Find the vector equation that represents the curve of intersection of the paraboloid z = surface y = e. Write the equation so that one of the functions is simply t. x(t) y(t) z(t) = = 2x² + y² and the

Q: Write Z₁ and Z2 in polar form. Z1 = Z2 = Z₁ = 2√3-21, Z₂ = −1 + i Find the product Z₁²₂ and the…

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Q: 6x Find the derivative of h(x) = 2 h'(x) = 36log, (x) 6

A: Topic:- application of derivatives

Q: Use logarithmic differentiation to find the derivative of th y = (In(x)) cos(2x) y'(x) = ||

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Q: The area under the curve y= 7x bounded by the lines x = 8 and x = 17 above the x-axis is = Square…

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Q: Write the equation of the line that passes thruigh the point (2, -3) with the slope value 2. Express…

A: To write the equation of the line in slope intercept form

Q: Find the partial derivatives of the function dw Or dw dw Ot W= √√2r² +58² +4t²

A: We can find the partial derivative of the function .

Q: 1.23 Solve each of the following problems by direct integration. a. b. C. d. e. 4x = 3t 5x = 2e-4t…

A: As per the guidelines I am supposed to first question among multiple problems. So here I am doing…

Q: Evaluate the function at the points (-8, 0), (6, -6), and (0,24). k(x, y) = xe-3 (Express numbers in…

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Q: limx→3 0 4 01 O O 3-x 4-√√²+7 O None of the above

A: We need to find: limx→3 3-x4-x2+7

Q: Write the equation of the line in slope-intercept form that passes thorugh (-3,4) and (5,4). Then…

A: Horizontal axis is x-axis and vertical axis is y-axis

Q: Find the absolute maximum of the function f(x)=x²-1x +4 on the interval [0, 2]? (a) The absolute…

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Q: Q3 Calculate the area of the shaded region in the given figure y Focus point Parabola curve P- 2p 8p…

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Q: conical tank with the point oriented down, a height of 20 feet, and a radius of 3 feet has sprung a…

A: Given query is to find rate of change of height.

Q: The instantaneous rate of change of the value of a certain investment (P) is proportional to its…

A: We have given  dPdt=r P If r= 8 and P(0)= 5000, then Find P(t).

Q: 8 ln(sin(x)) 8x tan(x) +C

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Q: What initial investment at 7% compounded continuously for 9 years will accumulate to $70,000? (Round…

A: We have to find the initial investment at 7% compounded continuously.

Q: oduced, while R(q) and C(q) are in total dollars ction. (Be sure to use the proper variable in your…

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Q: 3. (a) Find the Laplace transform of (i) f(t)=17te-2-3 sin(9t) (ii) fo

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2. Given r(t) = (2, e³t-3, 6t+2) with r(1) = (2, 1, 7) and r'(1) = (2,0, 5), find r(t).

A: The objective is to find r(t).

Q: Evaluate the definite integral. 1 lis 0 (5* −_4*) dx

A: solution:-∫015x-4xdx=∫01exln5-exln4dx=exln5ln5-exln4ln401=e1ln5ln5-e1ln4ln4-e0ln5ln5-e0ln4ln4=5ln5-4…

Q: Find the indefinite integral. (Use C for the constant of integration 2 cosh(√x) X dx

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Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: evaluate / sin²(z) cos³(x) dx we use the identity sin²(x) + cos²(x) = 1 to obtain [ sin²(2)( cos(x)…

A: Given query is to find the substitution applied.

Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 12 s² + 16 Your answer should be…

A: To find the inverse Laplace transform L-1Fs of the given function.Fs=12s2+16

Q: 5. Suppose a novelty cake has a base which can be described as the region bounded by y = 4x² and y=…

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Q: A population grows according to an exponential (Malthusian) growth model. The initial population is…

A: Growth model :-Pn=P01+rnr=growth rate Here r=0.3 P0=5⇒Pn=51+0.3n⇒Pn=51.3n

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 6t² – 24t +…

A: Given : vt=6t2-24t+18 we know that when particle is moving to right v(t) > 0

Q: Determine the area of the region bounded by two the curves f(x) = x² - 18x +36 and g(x) = 9x + 18.

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Q: Find the inverse transform of the given function of s. 5 F(s) == / A There is no correct answer from…

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Q: f(x,y,z) = 4x5+2xy-4z4 f(x.V.Z) =

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Q: is the relation defined by the table a function of x

A: If each input value leads to only one output value, classify the relationship as a function. If any…

Q: lim x3 x²+2x+3 x+3

A: Given query is to find the limit of the expression.

Q: Find the distance the Point PC9₁-6, 37 is to lline through the two Points. 1Q (5-=-= 3,01 and R…

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Q: Show that (csc(x)) = -csc(x) cot(x). d dx d dx -(csc(x)) H = = d dx sin²(x) 1 sin(x) 1 = -csc(x)…

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Q: Need Help? m/min. Read It Watch It Master It

A: Topic:- application of derivatives

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,2) on the surface…

A: Let fx,y,z=2x2+3y2+z2-9 Gradient vector ∇fx,y,z=fxx,y,z,fyx,y,z,fzx,y,z

Q: 5 -5 x dx =

A: Topic = Integration

Q: 2x +3 x:²-9 da

A: To evaluate the given integral.

Q: 1) Find the domain of the function f(x) = √3-x x+4

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Q: f(x) = 5x³ + 6x - + Use g '(x) = g'(−2)= 6x-2 has an inverse g(x). 1 ƒ'(g(x)) to find g '(-2).

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 25 m/s, its height…

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Q: d) Compute the angle in Degrees between 3 and 4

A: We have to find angle between vector V3 and V4

Q: 7. Suppose that the graph of the velocity function of a particle is as shown in the figure, where t…

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Q: Find x. Round your answer to the nearest tenth of a degree. 44 X 24 -0° x =

A: We have given a right angle triangle  From given triangle  Perpendicular (p) = 44 Base(b) = 24 Using…

Q: The following table shows retail sales in drug stores in billions of dollars in the U.S. for years…

A: NOTE: Refresh your page if you can't see any equations. . from the graph, we can see that the given…

Q: 7x – 4x − X

A: Topic = Integration

Q: Consider the following. lim x→0+ (a) Describe the type of indeterminate form (if any) that is…

A: If a limit limx→cf(x)g(x) is of the indeterminate form 00. Then…

Q: For the function f(x,y,z) = 4x - 3y 5z + 1 find fx, fy, fz, and fyz. 9

A: f(x,y,z)= (4x-3y)/(5z+1)

Q: Find the volume of the parallep lapiped with adjacents edges PQ, QPR, PS where PLO, -4,₁-4), Q (²-1,…

A: Concept: The volume of a parallelepiped with adjacent sides PQ, PR and PS is given by,…

Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The objective of the question is determine the gradient at  a point and directional derivative at a…