A carbon sample contains 4000 atoms of radioactive element 235U. Given that 235U has a half-life of 800 years, how long would it take to decay to 150 atoms. Note: Half-life = (Ln2)/k a. -3500 years b. 3500 years c. 4000 years d. -4000 years e. None

Q: Solve the differential equation. dy + 5y dx = e-5x dx A y = 5x + ce-5x By=e-5x (x + c) C) There is…

A:

Q: A television camera is positioned 4000 ft from the base of a rocket launching pad. The angle of…

A: A television camera is positioned 4000 ft from the base of a rocket launching pad. The angle of…

Q: Use partial fractions to evaluate the integral 1² 2²-24-3d² 2x

A: Given :∫02-4x-3x+1dx

Q: equation for the parabola that has its vertex at the origin and has directrix at x=−121x=-121. The…

A: Given query is to find the equation of the parabola.

Q: Assume a population of fish grows exponentially. A pond is stocked initially with 500 fish. After 6…

A:

Q: Find the particular solution to the differential equation below such that y(0)=−8.…

A:

Q: Find the gradient Vf of the function f given the differential. df = (3x² - 1) ye dx + x³e dy

A:

Q: d the equation of the tangent line to the curve at the given point using implicit differentiation.…

A: Given query is to find the equation of the tangent.

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A: concept  Graph of the Function: The given function is expressed in the product form too but we shall…

Q: The radius of a spherical tumor is growing bycentimeter per week. Find how rapidly the volume is…

A:

Q: Find the derivative of f(x) = (x8 – 9x) (x² = + 2x -6)

A:

Q: The half life of carbon-14 is approximately 5568 years. If we have 250 grams carbon-14 today,…

A:

Q: a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute…

A:

Q: O Setup the Riemann sum 5 x³ dx = lim n→∞ n k=1 f(x) dx = lim Σ f(x) Ax for the given integral. n→∞…

A:

Q: 4. For any kл, where k = Z, O Always True O Sometimes True O Never True 1+cos 8 sin Ꮎ

A: Topic - Trigonometry We are given, sin θ1+cos θ=1- cos θsin θwe know thatsin2θ+cos2θ=1

Q: Find an equation of the tangent line, at the designated point, to each of the following: a) f(x) = x…

A:

Q: ving integral equal? -21 [²+ f(x)dx = 7 93 and g(x) dx = 16 and h(x)dx = 27 -21 -93 21 -93

A: We have to find the value of the given definite integral according to the given information

Q: The indefinite integral (4x – 5)e4* dx can be evaluated using integration by parts. Even though you…

A:

Q: D(x) = 960 25x is the price, in dollars per unit, that consumers are willing to pay for x units of…

A:

Q: Evaluate, using substitution f 24t5 4t6 +3 - dt. T

A:

Q: Answer using Differential Equations  A thermometer is brought outside from the inside of a house…

A: According to the Newton's Law : T(t) = Ts + (To – Ts) e-kt Where, t = time, T(t) = temperature of…

Q: A runner is jogging at a constant speed of 3.1 miles per hour. a. Find the distance d that the…

A: We need to find the function for the distance traveled by the jogs as a function of the time.

Q: 11. A church window is in the form of a rectangle of heighth with a semi-circular section added to…

A: CONCEPT: In geometry, the perimeter of a shape is defined as the total length of its boundary. The…

Q: 9) The Mean Value Theorem shows that for a differentiable function the average rate of change over…

A: Since this is a multiple question, according to the Bartleby answering rule, only the first question…

Q: Y -4).0 . C is the path along (x + 2)² + (y + 2)² = ≤ y-1' x+4 exactly once, starting at (1, -2) and…

A: Please see the below picture for detailed solution.

Q: Section 1: Real Numbers Note, Paccign. 1. Rationalise and fully simplify the denominator of the…

A:

Q: Given the vector-valued function u(t)= (t²- 3)i + (2t + 4)j + (t³ - 3t)k, d calculate [u(t) × u'…

A: Explanation of the answer is as follows

Q: 0.2x Find the average value of the function f(x) = e Express your answer in exact form. on the…

A: Topic = Function

Q: Suppose that an object initially having a temperature of 20°C is placed in a large temperature…

A: newtons law of heating T - TsT0 - Ts = ekt where T = temperature at time t T0 = initial…

Q: 3-t Let F(x) = √² + 40 (a) Find the value of a where F obtains its maximum value. x = dt for -∞0 < x…

A:

Q: The price (in dollars) p and the quantity demanded q are related by the equation: p² + 2q2 = 1100.…

A: Solution-   Given A=(2q2-550)/q and dR/dt=A*dp/dt   b) dp/dt=3 and q=15, then dR/dt=?   Now put…

Q: 13. The statement "p implies q" is true. O Always True O Sometimes True O Never True

A: To determine whether the statement "p implies q" is always true, sometimes trueor never true.

Q: 2. Given the vectors and u = (3,−4), v = (−1,2) find |2u + v, |2u|+|v|| Answer: √61,10 + √5

A:

Q: Use integration by parts to evaluate the definite integral S te-t dt.

A: We need to use the integration by parts to solve the definite integral.

Q: Eliminate the arbitrary constants lnx = Asin3y + Bcos3y + 9x2 - 5

A:

Q: Find the work done by the vector field F = (4z, 4y, 3x) in moving an object along C in the positive…

A: Solve the following

Q: Write an equation for a sphere centered at the point (-7,6,-8) with radius 7.

A: tandard equation of sphere ( x-h )2 + ( y - k )2 + ( z - s )2 = ( r )2 where ( h, k,s ) -…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. R/8 Jo cos(4x) dx

A:

Q: Graph the equation. Include the coordinates of any local extreme points and inflection points. Show…

A: NOTE: Refresh your page if you can't see any equations. . here the coefficient of x2 is positive,…

Q: Let (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengths…

A:

Q: The half-life of cesium-137 is 30 years. Suppose we have a 160 mg sample. (a) Find the mass (in mg)…

A: Topic - Exponential function We are given The half life of cesium-137 = 30 years initial mass of a…

Q: Covid pandemic caused a company annual revenues to drop from 530M in 2019 to 386M in 2021. If the…

A: Let's find expected revenue in 2023.

Q: Use the substitution X 2 sec t to evaluate the integral - = dx x√x²-4

A:

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A: Given, y=x-13+5

Q: The area of a rectangle with one of its sides s is A(s) = 17s². What is the rate of change of the…

A:

Q: Evaluate the integral: S (2-1)(2+1)2 dx : +C

A:

Q: A contour map for a function f is shown. 5-4 8 7 16 in 6+ 4+ M 24 10 30 。 40 50 Use the contour map…

A:

Q: Let 0 be an angle in quadrant one such that cos0=3/4 find the exact values of csc0 and tan0. Thank…

A: The objective of the question is determine the values.

Q: Solve fr5 ln(x) dx using Integration by Parts. Use u = ln(x) and v' = x5. Answer: 9.

A:

Q: The first derivative of a continuous function y = f(x) is given. Find y'' and then sketch the…

A: