Find Vectors and Perform Vector Operations in R³ Let a = (0, – 5, 5) and 6 = (4, 2, — 5). Find – 2ā + 27. - 2a + 25 =

Q: og of 9-14 Find the intervals on which f is increasing or decreasing, and find the local maximum and…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Problem 2. Consider the region R bounded by the the graphs of y = 4 - x², and y = x² - 2x. Sketch…

A: To set up an integral which gives the exact area bounded by the given graphs.

Q: At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship…

A: Given that. At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 15…

Q: given curves is revolved about the y-axis. ■= ex², x x = √√√2, x = 2, y = 0 Volume = FI

A: V= ∫ab(2πx f (x))dx

Q: Find the derivative of y = (3x5 - 4x + 2)g(x)

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Q: cost C, in dollars, to build a fence around a rectangular field with an area of 1000m^2is given by…

A: Given query is to find the value of x to minimise the cost.

Q: Find the absolute minimum of f(x, y) = 5xy - 4x - 4y on the triangular region R that has vertices…

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Q: (4) Solve the initial value problem: y" - 6y + 25y = 0; y(0) = 3, y'(0) = 1.

A: I am attaching image so that you understand each and every step.

Q: pr 1) Given the position function s(t) = 2+²³ - 2 + ² - 60t + 3₁ where it is in seconds and s is in…

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Q: Find the length of the curve Arc length = y² = 4(x+4)³, 0≤x≤2, y>0.

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given vector:- rt=2ti+etj+e-tk

Q: d) f(x) = x sin x + cos x [0, 2π]

A:

Q: Box office revenue at a multiplex cinema in Paris is R(p) = 3600p - 8p³ euros per showing when the…

A: given that,R(p)=3600p-8p3 and p=7use the linear approximation to estimate ∆R

Q: Find the derivative of the function. Simplify if possible. y = arccos (e³x) y' =

A: Solution : Given that

Q: Find the first five non-zero terms of the Taylor series for f(x): 8 + Written compactly, this series…

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Q: 2) A company produces and sells smartphones. The revenue for one smartphone is $900. The cost to…

A: NOTE: Refresh your page if you can't see any equations. . the give cost function is  where x is the…

Q: Given the function below ✓50x³ + 75 Find the equation of the tangent line to the graph of the…

A: Given, f(x)=50x3+753

Q: from a = = 2 to x = 6. The length is y = 6x³/2 - 5

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Q: . Show two different ways of solving answers. sin x cos x dx. Explain the difference in appearance…

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Q: Find r(t). u(t). r(t) = (7t − 8)i + t³j+ u(t) = t²i - 9j + t³k r(t) u(t): Is the result a…

A:

Q: a Th

A: Given s(t) =2t3-92t2 -60t +3the total distance travell during the first 6 sec = d

Q: Find the derivative of: 9 sin² (4x²). 2 Hint: sin²(x) = [sin(x)]².... ...so use the chain rule…

A: Let's find derivative of given function.

Q: The force on an object is F=- 24j. an for the vector P = -40i+ }, Find a) The component of F…

A: Given the force vector  F→=−24j

Q: Find the equation for a polynomial f(x) that satisfies the following: Degree 3 ■ Zero at x = 2 ■…

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Q: 12. Find the area of the surface generated by rotating the curve y = √√x the y-axis. Do not…

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Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 4x + 5 y = 12 where x is the…

A: Given: As nothing is mentioned, we will be answering graphically.

Q: A pet rectangular box has length 6 inches, width 4 inches and a height of 17 inches. Find the angle…

A: Let's find angle between diagonal and its base.

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

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Q: Directions: Consider the following function f(x). Use the logarithmic laws to rewrite this function…

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Q: A hamster "runs in place" on a circular treadmill, causing the treadmill to rotate at constant…

A: time= 4 sec  diameter= 12 inches

Q: The graph below is the function f(x) -5 -4 -3 -2 -1 Find lim x 27 Find lim 5 4 3 2 1 x → 2 + -5 1…

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Q: For the sequence an = its first term is its second term is its third term is its fourth term is its…

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Q: Solve the differential equation = y²ex dy dx

A: Given, dydx=y2ex

Q: Find the derivative of: 9 sin² ( − 4xº). 1 Hint: sin²(x) = [sin(x)]²... 9 cos cos²(-429) -36x8 ...so…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: q are constants. Assume further that y is a differentiable function of a such that x²y = (x+y)p+q.…

A: To find the derivative using logarithmic differentiation

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: The diameter of the hemisphere is 45 meters. The volume of the hemisphere = V(r)=23πr3

Q: If v= 51 +6] and w= 151 + 18), find projev. Then decompose v into two vectors v₁ and V2, where v, is…

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Q: If g(x) = (t(x)) / (e3x), find and simplify g' (x)

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Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

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Q: At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship…

A:

Q: Identify the level curve of the function g(x, y) = xy − 9x for c = 8. Write your answer in terms of…

A: given function g(x,y)=xy-9xwe need to identify the level curve for C=8

Q: implicitly differentiate 3xy = 2

A: given  3xy = 2  differentiate with respect to x

Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

A: Let's find amount of solid 1 second later.

Q: Precalculus express the logarithm in terms of In 2 and In 5 In 2000

A: Here we have to solve the logarithm.

Q: For the function g(x)=x5 - 4x³ solve the following. g(x) < 0 Select the correct choice below and…

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Q: A constant force F = -3₁ +2j-1k & is applied to a object that is moving along a straight line from…

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Q: pyramid centimeters per second. The pyramid, at the top, has the shape of a square with sides of…

A: let v be the volume then given dvdt=65cm3seclet side of square base = a height = h volume ( v)…

Q: Evaluate the double integral over the given region R. SS. R ex-Ydx dy R: 0≤x≤ In (3), 0≤ys In (6) SS…

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Q: Find the volume of the solid obtained by rotating the region bounded by the curves X = = -3y²…

A: Given that the region x = -3y2 + 12y - 9 and x = 0

Q: If a ball is thrown vertically upward with an initial velocity of 96 ft/s, then its height after t…

A: Given height :- s=96t-16t2