A sample of radioactive material with decay constant 0.08 is decaying at a rate R(t) = -2e-0.08t many grams of this material decayed after the first 14 years? grams per year. How

Q: The graph of a function f(x) is given below. Use the midpoint Riemann sum with 4 sub-intervals to…

A: A graph of the function is given.The aim is to find the midpoint Riemann sum with  subdivisions.

Q: Given the graph of f(x) below, find the graph of the derivative of f(x). Select the correct answer…

A: From the given graph

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A:

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A: Let, .We know that,

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A: The given set is the set of points in space whose coordinates satisfy the pair of equations .The aim…

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A: we need to find out the slope of the function.

Q: Evaluate the improper integral O a.-2 O b. 1 042 C 3 X

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A:

Q: What is the derivative of f(x) = −‡x³ a at the point x = 3? Type an exact answer.

A: f(x)=−43x23 at the point x=3Using the power Ruleddxxn=nxn−1

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A: The objective of this question is to find the intervals on which the graph of the function f(x) = -x…

Q: NASA launches a rocket at t=0 seconds. Suppose its height, in meters above sea-level, as a function…

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A:

Q: You are asked to write the quadratic function with the smallest possible integer coefficients that…

A: The given roots of equation are

Q: -10-9-8- -1⁰+ Given the graph of f(x) shown above, evaluate lim f(x). Select the correct answer…

A: The condition of the existence of limit at

Q: Given the graph of f(x) below, find the graph of the derivative of f(x). 1-6-5-4-3-2-1 1.7

A:

Q: 3) Use the method of Lagrange multipliers to find the points on the curve x²y = 2 nearest the…

A: The given equation of curve is Let the point  on the curve which is closest to origin

Q: H Use Stokes' Theorem to evaluate Sc F. dr where F = (x + 6z)i + (5x + y)j + (8y-z) k and C is the…

A:

Q: A cell culture contains 4 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Substitute t=5 in r(t) and solve, an then add 4 thousand to it.

Q: Find the derivative of  f(x)=X4.23x

A:

Q: K Evaluate the following integral. X 2 X 2 x +3 +3 dx dx =

A: The given integral is x/(x2+3).

Q: Find F as a function of x and evaluate it at x = 0, x = π/4, and x = π/2. ftc F(x) F(0) F(x) I = =…

A:

Q: Time (secs) 0 30 60 90 120 150 180 Speed (mi/secs) 0.00 0.03 0.08 0.16 0.27 0.42 0.65 9. The table…

A: Given Information table is as follows

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A:

Q: the U.S. postal service will accept a box for domestic shipping onl if the sum of its length and…

A: Let b be length of the box and a be the length of the side of the square.The volume V of the box…

Q: 2. Find the Maclaurin series of the following functions. 1. f (x) = xm 1-x³9 2. f (x) = x² sin² (4x)…

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Q: Find the exact values of the following expressions. sin (630°) and cos (630°)

A:

Q: Evaluate the following 2 j (x² + 3x-10) dx -5 √(x²+3x-10 +3x-10) dx = -5 (Type an exact answer. Use…

A: The given integral is .The aim is to find the value of the integral.Formula used:

Q: Let u = (5,-4) and v= (-4,7). Find the (a) component form and (b) magnitude (length) of the vector.…

A: The vectors are given by(a) The component form of the vector  can be obtained as follows:

Q: 7. Evaluate cln 8 √th 0 [² Sin pln(2y) In y e+y²-drdydz.

A: To evaluate the following integral.

Q: Show that the function f(x) = x4 + 8x + 6 has exactly one zero in the interval [-1, 0]. ... Which…

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Q: *P(zx) ulg*J

A:

Q: For the following equation, determine the values of the missing entries. Reduce all fractions to…

A: To find the value of y, substitute the value of x and solve for y.To find the value of x, substitute…

Q: Evaluate the following limit. lim x⇒0 6x - sin(6x) x3 Type only your final answer in the blank, eg,…

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Q: Determine the integral by making the appropriate substitution. 1 2 x In 3x dx ⠀⠀

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t²…

A: The velocity function (in meters per second) is given for a particle moving along a…

Q: Evaluate I = (sin x + 2y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. y C B A=…

A: Here  we have to find the integral along closed path.

Q: Find the area of the part of the plane with vector equation r(u, v) = (6 + v, u - 5v, 9-4u + v) that…

A:

Q: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

A: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

Q: A retail business owner wants to build two adjacent retail stores on a rectangular plot of land. The…

A: The figure

Q: Find local extrema f(x) = 4 of the function, if any. x6 - 6x² A. There is no local extremum. B. f(0)…

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: Draw the region whose area is given by the definite integral. (6-2 (6 - 2x)dx

A:

Q: Rocky Mountain Tire Center sells 7,000 go-cart tires per year. The ordering cost for each order is…

A: a) Given that:Annual Demand (D) = 7000Ordering Cost (S) = 40Holding Cost (H) = 30% of Purchase…

Q: Adding a vector to the zero vector O a) preserves the non-zero vector O b) reduces the vector's…

A: The zero vector isSuppose we have a vector asOn adding the vector with the zero vector we get

Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pairs…

A: Give a geometric description of the set of points in space whose coordinates satisfy the given pairs…

Q: Find a, b, c, and d such that the curve ?=??3+??2+??+? has its tangent line at(1, 1) and at (0, -2)…

A: The objective of this question is to find the coefficients a, b, c, and d of the cubic function y =…

Q: Consider the following function. 1 (x-4)² Step 1 of 2: Determine the more basic function that has…

A: The given function is,

Q: Determine the integral by making the appropriate substitution. √9(x-1) 9(9x-10)' 'dx

A: To determine the following integral by making the appropriate substitution.

Q: x = 3 sin(t), y = 4 cos(t), 0 < t < 2π (a) Eliminate the parameter to find a Cartesian equation of…

A: