T The position vector r(t) = 4ti + 2tj+ t´k describes the path of an object moving in space. Find the acceleration 6 aft) of the chiect

Q: I Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A: Given that Line is passes through A(1,2,3) and B(5,1,7) And plane passes through C(1,0,2) D(5,1,6)…

Q: Find the producers' surplus at a price level of p = $56 for the price-supply equation below. p=…

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Q: The voltage Vin a simple electrical circuit is slowly decreasing as the battery wears out. The…

A: This question can be solved using the concept of rate of change.

Q: A balloon rises at a rate of 3 meters per second from a point on the ground 60 meters from an…

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Q: B)Convert r = √2 cos(8-) to cartesian.

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Q: Proceed as in this example to find the solution of the given initial-value problem. Evaluate the…

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Q: Use the Inverse Function Theorem to find (h-¹)' (7) given that h(x)=√10x + 9. Note that h(4) = 7.…

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Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

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Q: Let one week's supply and demand functions for gasoline be given by p= D(q) = 288-39 and p = S(q) =…

A: Here, the demand and supply functions are: D(q)=288-43q & S(q)=23q which are the linear…

Q: Which point is the vertex of the parabola y = 6(x+3)^2 - 5?

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Q: Homework) read the following mathematical steps of finding sum of series. Σ 2n = 1+2+4+8+16+ ....…

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Q: S = u(x+*)

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Q: Evaluate the definite integral. 2 X dx 1 + 4x 0

A: Take (1+4x)1/2 = t

Q: Q2A)Matrix A =[42],find Eigen values of A².

A: We need to find eigen values.

Q: Find the domain of the following function. 1 f(x) = 2 25-x

A: Given function f(x)=125-x2we know that fraction abis defined when b≠0the function is not defined…

Q: Assume that f is continuous on the set of real numbers. Find a and b given that b 3 [ f(x) dx - f₁…

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Q: use the definition of Laplace transform, to calculate the transform of f(t) if it is known that: 2e…

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Q: The voltage Vin a simple electrical circuit is slowly decreasing as the battery wears out. The…

A: We have given  Resistance (R)= 423ohm  Current (I)= 0.05A  dV/dt= -0.06V/s  dR/dt= 0.04ohm/s

Q: 19 Can a graph with three vertices of degrees 2, 1, 4 exist? Yes No

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Q: If 5 5 f(x) dx = 4 and 2 Š² f(x) dx + O -2 O 10 O 2 0 0 4 g(x)dx? g(x)dx = 6, what is

A: Given

Q: The slope of the oblique asymptote to the curve f(x) = x +11 corresponds to

A: folllow the procedure given below.

Q: d²y dx² 2 (2x-3)² Find y = O O d²y dx² d²y dx² d²y dx² O d'y dx² = = = = 12 (2x-3)¹ -12 (2x-3)4 48…

A: Given

Q: Find and sketch the domain of the function. f(x, y) = √√√√4x²-√√25-y² O -6 DO -4 -6F 4 6 -6 -4 4 4…

A: The set of points (x, y) where the function f(x, y) is called the domain of f(x,y).

Q: If 3x² + 2xy + y² = 2, what is? dx

A: Follow the procedure given below.

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

A: Given that a = 2 + 7i and b = 4 - 2i. We have to find a*b. Clearly as  a = 2 + 7i and b = 4 - 2i so…

Q: 31 Matrix A =[42],find Eigen values of A².

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: Solve using Inverse Operaators. y"" - y' = 4e-x + 3e2x; Particular Solution: Y=C₁+ C₂ eax + C3 ebx…

A: See the details solution in below

Q: If f: R → R is a function such that f'(4) = f'(8) = 0 and f"(x) = 18x - 108 so, f(m) is a local…

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Q: the complex number 6√3+6i in polar form* 12(cos(n/6)+isin(n/6) 12(cos(n/4)+isin(n/4)…

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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) 3.…

A: solve

Q: the complex number 6√3+6i in polar form O 12(cos(n/6)+isin(n/6) O 12(cos(n/4)+isin(n/4) O…

A: As we know that; The complex number z=a+ib can be written as polar form; z=rcosθ+isinθ Where;…

Q: Determine which of the graphs below have Euler circuits. Vo Vg VI 3 m (US S 5 e6 4 33 V3 Ug (US 27…

A: Euler circuit: An Euler circuit starts & end at same Vertex Here in the given problem we have to…

Q: 17 What is the degree of vertex 4? O 1 ez el V2 V₂ Des

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Q: 4 Find the coefficient of the given term when the expression is expanded by the binomial theorem…

A: Find the coefficient of x2y7 in (2x+3y)9 using binomial expression.

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

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Q: let a a E R - {0} and g the function defined by : sen (2) si z #0 az g(x) = 5 si z = 0 The function…

A: In this question, we want to know for what value of a , the given function g will be continuous on…

Q: (cose + i sine)" = cosno + i sin ne

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

A: Here we have to solve the differential equation.

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Suppose the revenue from producing (and selling) x units of a product is given by R(x) = 15x-.06x²…

A: To find marginal revenue at production level of 35.

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

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Q: π/2 B)Evaluate the integrals: i) f/2 sine rdrde, π/2 ii) f/25/2 sinxz² siny dz dy dx.

A: See the details solution in below

Q: dx 5 - 2x Evaluate: S O2 ln |5-2x + C -2 + C 5-2x O -1 2(5-2x) + C On 15 - 2x + C

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

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Q: (a) (8,4) r> 0 r 0 r 0 r< 0 -5) 3 = = (r, 0) (r, 0) = (r, 0) = (r, 0) =

A: Follow the procedure given below.

Q: If f³ f (x) dx = 6 and ſ ƒ(x)dx = 4, then ſ5 (3 + 2ƒ(x))dx : = 35 10 23 20

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Q: Integrate the following: 1. fxsinxdx 2. fæcos2xdx 3. fe sinxdx

A: The given integrals are' 1) xsinx 2)xcos2x 3)exsinx.  Repost the next parts.

Q: B)Solve the differential equation da x+4y

A: