14) The half-life of carbon-324 is 700 years. I have 400 grams of carbon-324 right now. How much will I have left in 3000 years?

Q: Find the gradient vector field of f. f(x, y) = xe5xy Vf(x, y):

A:

Q: -2 о 1 O 2 Find the absolute maximum of f(x) = √4 – x² on [−2, 2].

A:

Q: The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal…

A:

Q: et f(x) == be defined on the interval X [1,3] Find the number satisfying the Mean Value Theorem's…

A:

Q: Suppose x = 12, y = 16 and z = 20 in the figure, which is not drawn to scale. Find the following.…

A: here in the triangle z=20 is the biggest side and we have z2=x2+y2 (20)2=122+162 400=144+256 400=400…

Q: Determine whether the following series converges. Justify your answer. IM8 (4k)! k=1 (k!)4 Select…

A:

Q: FIND y’’ OF y = square root of (x^2+1).

A: We need to find out the double derivative of the given function.

Q: 8. Find the solution set of the system of linear equations x12x2 3x3 2x14x2 -3x1 1 4x4 = 2 5x3-7x4 =…

A:

Q: Limits at infinity are associated with O straight lines O vertical asymptotes horizontal asymptotes…

A: To fill in the blanks

Q: Let y = 15 sin(3x + 2). What is the amplitude? What is the period? What is the phase shift? [NOTE:…

A: Let's find amplitude, period and phase shift.

Q: Find two numbers with difference 110 and whose product is a minimum. Enter your answers in…

A:

Q: got

A:

Q: The limit lim h→0 a. f(x) b. a = - 2 (2 + h) ³ - 23 h is the derivative of some function f(x)…

A: The answer is given below:

Q: sosyos!! ¤¤¹0 dzdxdy 1+x² 1

A:

Q: Let The amplitude of this function is its period is its phase shift is and its vertical translation…

A:

Q: Determine if the limit 3x + 1 xxx²-x+5 exists, and if it does, find its value. lim 1. limit doesn't…

A:

Q: 1 √√x²z+2y g(x, y, z)=- +yln x ; find g (1,0,1). zyx

A:

Q: A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight…

A:

Q: tan 0 (2 sin 0+√3)= = 0

A:

Q: Assume cos(x) √41 4/3 = -4/3 and is in the fourth quadrant. What is tan(x)? none listed are correct

A: given  cos(x)=45 and x is in fourth quadrant tanx=sinx cosxsin2x+cos2x=1in fourth quadrant tanx and…

Q: lim (x,y)-(1,0) x² + y²-1 +y

A:

Q: NEEDA HELP WITH THIS

A:

Q: 12. Let f(x) be a function with f(1) = 2, f'(1) = 6, ƒ"(1) : = -12. Which of the following is the…

A: 12)    formula for taylor series is  f(x)=f(a)+xf'(a)+x22f''(a)+x36f'''(x)+.........given…

Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

A:

Q: 1. In the order of dzdydx, find the volume of the solid bounded by x² + y² = 4 and the planes x + z…

A:

Q: Resale Value The estimated resale value R (in dollars) of a company car after t years is given by…

A: Given The estimated resale value R(in dollars) of a company after t years is given by…

Q: Blood Pressure and Age A research group developed the following mathematical model relating systolic…

A:

Q: COMPUTE: 5. r' (t)

A: Givenr(t)=-8t4+5t,sec2tπ6,3et-2tln(t)   We are required to find the value of r'(t)

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = ex/8…

A: Given, f(x)=ex/8, from x=0 to x=8

Q: What is the maximum product of two numbers whose sum is 10? 30 O 36 25 O 28

A: To find the maximum product of two numbers given that their sum is 10.

Q: 36. 2² √2² +3° dt

A:

Q: In2 ln 2 1 y ST 0 yexy dxdy

A:

Q: 5.) USE IMPLICIT DIFFERENTIATION TO FIND dy/dx. WITH THE GIVEN EQ’N: x^3 y^3 + x cos y = 7.

A:

Q: For the curve determine each of the following: Note: Use a negative for a shift to the left. y =…

A:

Q: If what does the following integral equal? 0 -5 y(v)dv = 7 y(v)dv = 25 and y(v)dv = 7.1 -5 7 [²D(0)…

A: Please see the below picture for detailed solution.

Q: S e5x e5x + 3 dx

A: Given query is to find the integral.

Q: 3 √x²x³-1 3 1 dx

A:

Q: The graph of the DERIVATIVE of f(x) is below: 6 -6 -5 -4 -3 -2 -1 54 4 3 2 1 7 -2 -34 14 -5 -6 -7-…

A:

Q: Suppose y (a) The midline of the graph is the line with equation (b) The amplitude of the graph is…

A:

Q: Choose the correct answer. O A. B. log ₂6. log ₂y + log 2² log ₂6+ log 2y + log 2² C. This cannot be…

A:

Q: 2. Use the graph below to evaluate the following: y=2x-8 (a) Using geometry, compute the net area…

A:

Q: Confirm that the below limit meets the conditions to apply Hôpital's Rule and then solve the limit.…

A: Answer: The solution is given below:

Q: For the function, find the indicated expressions. f(x) = x² In(x) = x² (a) Find f'(x). f'(x) = X (b)…

A:

Q: Solve the following relations for x and y, and compute the Jacobian J(u, v). u = 9xy, v = 3x x=y=…

A:

Q: 1. Find the intervals on which f is increasing and 3x²+2x+2 11 + 2z. x²+x+2

A: for incresing  f'(x)>0  and for decreasing f'(x)<0for critical points put f'(x)=0dxndx=nxn-1

Q: f(u) = Using the u-substitution u = 3x² + 1, identify f such that the integral help (formulas) X 3x²…

A:

Q: Consider the following function. f(t) = e 0-1²

A:

Q: If what does the following integral equal? - 17 √ - 64 [6f(x) + 4g(x) − h(x)]dx = = - 17 [ - 64 f(x)…

A:

Q: Which of the following equations represents a parabola with vertex (5,2) and directrix y = - 2? (А)…

A: Let's find equation of parabola.

Q: Question Use Fubini's theorem to compute the double integral ff f(x, y)dA where f(x, y) = 4y and R =…

A: