Find the value(s) of t so that the tangent line to the given curve contains the given point. r(t) =3ti + 2t²j-2t²k; (0, -32,32) (Use a comma to separate answers as needed.)

Q: Balwyn High School is planning to establish a Balwyn Island Theme Park. One of the attractions will…

A: Using concepts of limit and continuity, we can solve the question.

Q: 2. If u = (a, b, 1) is perpendicular to both = (5, 1, -2) and w=(3,-3, 6), find a and b.

A: given that vector u=(a,b,1) is perpendicular to v=(5,1,-2) and w=(3,-3,6)

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise.…

A: ,The region

Q: дz Use the chain rule to find and Əs дz əs дz at 11 || Z= sin(0) r дz at r = st, 0 = s² + t² S 75…

A: z=sin(theta)/rr=stTheta=s7.

Q: Using the Law of Sines to find a triangle with one obtuse angle if ZA = 45%, a 27,6 = 29. If no…

A: Law of sine  Where a , b and c are the side length of the triangle A , B and C are the angles of the…

Q: Find the graph of the following ellipse. Identify the domain, range, center, vertices, endpoints of…

A: The given equation is,Compare this equation with the standard form of the ellipse. So here we have,…

Q: (a) Between the two limits shown, L'Hospital's Rule can only be used to evaluate one of them. Which…

A: L hospital rule used to evaluate the limit of indeterminate forms

Q: 72 Write the equation of the line tangent to f(x) = 42x + X y= Write the linearization of fat x=2.…

A:

Q: Use the chain rule to find the indicated partial derivatives. Р+9 p+r aN ди aN av an = = N = ƏN ди…

A:

Q: Two forces, with magnitudes 200 N and 50 N, act on an object at 90° to one another. Determine the…

A:

Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Using the given definition of Laplace transform, we can find Laplace transform of given function.

Q: avel agency group tour group exactly $290 per person above the 35, then the revenue is given by the…

A:

Q: 2. Given the vector a = (3,-4,5) and vector b = (-2,3,1) determine the following in the most…

A: Since you have posted multiple subparts question in this question which are not interlinked so i…

Q: An investment appreciates 2% per year. Originally $5000 is invested. After how many years to one…

A:

Q: Find f such that f'(x) = x² +5 and f(0) = 7.

A:

Q: Volume of the Solid Beneath -* and above the region Find the the cylinder f(x,y) = e r = {(x,x): 0 ≤…

A:

Q: If the unit selling price p(x) and the quantity supplied of a certain product is given by p(x) = x5…

A:

Q: Forecasting Commodity Prices Government economists in a certain country have determined that the…

A: We are given that p = f(x) = , where the unit price p is expressed in dollars per bushel and x, the…

Q: 5. Find the equation of the tangent to the curve y = 4x² In xat the point (2). Explain and show the…

A:

Q: 2. One minute after a 100-mg sample of Polonium-218 is placed into a nuclear chamber, only 80-mg…

A: Note:-Since you asked multiple question , according to our policy we can answer only first question…

Q: Let ƒ(x) = ln[x³(x + 4)¹(x² + 4)5] f'(x) = You need not put it over a common denominator.

A:

Q: If 12√x+9√y = 159, find y'(x) by implicit differentiation. V Find the exact value for y'(25) in…

A:

Q: (−2,−1) -2 2 0 --1- (0, 1) 1 2 (2, 1) (3,1) 3

A: We have to solve for the piecewise function.

Q: Find the linearization L(x,y,z) of the function f(x,y,z) = √x² + y²+z² at the points (7,0,0),…

A: To find the linearization  of the function  at the points , and .

Q: 7 Consider the complex number z = (a) (b) (c) 4-2j 3+j By multiplying top and bottom to get a real…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use geometry to evaluate the definite integral. 10 1 S ½/x dx -x

A:

Q: The Equations for the asymptotes for a hyperbola with a vertical transverse axis are given by:…

A: asymptotes of the hyperbola with a vertical transverse axis.

Q: 2 S²₁lex - 11 dx -

A:

Q: Given the vector u = 67-37, find the magnitude and angle in which the vector points (measured…

A:

Q: Write the standard form of the equation of the hyperbola subject to the given conditions. Corners of…

A: NOTE: Refresh your page if you can't see any equations..The corners of the rectangle are;Plot all…

Q: Calculate[ri(t) · r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly and…

A:

Q: Find the integral. 1 So -dx

A:

Q: Determine the radius of the circle. If necessary, enter your answer rounded to 4 decimal places.

A: The given point is on the terminal side of an angle in standard position.Find the radius of the…

Q: 8. Consider the power series: [(-3) ² n=0 a. Determine its radius of convergence. b. Determine its…

A:

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A:

Q: Consider the following function: f(x)=ln(x+1) Determine the intervals at which the function is…

A:

Q: A contractor wants to build a swimming pool that is to have area of 144 m². The pool must have a 4-m…

A: A constructor wants to build a swimming pool that is to have area of 144m2. The pool must have 4m…

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

A: Given :find the local maximum and minimum values and saddle points of the function.

Q: In the year 2000, the population of Toledo, Ohio was approximately 530,000. Assume the population is…

A:

Q: (c) Determine the inflection point (s) of f(r)=-6² +9r. (d) Determine the global maximum and global…

A:

Q: Find f(x) such that f'(x) = == +9√ and f(1) = 17. X 4 f(x) = +9x³/2 +4 x² O f(x) = 4 ln |x|+9x³/2 +8…

A: Formula used:

Q: Point-masses m, are located on the x-axis as shown. Find the moment M of the system about the origin…

A: We find the moment M of the system about the origin and the center of mass X.

Q: Direction: Test for the Homogeneity and state the degree of the following functions.

A:

Q: Oil leaks out of a tanker at a rate of r = f(t) liters per minute, where t is in minutes. If f(t) =…

A:

Q: D The region D above lies between the two red lines and 2 the red parabola y = ². It can be…

A:

Q: 4. (a) (b) Find the critical point (s) of f(x)=³-67² +9r. Classify each critical point from (a) as a…

A:

Q: What does a = 10^b mean? Ob= 10^a b = a^10 Ob = log(a) Oa= log(b)

A:

Q: A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that…

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: The masses m, are located at the points P. Find the moments My and My and the center of mass of the…

A: The masses and its locations are given by:-