Use a graphing utility to graph the polar equation. inner loop of r = 10 - 15 sin(0) Find the area of the given region. (Round your answer to four deci

Q: Consider the following. u =(4,-1,0) v = (-4, 7, 0) Find u x v. Determine if u x v is orthogonal to…

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Q: A rock is thrown directly upward with an initial velocity of 50 ft/sec from an initial height of 10…

A: The initial height of the rock, hi = 10 ft The velocity function is modeled by the following…

Q: Given f (x) = = x + 16 X for x = 0, find the values of x corresponding to local maxima and local…

A: The given function is: fx=x+16x, x≠0

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (2, -4) and the direction in…

A: f(x,y)=lnx2+y2point is (2,-4)maximum rate of change=∇f(x0,y0)

Q: The height h (in feet) of an object falling from a tall building is given by the function h(t) = 144…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Calculate the derivative indicated. d'y dx4x=9, y = 4x-3/4

A: Given query is to find derivative.

Q: 9

A: Given: In order for a matrix B to be the inverse of A, both equations AB=I and BA=I must be true.

Q: For the sequence defined by: a₁ = 3 an+1 Find: a2 = a3 || a4 = 5 an - +3

A: given  a1=3an+1=5an+3

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: The volume V of the right circular cylinder of height 9 m and radius r m shown in the figure is V =…

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Q: Let f(x)=−5x^4+10x^2+10 How many critical points does this function have?    How many inflection…

A: To find the number of critical points of given function.

Q: The first five terms of the sequence tn = 6(-1)n-1 are....

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Q: 3 5.³ 0 x√1 + x² dx.

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Q: Suppose that f(x) = 18eª — exe. Find ƒ'(3). ƒ'(3) =

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Q: Find the volume of the solid E whose boundaries are given in rectangular coordinates. {(x, y, z)…

A: Given that z≥x2+y2z2≥x2+y2 and z≤49−x2−y2z2≤49−x2−y2x≥0,y≥0 Radius of cone and…

Q: 15. g(0) = sin² 0

A: Given query is to find the critical number.

Q: Evaluate the limit for the graph: lim f(x). X+2+ O -4 +00 0-1 01 -00 4 2 -20 -2 24 4 8

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Q: The graph of y=x² + 1 is shown below (not drawn to scale). P (a) If a = 50, find the coordinates of…

A: The graph of y=x2+1 is given as ,

Q: f+lc 2. A conical oil tank with vertex down has a radius of 24 feet at the top and is 36 feet high.…

A: Given: The radius of the oil tank =24 feet.Height of the oil tank=18 feet3.

Q: Let f: R² → R be defined by f(x, y) = 3x¹ + 7y³ +7 and set z = f(x, y). Find an equation for the…

A: To find the equation of the contour line of f at level z=9, we need to solve the equation f(x,y)=9.…

Q: Find all critical points of the function f(x) = x² - ²x² - 54x + 5. (Use symbolic notation and…

A: Given that the function is fx=x3-92x2-54x+5. It is required to find the critical points of the…

Q: A quadrilateral has vertices A(−3, 1), B(1, 8), C(6, 7), and D(5, 2). Which kind of quadrilateral is…

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Q: Use the chain rule to find and, where First the pieces: дz dr dr მs ду მა || 11 11 9- = 94 And…

A: z=x2+xy+y2x=4s+4ty=8s+7t∂ ∂x(xn)=nxn-1∂ ∂x(constant)=0

Q: A small business buys a computer for $2500. After 4 years the value of the computer is expected to…

A: Note : as per guidelines we support only three subparts of the question. Kindly repost next question…

Q: Integrate sinx given integral by 20 2 w5 x= sing the using sin: 1 + si

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Q: Problem #8: Evaluate the following limit. lim (x, y) (0,0) If the limit does not exist then enter…

A: J=lim(x,y)→(0,0)xx+4y

Q: Write (but do NOT evaluate) the iterated integral that gives the volume of the solid bounded above…

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Q: Find D53 te (₁² +²²²) 20-²). Note: Read "D" f(x)" as "the nth derivative of f(x)"

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Q: 4 2 find all of the critical points of z = =+ = -xy. Identify each Y local minimum, maximum, ora…

A: Partial derivative of any function refers to its derivative with respect a particular variable. For…

Q: The graph gives the number of farms in the United States from 1850 to 2000. y 7000 6000 5000 4000…

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Q: Translate the given matrix equation into a system of linear equations. (Enter your answers as a…

A: Given :- 2-12-43413-800xyz=9-10

Q: Find the tangent plane to the surface x² - y² + z² = 6 at the point P(1,2,3). andy Moon by w foon…

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Q: Differentiate the function below with respect to a. f(x) =ln (−4 x² − 5 x + 8) Note: • In Text mode…

A: Given function is f(x)=ln(-4x2-5x+8)

Q: e graph of y = f(x) is shown. Assume f'(x) is continuous. 8 7 6 5- 4 3 2 -7 -6 -5 -3 -2 -1 nd xf(x)…

A: Given query is to find indicated limit.

Q: If f(x, y) af (0,1)= ду = cos(2xy) + sin(2xy) then

A: As we know that, The Chain Rule: fgx'=f'gx·g'x The Power Rule: ddxxn=nxn-1 Use the common…

Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 1}. 2 Then the double integral of f(x, y) over…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: g(u,v)=u2e-vpoint is (8,0)v=3i+4jDvg(u,v)=∇g(u,v).a→

Q: how does [x^3/3] become 9^3-1^3?

A: Problem is how x3319=1393-13

Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

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Q: 5. Compute the derivative of f(x) - x³ (x-7) tan(x) √1-x (You do not have to simplify your answer.)

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Q: Find x² - 4x equation of the plane tangent to: z = 4e" at (8,16,4)

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Q: Consider the graph of Ax + By = C where A, B, and C are positive constants and A B. If the value of…

A: Solution: Given data, Ax + By = C where A, B, C are positive constants Ax+ By = C → (i)   X-…

Q: 8. Determine constants a and b such that f(x) is continuous for all values of x. ax + 3, if x > 5 8,…

A: Here we have to find the value of a and b.

Q: 1. Explain why lim x-1 does not exist

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Q: The elasticity of demand for x = f(p) = 1,875 - p² when p = 40 is Banco de palabras: inelastic…

A: we will find the required.

Q: The average rate of change of f(x) = ax³ + bx² + cx+d over the interval -1 ≤x≤0 is Oa+b+c 2d a-b+c

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Q: Suppose f(x) and g(x) have the following values: • f(8)= -4 and f'(8)= -6, g(8) 1 and g'(8) = -3. =…

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Q: 2n 4n This sequence is [Select an answer ✓ This sequence is Select an answer ✓ Does this sequence…

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Q: 97d A company that makes bicycles has determined that a new employee can assemble M(d), where M(d) =…

A: M(d)=97d22d2+7(a) rate of changr is M'(d)d dx(ab)=b×dadx-a×dbdxb2

Q: The elasticity of demand for x = f(p) = 1,875-p² when p = 15 is Banco de palabras: inelastic unit…

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