Refer to the model Q (t) = Q0e^-0.000121' used for radiocarbon dating. At an archeological site, scientists uncovered human remains. A sample from a human bone taken from the site showed that 38.2% of the carbon- 14 still remained. How old is the sample? Round to the nearest year. Do not round intermediate calculations.

Q: 77°F Sunny Which of the following functions could make the graph 27 18 16 14 12 10 N. Of(x) =…

A: Graph of a polynomial function

Q: Consider the given vector field. F(x, y, z) = x²yz i + xy²z j + xyz² k (a) Find the curl of the…

A: The expression of the curl of the vector field F=F1i+F2j+F3k is: curl F=∇×F=ijk∂∂x∂∂y∂∂zF1F2F3 The…

Q: 10. Which of the following matrices is in reduced row echelon form? Select the augmented matrix…

A: A matrix is in reduced row-echelon form if it satisfies the following: In each row, the left-most…

Q: Find the area of the region that lies above the x-axis, below the curve I = t²+2t +9, y=et with 0…

A: The given curve is:x(t)=t2+2t+9,    y(t)=e-t       with  0≤t≤1

Q: Find the determinant of the matrix. -28 1/3 5 2

A:

Q: Find the length of the spiraling polar curve r = 4e58 From 0 to 2π . The length is Question Help:…

A: Length of curve=∫abrθ2+r'θ2dθ

Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = (a) Find a function f…

A: Consider F and C Fx,y=x2 i+y2 j C is the arc of the parabola y2=4x from -1,4 to 1,4

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A:

Q: and x = 4. y 15 10 -10 2 2 Find the area of the region bounded by the curves y = x² + 8, y = x², x =…

A:

Q: 2. Find the centroid of the region R = {(x,y): x ≥ y²/2, x ≤ y}.

A:

Q: Find the volume of the solid generated by revolving the region enclosed by x=√√15y², x = 0, y = -3,…

A: The given curves are: x=15 y2 ,     x=0,       y=-3     and     y=3

Q: Which polar coordinate pair labels the same point as the one shown below? 4x Select all that apply.…

A: We have to find the coordinates that label the same point.

Q: A boy is selling lemonade throughout the hot summer. Suppose the number of cups sold is given by the…

A: Solving the following problem

Q: Find the directional derivative of the function f(x, y) = x² + at the point (x, y) in the direction…

A:

Q: Given the function g(x) = 8x³ − 60x² + 144x, find the first derivative, g'(x). g'(x) Notice that…

A:

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: y= √(64-x2)  We have to evaluate volume of solid formed by revolving the region about y axis

Q: 4. Write the first 4 terms of the sequence [d₂}. d₁=64(-1)^

A:

Q: To find local extrema (maximums and minumums), the first step is to find critical points. Critical…

A: (i) To find local extrema (maximums and minimums), the first step is to find critical points. To…

Q: Evaluate (cos3A) dA.. A. B. C. D. x/6 27T 363 35T 768 23T 765 12π 81

A: To evaluate ∫0π6cos3A8 dA. Note: Since the student has posted multiple questions and does not…

Q: PROBLEM NUMBER 6 Solve 3y²+x=0, where y=5, when x = 0.

A: We shall use separation of variable then direct integration to solve IVP

Q: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

A: Fx,y=e2x+x2y, e2y-x2y   C is the circle x2+y2=4 oriented clockwise. Here r=2

Q: Evaluate fay'da + aªdy, where C is the rectangle with vertices (0,0), (1,0), (1,4), and (0,4)

A:

Q: √x√√7-x² d dx - S

A:

Q: x = -3 sec (t), y = 3 tan (t), 4- 2 <t< 2

A: We know that the formula sec^2(t)-tan^2(t)=1

Q: π Determine the slope of the tangent line, then find the equation of the tangent line at t = 6 x = 2…

A:

Q: Solve given Linear Differential Equation Q4.5

A: To solve the following

Q: 4 -2 -3 -4 1 At the point shown on the function above, which of the following is true? O f'>0 and…

A: To solve the following

Q: 1 = [0) R : R-xd= xp

A: given,  dydx=ex-y  and  y(0)=1

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given :- y=x,y=0 x=3,x=6 about the x=1.

Q: Evaluate the definite integral. 5 [³9. √/7² dx

A: The given integral is ∫059.x23dx To evaluate the integral.

Q: find the equation of the tangent line at (2,1) given ln(y)=4y^2-x^3+4

A:

Q: A population of insects increases at a rate of 210 + 14t + 1.2t² insects per day. Find the insect…

A: dP/dt = 210+14t+1.2t2

Q: how the Taylor formula was applied how did we get those numbers and why is x in absolute value

A: As given in the question, dom f = x∈ℝ| x2+3x=xx+3≥0 = (-∞,-3]∪[0,∞) f(x)=x2+3x is a polynomial…

Q: An invasive population of 40,000 Nutria is being hunted in a local swamp. The amount of Nutria…

A:

Q: Evaluate the integral ſ (In x)" X dx

A:

Q: F Calculate the circulation of the field F around the closed curve C. F=(-x-y)i + (x+y)j. curve C is…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the given curve and lines…

A:

Q: F. dr. (Check the orientation of the curve before applying the theorem.) Jc F(x, y) = (e2x + x2y,…

A: Green's Theorem ∫F1dx + F2dy = ∬( ∂F2∂x - ∂F1∂y )dxdy

Q: Find the rate of change of the volume of the increasing radius of a sphere when r=11. V=4/3*pi*r^2.,…

A:

Q: Write an equation (any form) for the quadratic graphed below 5-4-3-2 32 -2 12 to वॅ

A: The quadratic function in the vertex form is of the form  y=ax-h2+k  ...(1)

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A:

Q: Compute the volume of the solid bounded by the given surface. z=x+1, z-y-2,x=y²-2,x=y

A:

Q: Find the volumes of the solids generated by revolving the region between y=3√x and y= about a) the…

A:

Q: Find the average value of the function f (x) = x x on the interval [0, 2]

A:

Q: 2. Find the area bounded by the curve y = the x-axis, and the vertical lines r = and x = 1.

A: The area bounded by the curve y=1x,the x-axis,and the vertical lines x=12 and x=1 Graph

Q: Use cylindrical coordinates to find the volume of the solid. Solid inside x² + y² + z² = 16 and…

A:

Q: find the unit tangent vector N(t) to the curve r(t)= when t=1

A:

Q: = 1 VX dt It = 1

A:

Q: (ir, cos³e day+ycosx тусова = Sinz

A: The given differential equation is: cos3x dydx+y cos x=sin x

Q: y dr (1 ㅗ Russe ; (대전)R

A: