In the aftermath of a car accident, it is concluded that one driver slowed to a halt in 11 seconds while skidding 500 feet. If the speed limit was 30 miles per hour, can it be proved that the driver had been speeding?(Hint: 30 miles per hour is equal to 44 feet per second.)We can guarantee that at some time from when the driver first pressed on the brake to when the car came to a complete stop the car was traveling  mph.Therefore we  (can/can not) conclude that the driver was speeding from the information given.

Q: Suppose f(x, t) = x sin(5t). a) At any point (x, t), the differential is df = b) At the point (-2,…

A: The given function is .

Q: Find the equation of the tangent to the function f(x) = x + 3 & I 4 x4 if x = 1

A: Given the equation of curvef(x)=1x+2x2−3x3−4x4To find: equation of the tangent

Q: If w = x + y²z, then the differential, dw is 0 1 + 2y 2ydxdydz dx + 2yzdy + y² dz 01+ 2yz + y² O dx…

A:

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = x² − xy + y² − 4x + 4y…

A:

Q: Differentiate and simplify each of the following. a) f(x) = 8x³ +7x² − 3x+14 c) f(x)=(x²+1)'(7x +…

A:

Q: Suppose f (x, y) = −3x² + 1xy − 3y², P = (−1, −1), and u = (20, 20). A. Compute the gradient of f.…

A:

Q: Evaluate the following integral. 5 x(x² + 2)² dx 5 In x² +2 In|x²| 1 √ + 0 = 0 _ _ _ ) - 0 dx 5 + +…

A:

Q: For Complete Kn, n-cube Qn, and complete bipartite graph Km.n . a) How many vertices and how many…

A: The objective of this question is to determine the number of vertices and edges for three types of…

Q: the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at (3,…

A:

Q: #2: Given f(x, y) = x³y6+6xy, which of the following vectors points in the direction of steepest…

A:

Q: Determine the area of region between y = |x²_9 | and y=9 Note: In this problem you should set up and…

A:

Q: 14. Find the point(s) of the tangent to the curve f(x): -34x + y = 12 *Round answers to 1 decimal…

A:

Q: Find the tangent to y=x²-x+9 atx=1. oy=√x²-x+9 atx=1 is y=0 The tangent to y=√1

A:

Q: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and which…

Q: If f(x, y) = xy² + arctan(cosx), then fyy is

A:

Q: Find the tangent vector for the position vector r(t)=ln(1-t)i+(t-t^3)j+e^-3t k

A: Explanation of the answer is as follows

Q: 4. Here are the first few terms of a sequence: 1 2 2 3 3' 4' 1 (b) Is this sequence monotone? Is it…

A:

Q: #3: Solve the initial value problem y"-4y - 12y = 0, y(0) = 1, y'(0) = -1

A: y"-4y'-12y=0y(0)=1, y'(0)=-1

Q: Please use Differential equation or intergral equation to solve thanks

A: Done.Explanation:Done

Q: (2.) r(t) = (t, cos(2t), sin(2t)), t = [0, π] describes one circular arc of a helix. (a. Determine…

A:

Q: (4.) Let v(t) = (2+1, sin(3t), e¹) give the velocity at time t for a particle that is initially at…

A:

Q: log(x) + log(x + 1) = 6

A: log⁡(x)+log⁡(x+1)=6

Q: Evaluate the derivative of the function at the given point. f(s) = -2√5-3, a =9 f' (9)= (Simplify…

A:

Q: What is the equation, in standard form, of the tangent to y=x--at (1, 0)? X

A:

Q: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

A:

Q: Let p(x) be the density function given by Find the mean value of p(x). p(x) = 2 192 2 16 0 X - if…

A:

Q: Find all critical points of the function f(x) = x-² - x-³. (Use symbolic notation and fractions…

A: Need to find out the critical points for the given function.

Q: Find the difference quotient f(x) = f(2) x-2 when f(x) = 4 - 5x + 5x². Simplify the expression fully…

A:

Q: f(x) = 1-x², ax + b, ((x-1)³ + 2, x ≤ 0 0 1

A: f(x)={1−x2,x≤0ax+b,0<x≤1(x−1)3+2,x>1

Q: The radius of a right circular cone is increasing at a rate of 4 inches per second and its height is…

A: Formula

Q: The transformation equations from the x-y to u-v co-ordinate systems are given by Construct the…

A: The transformation equations from x-y to u-v coordinate systems areThe triangle ABC in the x-y…

Q: The DeWitt Company has found that the rate of change of its average cost for a product is 100 C'(x)…

A:

Q: 13. The limit will never exist at a discontinuity. 14. The average rate of change is the slope of…

A: The given statements,13. The limit will never exist at a discontinuity.14. The average rate of…

Q: Which of the following series diverge? = N/W 2 K² +1 1. Z K=05K² +7 I. II. Ex-2(-1)*(x²+4) m. ΣΧ.…

A:

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (-1t sint,…

A:

Q: MR₁ = To Let R₁ and R₂ be relation on a set A represented by the matrices 50 1 07 1 1 0 1] 0 1 0 1 1…

A: The objective of the question is to find the matrices that represent the union, intersection, and…

Q: 2. Sketch the graph of f(x) = 3x3/2. Highlight the graph over the interval [2,3]. Now find the arc…

A:

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function f(x)=x² - 2x…

A:

Q: Consider the same system as given in the previous problem: S 6x² + 4yv4 = 10 3xy(²-²) = 0 It is…

A:

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A:

Q: Consider the function h(x) x² 2x + 3,x € R. For what values of æ is the gradient of the curve of…

A: The given function is .The aim is to find the values of  is the gradient of the curve of  negative.

Q: Speeds of a Michaelis-Menten enzyme reaction v (in micromolar/minute) as a function of the substrate…

A: Hence solved.Explanation:a) For Straight line transformation = ([s]1​,v1​) b) Given : y= 0.500981 .…

Q: Let f(x) = 1. f'(x)= 2. f'(3)= tan(x) - 5 sec(x) Find the following:

A:

Q: The Maclaurin series Σ Select one: a. x²e-7x³ O b. -7cos(x³)+2 O c. -7e³x+2 O d. x sin(-7x³) 100…

A:

Q: A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing a…

A:

Q: Please show your answer to 4 decimal places. Suppose that f(x, y) =e ²²-y²_2_2y then the maximum is

A: Suppose that .To find the maximum of the function.

Q: 6. The quadratic Taylor approximation of f(x, y) near (x, y) = (a, b) is given by f(x,y) ≈ Q(x, y) =…

A: Given: To Find: To  find the quadratic Taylor approximation of .

Q: 8. Sophie told her friend Jesse that he needed to know for the calculus test that the derivative of…

A: Sophia told her friend Jesse that he need to know for the calculus test that the derivative of a…

Q: Let f(x) = 2x² + 13x + 15 -7x+5 2x² This function has: 1) A y intercept at the point 2) x intercepts…

A: Let To find the following: (1) y-intercept(s)(2) x-intercept(s)(3) vertical asymptote(3) horizontal…