Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 9 cubic feet per minute. If the pool has radius 7 feet and height 11 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 8 feet

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.…

A:

Q: dy dx 1 xy+y y(0) = 1

A: Given dydx = 1xy+y,   y(0)  = 1

Q: Prove Ĵ Ha (as) th(x) e che = Hm (x) Hn(x) e^ dx = √x 2.11.8mm

A:

Q: Integrate f(x) = 0.5 + 20x + 3x¹ from a=0 to b=3, given N=12 by using a) Simpson's 3/8 approximation

A: To evaluate the definite integral ∫abfxdx by Simpson's 38 rule, use the following formula.…

Q: dy B)Solve the differential equation dx x6 +4y ४

A: Given differential equation is dydx = x6+4yx

Q: B)Is w = Zez analytical function or not?

A:

Q: . For each graph, determine the number of edges, the number of vertices, the number of vertices that…

A: Since you have posted multiple questions and we can answer one question. So, answering the first…

Q: Let V=R²³ be a vector space over R and w = {{ x, y, z) € R³ : x = y +z, y, z, XER} show that w is a…

A:

Q: Q1 find f'(x) using (forward finite difference formula ) at x = ½ for f(x) = sin x - e* with h= 0.1,…

A: Sol

Q: 19 Min Z= 2X1+3X2 S.t: X1 ≥ 125 X1+X2 ≥ 350 2X1+X2 ≤600 X1. X2 > 0 Using the simplex method, In the…

A: We have to use the simplex method to find the table of optimal solution. First we have to convert…

Q: y X = + 2.2 When solving the differential equation y' singular solution, depending on the parameter…

A: For non linear equation there exist a general solution and may be particular solutions.

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A:

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: Given curves are y=0 and y = x-x2

Q: Q#10) For the data (1,2), (3,4), (5,2) 3 if L2,1(x) == Find x? 4

A: 10 Given data is 1,2, 3,4 and 5,2 and L2,1x=34. We have to find the value of x. We know that…

Q: 36. The problem below shows steps in finding the product of two two- digit numbers using this…

A: First we need to find first entry and then we do normal multiplication as always do.

Q: B)Convert r = √2 cos(0-7) = √2 cos(0-) to cartesian.

A:

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A:

Q: • It is required to solve the Z • System of eduations using the 6 Cram & method. method01102 to • 3X…

A: We have to solve the given system of equations using the Cramer's method.

Q: he Taylor series of the function f(x) = cosx at x=0 is [co (1), 2n 2n=0 (2n)! (-1)"x²n n=0 (2n)!

A:

Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

A: Let us consider the parametrized curve x(t) and y(t)  The length of the curve is obtained as…

Q: Solve differential equation dy -(x²+y) x+siny

A: We have given a differential equation , dydx = -x2 + yx + siny This is exact differential equation.…

Q: Given Σ(x-μ)² = 78 and N= 80, then the standard deviation, a, is approximately a) 0.994 Ob) 0.110 c)…

A: We have to find the correct choice.

Q: 5 -2 [x1] Given A=-2 6 2 and X=X₂ [x3] 2 7 show that XTAX = 27, suggest that 5X + 6X2+7X3-4X₁X₂ +…

A: Given A = 5-20-262027  and  X = x1x2x3

Q: whats 065 when $ is oilers Fundion

A: Solving first question.

Q: In numbers 1 and 2, solve the given IVP using Laplace transforms and the following substitutions.…

A:

Q: ind the Laplace transform and inverse Laplace transform for the given function (a) f(t)=41²-2e"…

A:

Q: I. Prove the following assertions using a direct proof. a. If x is an odd integer, then x+5 is even.…

A: According to guidelines we can solve only 3 subpart.

Q: let a=2+7i b=4-2i Choose the correct result of a/b* O (6-361)/20 O (-6+361)/20 O (-6-361)/20 O…

A:

Q: Find the magnitude of the vector v = 9 cos(90) i +9 sin(90) j. (Give an exact answer. Use symbolic…

A: We have given a vector ,  v = 9cos9θ i+ 9sin9θ j We need to find magnitude of vector v. Magnitude of…

Q: 21 = 2(cos(267)+isin (267)) and 22=18(cos(60) + i sin (60°)). Compute each of the following (without…

A:

Q: 6.2 What is a differential equation, y depending on x, whose general solution is the function 21…

A: Explanation of the answer is as follows

Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

A:

Q: Z {a} is a z-a True False

A:

Q: 31 Q2A)Matrix A [42],find Eigen values of 4².

A:

Q: 3) Find the directional derivative of f(x, y) = xex-yx² at (-2,1) in the direction v=i-j B) g(x,y) =…

A: The directional derivative of the given function at p in the direction of u→ is  Duf(P)=∇f(P)·u^ Let…

Q: Using the Inverse Function Theorem, what is (-¹) (8) given that r(x)=√6x-2? Note that /(11) = 8. (Do…

A:

Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) .…

A: Sol 1 .    f(x)*g(x) 2x-3-4x2+9Apply FOIL method:  a+bc+d=ac+ad+bc+bd2x-3-4x2+9=2x-4x2+2x·…

Q: let a=2+7i b=4-2i Choose the correct result of a*b* O 24+22i O 22+22i O22+241 O 22-24

A:

Q: (a) Let f(x, y) be defined on (a, b) × (c,d). (i) Give an example to show that existence of partial…

A:

Q: 6. Solve the following system of differential equations y₁ = -2y₁ - 4y2₂ +e-²tu(t), y₁ (0) = 1 y₂ =…

A:

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z)= x³y²z² - 4 At point (1,-1,2).

A:

Q: Find the distance from the point (2, 1,-1) to the line: x=2t, y = 1 + 2t, z = 2t.

A:

Q: y" (x) + 4y"(x) + 9y'(x) + 10y(x) = -24e*; when x = 0, y = 0, y'= -4, y" = 10

A: Properties of Laplace transformation…

Q: Q3A)Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

A: We have to solve given problems:

Q: e the recursive formul

A:

Q: If L {f(t)} = F(s) then L{t"f(t)} = (−1)n dm F(s) -F'(s) dsn (-1) F(s) (1) F(s) dn dsn dxn خيار 2…

A:

Q: Q5A) Find volume of body from above Z = √4x² - y² and below Z = Triple integration. 1 using

A:

Q: (s-14)4 te-14 6 tBe4t 5) 6 t324t =) 6 a) then the function f(t) can be: 82 +58 + 14. 8 7 31 s²+ } 8²…

A:

Q: valuate * 2, dydx 175 3 Option 1 Option 2 175

A: We have to solve given problems:

Q: 2] Evaluate the double integrals over the given region R. afferan alle R: 0≤x≤ In2, 0≤ys in 2 bll…

A: