Find the angle between the vectors. (Round your answer to the nearest degree.) a =j+ k, b = i +4j - 2k

Q: Find the derivative of the function using the chain rule. y = log10(7x)

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Q: B. Find the area bounded by the given curves Show the graph (you can use any graphing software,…

A: A detailed solution is given below.

Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,

Q: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

Q: 1. y=(sin ¹x² + X 1+tan x

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Q: Recent studies indicate that the average surface temperature of earth has been rising steadily. Some…

A: To find the slop and  t intercept.

Q: f(x5) (16-x²)³/² dx

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Q: 1. A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

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Q: Find the derivative of the trigonometric function. Use the chain rule. f(t) = 5 sec9(pi(t) − 4)

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Q: 3. +ANIA (3x - 1/2 + sin x) dx

A: As you mentioned question no. 3 solved

Q: In the Taylor series expansion of e* about x = 2, the coefficient of (x - 2)4¹ is (a) 24 (b) 4! (c)…

A: Taylor series of function fx at a is defined as:…

Q: 5. A ball of mass 2 kg is dropped from rest in a viscous fluid, the resistance of which is 0.001v N…

A: By solving differential equation

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 8,…

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Q: Find the root of f(x)=(x^2)-5, in interval [0,4] by using bisection method.

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Q: Leª dx

A: We have to find the integral

Q: differentiate 3thetacos(2theta)+2sin(2theta)

A: A detailed solution is given below.

Q: 2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: It is required to find the initial temperature of the inside room using the given conditions…

Q: 4 fsin 2xcos²2xdx

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Q: Determine the domain and range of function f(x) = elnñ — arcsin (1²²)

A: This question can be solved using the concept of domain and range of inverse trigonometric…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Solution

Q: Find a formula for the quadratic function whose graph is shown. y X 15 f(x) = -5 30 20 10 f 5 (5,2)…

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Q: Q1/ Find the derivative of the following functions: where x>0,x #1 a- y = x** x√√2x+1 b- y = exsin…

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Q: 5. (a) Use Newton's binomial theorem to calculate √50 with 4 terms.

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: Differentiate each of the following functions. (1) F(t) = (2t − 3)²

A: Differentiation

Q: 5. If y Loo 2w-4 w+4 u √u+3-u determine W=- dy dx at x = -2 niz notation chow all and 12 2 x + x o…

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Q: All exponential functions can be written in many forms. Write the function f(t) = 6100e0.07t in the…

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Q: Consider the following graph. y 5A 3 y = 5 (arcsin (x)) 2 A H 2 -1 1 2 2 3 3 2 Given the function y…

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Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: Which of the following is not an indeterminate form? * ∞-∞ O Option 1 0/0 O Option 2 1∞ 1/0

A: Topic = Limits Correct option = 4

Q: 2. Find the value of 1 3x + 13 x² + 4x +3 dx

A: We can you valve the given definite integral by using the partial fraction method.

Q: By the definition of derivative prove that f(x) = = √x² + 5 is differen- 4. tiable at x=2.

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Q: dy dr = cos(²) +

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Q: 6. - Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: We have to set up the integral that will give the volume.

Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10)

A: We know, f'(x)=f(x+∆x)-f(∆x)∆x Let, x=-10 and ∆x=0.4

Q: Evaluate the given indefinite integral. 7 c 7 cos √6x dx= [ (Type an exact answer. Type an…

A: Solution: ∫7cos 6xdx Apply integration by parts

Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

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Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10) ~ ≈ 94

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Q: 3. What value of k will make the line with symmetric equations - (1,−1,3)+s(3,2,2) p vector equation…

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Q: y = 3-x²

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Q: Prove that √1+i√3+√1-i√3 = √6

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Q: The function f(x) = √√x-2 + √√4-x is. increasing on its natural domain O increasing on (2, 3) and…

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Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: Find the distance between the points. 2 (3, 3), (3, -1) 2 units

A: To find the distance between given to points.

Q: Calculate the derivative. ƒ"(1), f(t) = 15t t+1

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Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: Find the surface area generated by revolving the curve x=y³²-y about the y-axis for 1≤ys 3/2 1/2 3

A: Solve the following

Q: Q: IF A=[4] and, I= identity matrix Then, Y=A² + A - 21 Find Matrix Y ? 1. [16 16] 10 2. [16 781 3.…

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Q: Find the Mass, Moments along x and y, Center of Mass, and Moments of Inertia of the region bounded…

A: The given region is bounded by x+y=2, x=0, y=0 as shown below: The region is given by R=x, y:…

Q: Find the area of the region enclosed by the circle r = 16 sin θ.

A: A detailed solution is given below.