| between In dx x(x − 1)(x…

A:

Q: what does f'(m)= ?

A: We need to provide meaning of f'(m).

Q: 3. Find any vertical, horizontal, or slant asymptotes of the following functions. 7(x-3)(x+1) (a)…

A: To find any vertical, horizontal, or slant asymptotes of the following functions.

Q: Consider the following. SSTE z dv, where E is enclosed by the paraboloid z = x² + y² and the plane z…

A:

Q: B 0.439 1.189 0.189 2.189 7. Estimate the area under the curve of and the midpoint for the height.…

A:

Q: find dy/dx for: 1. y=(3x^2+3x-1)^4

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 5 If f f(x) dx false true 5 −3 and ƒ g(x) dx = 2, then [5f(x) - g(x)] dx = ƒ[5ƒ(x) 1 † 9(a) da = =…

A: We have given that ;.;

Q: Find the orthogonal trajectories of the family of curves y6  =  k x6

A:

Q: The wind-chill index is modeled by the function where T is the temperature (°C) and v is the wind…

A: Given the wind-chill index is modeled by the

Q: Please Solve Using Differential Equation Thank you!

A: Answer:The rate at which the radius of the raindrop is changing when it has a radius of 10 mm and is…

Q: K Y R = G Match each equation with a graph above y = 3(1.3)² - ✓ y = 3(1.58)* ✓y=3(0.72) y = 4(1.3)*…

A: y=3(1.3)x=blue (B) y=3(1.58)x =Orange(O) Both the above graph exponential and base is greater than…

Q: please solve using differential calculus

A: The coconut travels a distance of 59.1 m.  Here, we use calculus to derive the expression for…

Q: Let f(x, y, z) = x^2 + y^3 + z^5 and let u =. Find the directional derivative Du f(x, y, z).

A: The directional derivative Du​f(x,y,z) is 64/81​.Explanation:Step 1: To find the directional…

Q: Find the tangent to y=x²-x+9 atx=1. oy=√x²-x+9 atx=1 is y=0 The tangent to y=√1

A:

Q: Find the exact length of the curve. y = 0x312, 2x3/2 0 ≤ x ≤ 6

A:

Q: d) - dx = (x-1)² √x

A: To evaluate the following integral by using chain rule.

Q: Let f(x) = x²e19x (a) Find the critical values of f(x). (Enter your answers as a comma-separated…

A:

Q: Find any vertical, horizontal, or slant asymptotes of the following functions.

A: d) x =  4 is a vertical asymptote.it has no horizontal asymptote.y = 4x+16 is a slant asymptote e) x…

Q: Which of the following limits does not yield an indeterminate form? 4x³ lim x0 cos(x)-1 (A) (B) lim…

A: Given:we have given limits To find:which of the given limits does not yield an indeterminate…

Q: f(x) = 2 tan x Ꮖ

A: f(x)=2tan⁡xx

Q: Solve the following improper integrals. For each of them statewhether the integral is convergent or…

A: ∫0∞​xe−x is convergent and converges to 1Explanation:∫01​1−x​1​dx is not convergent by p test it is…

Q: Solve this differential equation: dy dt y(0) = 5 y(t) = = 0.2y (1 — - Y 700

A:

Q: uppose that f and g are functions such that f(5)=3, f'(5)=-2, g(5)=4, and g'(5)=-5. nd h'(5) where h…

A:

Q: Find one value of x that solves the equation by using the inverse sine or cosine function on your…

A: Ques 1 : (a) -0.253 (b) 1.328   Ques 2 : 1→b2→c3→e4→a5→fExplanation:

Q: The function graphed above is: Concave up on the interval(s) Concave down on the interval(s) There…

A:

Q: 16. Find an equation of the line tangent to the curve defined by x3+3xy+y3 = 28 at the point (2,2

A:

Q: Consider the equation ex+4y+ 5x + 16y + sin(xyz) +20= = 1 The implicit function theorem implies that…

A:

Q: Suppose that f(x) = (x + 8)(x-8)². (a) Find all critical values of f(x). (Enter your answers as a…

A:

Q: THIS IS CALCULUS (integral) in ft and lb please find the work done by the force to stretch the…

A: The objective of this problem is to find the work done by the force to stretch a spring 7 inches…

Q: dy gent of ורי זו quantity diverges,

A: