The area of an equilateral triangle is decreasing at a rate of 3 cm^2/min. Find the rate (in centimeters per minute) at which the length of a side is decreasing when the area of the triangle is 300 cm^2?

Q: Find both first partial derivatives. z = 10y?/x az ax az ду II

A: Solution-

Q: Choose the point which shows the correct location for the polar coordinate (-3, 315°). 90° WIN 150°…

A: Since the given polar coordinates are ( -3, 315⁰ ) Hence to plot the given point we have to follow…

Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

A:

Q: Use an iterated integral to find the area of the region. dy dx = y 6 5 4 3 2 1F -1 1 2 4

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Set-up the integral for the area A(R) of the region R bounded by the circles y2 + x² = 4, and y2 +…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: dy Solve dx (25 + x?)(49 + у?)

A:

Q: Graph 1 Graph 2 Graph 3 24y 6. 4+ 4. + -8-6-4 4 6 -8 -6 4 4 6 2. -4+ -4- -6. -8 -8- OYes OYes ONo…

A: Given that -

Q: mum/relative minimum or neither. ive. Then determine the intervals where f(x) concave down.

A:

Q: Find the volume of the solid generated when the region enclosed by y = Vx, y = 6 – x, and y = 0 is…

A: This is a problem related to integration. Based on the integral formula we will solve the volume by…

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

A:

Q: 4. Find the critical numbercs) for gx) =IRCX+1) t, en cuaracterize ealh, one as 1ocal min, or…

A:

Q: Find the area of the shaded region. (2,7) (0,3). 26 2/3 2/3

A:

Q: Use the method of undetermined coefficients to find the general solution of the equation y" + 16y =…

A:

Q: a²+ax+b The curve Y has a local minimum at (3, 8). Determine the values of a and b. x-1

A:

Q: Jse Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A:

Q: Simplify

A: Answer is no solution.

Q: Simplify arccot1. 4 no solution

A:

Q: Show that la 1 1 1 a 1 - (а + 3)(а - 1)3. - 1)³. %3D 1 1 a 1 1 1 a

A:

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x' + x + 1,…

A:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by y…

A:

Q: Use an iterated integral to find the area of the region. y = 4 – x2 dy dx = y 5| 3 2 -1 1 3 -1}

A: Given,              y = 4-x²

Q: graph for the function arctan(x).

A: f(x)=tan-1(x)

Q: Find the Cartesian coordinates of the point (−√2,(5π)/4)

A:

Q: Write each symbolic statement as an English sentence. p: Taylor Swift is a singer. q: Taylor Swift…

A: Following are some common logical connectives: ∨   -   Disjunction (or) ∧   -   Conjunction (and) →…

Q: Use a formula to express w as a function of t if w = s/s+4 and s = t2 + 2. w =

A:

Q: Choose the point which shows the correct location for the polar coordinate (3, –45°). 90° 512 WIN 4…

A:

Q: Evaluate the iterated integral by converting to polar coordinates. 8 - y2 Vx2 + y2 dx dy

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: p (a- )| Evaluate the Integral

A:

Q: Find the volume of the solid generated if the region bounded by the parabola y2 = 4px (p > 0) and…

A: Given

Q: Which of the following series can be used with the comparison test in order to conclu that the…

A:

Q: Sketch the region R of integration and switch the order of integration. /49-х2 f(x, y) dy dx y Show…

A:

Q: 3x – x² + 12x – 4 lim - 3x+ – x³ + 3x² + 2x – 1

A:

Q: A Ball is lauhched štraight up in the air from a height of 5 feet. Its velocity (feet/second) t…

A:

Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

A:

Q: (y + 1)dx + (4x - y)dy 0

A: Explanation of the answer is as follows

Q: Consider the curve y = 4x3. The sketch of the portion of this curve between x = - 1 and x = 8 is…

A:

Q: 4. Determine the possible pairs of values (a, b) which make the function below continuous…

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: The given function is: f(x,y,z)=x2+y2+z2 which is to be minimized with the constraint function…

Q: Evaluate the integrals. Use a capital C for any constant term. 5x + 6) dx = Preview syntax error…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: A lacker 20 feet lon3 is Kanin3 azainst th Wall of a house, The base Of the ladder iS PUICA allay ot…

A: According to the question diagram will be as below Given: dxdt=3 ft/sec To find: dydt

Q: 12) What is the value of A+B in the following ellipse? The points are foci. a) 30 B) 20 c) 15 d)…

A:

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

A:

Q: A joint density function of the continuous random variables x and y is a function f(x, y) satisfying…

A:

Q: 1. The area of a circle decreases at a rate of 3 feet square a. If the circle starts at a radius of…

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

Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

A:

Q: Identify the range of arctan(x) so that the relation is a function. ) - TI< y< 7[ 00<y<

A: here range of arctan(x) is -π/2 to π/2 because if we put π/2 it give infinte value  so range…

Q: 10. (Section 4.4) Find the area of the region bounded by f(x) = x² + 3x + 1 and g(x) = 6x + 1.

A:

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: A circle is inside a square.The radius of the circle is decreasing at a rate of 4 meters per minute…