03/ The dimensions of a rectangular solid at a given instant (t.) are : L(t) 13 cm. W(t)-9 cm. H(t.) 5 cm. If (L) and (H) are increasing at 2 cm/sec and W is decreasing at 4 cm/sec. Find the rate of change of surface area at time (to).

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: 2 x= - 5, x=2, y = 5x, y =x -6

A:

Q: Suppose that f(1, y) = 2z² + 2y – zy Then the minimum is

A: We need to find minimum value.

Q: Given the function f defined as: f: R-(2} R X+4 f(x) = %3D 2x-4

A: Here, the given function is: f:ℝ-{2}→ℝ and f(x)=x+42x-4

Q: a) Prove that, the characteristic of an integral domain R is either zero or a prime number. b) Let G…

A: Please follow the next step.

Q: r(10,3,3) dx (1,1,1) dy dz. - -

A:

Q: in terms of x and y for the points (x, y) A5. (a) Use implicit differentiation to find that lie on…

A:

Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: Given that The sides Equilateral triangle are increasing at a rate of 10cm/min.

Q: y2+x2 5- y' %3D y(1) = -2 xy

A:

Q: Evaluate the following indefinite integral. dt t In(t) Note: Don't forget your C! And be sure to use…

A:

Q: Solve the following differential equation: dv = Vcoto + V³cosece OP

A:

Q: Geometric Sequence A. Find the indicated terms of the following geometric sequences. 1. 12, 6, 18,…

A:

Q: x/2 2. dy Sin x dy +34 2- X 2

A: A detailed solution is given below

Q: divide f(x) and d(x), and write a summary statement in polynomial form and fraction form:…

A:

Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

A:

Q: Findithe equation fthe plane entrining the point (7-2-5) and uperpendcular to the line through the…

A:

Q: 16x²+9y²=144, (first quadrant area)

A: ∫a2-x2 dx = 12xa2-x2 +a22 sin-1xa+C

Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: Cnudan a pundre uuofree shrse trces nre prrabolae le » k).prrabolae ly - k). and kyyorobolne g = k).…

A: To find the quadratic surface whose traces are parabola(x=k), parabola(y=k) and hyperbola(z=k).

Q: Use the tabular method to evaluate the integral |* + 2x – 1) cos(42)dx

A: Explanation of the answer is as follows

Q: Let's practice on how to complete the square because this will help us to identify whether the given…

A:

Q: dA; R= {(r,y): 0srs1,1 sys 4}.- %3D IR

A: Topic: Double integration over a region R

Q: Distinguish First Derivative of a Parametric Equation from Second Derivative of a Parametric…

A: The given problem is solved below in detail.

Q: 13. (x? — ху + у?)dх — хуdy %3D 0

A:

Q: f (x) = x³ + 4xª + 3x³ – x² + & 1. ,2 -

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: I. PROBLEM SOLVING Directions: Read and analyze the problem then solve it. 1. COVID-19 is one of the…

A:

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

A:

Q: 3. Sy'edy

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

Q: Q4: Solve the following exact differential equation: 2xydx + (1 + x2)dy = 0

A:

Q: Find the following definite integrals. sin a dr

A:

Q: You measure 43 dogs' weights, and find they have a mean weight of 34 ounces. Assume the population…

A:

Q: dy Given the equation below, find de 1722 + 8x8y + y° = 26 dy dx Now, find the equation of the…

A:

Q: b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G is…

A: Given

Q: sin (x-1) lim x+1 x2+2x-3

A: To evaluate: limx→1 sin⁡(x−1)x2+2x−3 The given limit is of indeterminant form 0/0

Q: 81. Area Find the area between the graph of y = sin x and the line segment joining the points (0, 0)…

A:

Q: Let B be the region in the first octant inside both x + y + z? = 1 and Vx2 + y² . Z. 3= a) Find the…

A:

Q: Solve the given DE: dy e* – 2x cos y eу — хx2 sin y' dx ||

A: Differential equations is solved.

Q: y"+y'=t ; where y(0)=1 and y'(0)=-2||

A: Here, the given DE is: y''+y'=t Taking Laplace transform on both the side:…

Q: Find the area of the region bounded by the graphs of the given equations. y = 20x, y = x ... The…

A:

Q: FIND THE DIVERGENCE AND CURL OF U = i (x 2+ yz)+j Cy?+Zx) t K (z?+xy] %3D

A: Given :u=i x2+yz+jy2+zx+kz2+xy.We need to find the divergence and curl of u.

Q: Differentiate each function by applying chain rule. Match each item to a choice: y = x(x² + 3)² f…

A:

Q: 7.2Find the macrorin series of f(x)=(1+x)^(1/3) , by reacthe term n=4

A: Follow the procedure given below.

Q: Show all the necessary figures and solutions to each of the following problems. 1. Find the area of…

A:

Q: Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 50L0ºK®1 where L is…

A:

Q: Зx2+2 dx 0 2x²+4x+3

A: Adjust the numerator to get the known integral form.I have add and subtract the same value to get…

Q: tan z If f(x) = then f'(x) is ? z² – 1) soc? z (z² – 1)° O (2? - 1) sec²(x) æ – 2 (tan(æ)) 2z tan z…

A:

Q: Find the volume oF the solid obtained by rotating about the x-axis the region by y= x' and the lines…

A:

Q: 1/2 x3 dx 1- V3 - 15 15 2 16 Option 1 Option 2 1 15 V15 16 8. Option 3 UOption 4 IN

A:

Q: show that g(x) = (1/2)x has a unique fixed on [0,1]

A:

Q: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C