If 10% of a radioactive substance disintegrates in 4 days, what is its half-life

Q: Find the slope of the tangent line to the graph of y = √x − 1 at the point (5,2).

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given :r(t)=cos(πt)i-ln(t)j+t-14k ; t0=15To find : The domain of r(t) and the value of r(t0)

Q: B) Find for the Implicit function: dx x² – sin(xy) + y² = 5xy %3D

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Q: Find all second-order partial derivatives of the function f(x,y) = x + xy – 5x³ + In(x² + 1).

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x0 sin 2x x2-16 2. lim r14 (Yx+5)-3

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Q: Q2 Obtain the general solution for the following differential equation. b) y" – 4y' + 3y = 3e2x +…

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Q: 'If you have three functions: f(x) = x2 – x g(x) = 3x – 1 w(x) = x² – 2 So, find gof (x) and fow(x)…

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Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A: Let x be the acute angle made by the telescope with the vertical.

Q: An oil tank is being drained for cleaning. After t minutes there are Vlitres of oil left in the…

A: Determine the rate of change of volume at the time t = 10??

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (3t + 4)i + tj, 0 <t<1

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

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Q: The Inverse Laplace Transform for 5/3S - 2/ ((3(s+3)) is

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Q: 3. Find the absolute maximum value of the function f(x)=- 1+x2

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Q: 1 Suppose that L is a location function of an object, given as L(t) : We 2t – 3 will compute the…

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Q: 1. a dx 2. f(sec(4x)- 1)² dx 3. S 1+(Sx+1) dx

A: As per our guidelines, we are supposed to answer only the first three parts. Kindly repost other…

Q: g(b) Use the Substitution Formula, JKax) •gʻ(x) dx = [ | f(u) du where g(x) = u, to evaluate the…

A: The given integral,a) ∫-334rr2+22drb) ∫034rr2+22dr

Q: Find Inz3 dz

A: LetI=∫lnz3zdzLet z3=udifferentiate 3z2dz=duDivide 3z2 on both sidedz=du3z2dz=du3z2Divide z oboth…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 4t2 – 2 sin(5t)…

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Q: Approximate the integral using Taylor series method: xsin?x dx

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at x-2? %3D

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Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: Find the marginal profit function if cost and revenue are given by C(x) = 184 +0.3x and R(x) =…

A: This is a problem of differentiation . Based on the formula and concept we will answer the question.

Q: 4. Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to calculate indefinite integral ∫{(3x2+6) /(x3+6x) }dx Let us say  I = ∫ {(3x2+6) /(x3+6x)}…

Q: Find the net signed area between the graph of the function f(r) = -x-4 and the x-axis over the…

A: To find the area between the line and x axis.

Q: at x = 2 for the function below. dx Evaluate y = - 5u? + 4u + 9, where u = 9x2 – 2x + 4 Answer…

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Q: Determine the value of 3A+5B if 10x2 + 25x +5 A Cx +B (x – 1)(x + 1)² (x+1)² 1 - |

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Q: A man borrows Php 100,000 from the Social Security System for a term of one year. The interest…

A: Bank Discount  =100000×15100=15000

Q: Find the limit. lim (t i - 7 j+1² k) t-5 lim (t i- 7j+? k) = i i+ i j+ i k

A: To find the limit of the given vector valued function.

Q: Find the area of the region enclosed by the curves y=x^2 and y=6x by integrating with respect to y.…

A: To find the area of the region enclosed between the two curves.

Q: nd the linearization of f(x)= {Vx at c = 64. Use the linearization to approximate 64.05.

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Q: Let f be a function defined for t 2 0. Then the integral L{f(t)} = e-stf(t) dt is said to be the…

A: Given problem:-

Q: dy Q4) Find for the following functions dx 1. y = 2x? + e2x-1 2. y = sec x tan x 3. y = t2 + 2t t =…

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Q: Starting at age35 ​, you deposit​ $2000 a year into an IRA account for retirement.  Treat the yearly…

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Q: B. Solve the following problems using differentials and linear approximations. Show complete…

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Q: 1(10,15) 2. An ant farm population is growing at a rate of g()=15e and declining at a rate of…

A: The rate of growth of an ant farm is gt=15e5t and  the rate of decline of the ant farm is dt=15e5t.

Q: A. Identify if the given limit is NORMAL, OSL-RIGHT, OSL-LEFT or DNE. x-2 1. lim x--4 x2-2x x+4 2.…

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Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

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Q: Given the function g(x) = 6x° + 72r² + 270z, find the first derivative, g' (1). gʻ(x) = Notice that…

A: g'x = derivative of gx with respect to x g''x = derivative of g'x with respect to x if at  point…

Q: Describe the graph of the equation. r = -6i+ (1 – t?)j + t k O It is a parabola in the plane z = -6,…

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Q: Convert the point from spherical coordinates to rectangular coordinates. (2플) (х, у, 2) -

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: Given problem:- Find exactly T(t) and N(t) for x = et cost, y = et sint, z = et for t = 0

Q: 2 2 of

A: Please see the answer below.

Q: 3. The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

A: First write the volume of a sphere and then diffrenciate it and put all the values.

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

A: As per given  We have to solve above question  Given  V(t)=t2-2t-8

Q: Evaluate the integral. 3 if -2 < x< 0 f(x) dx where f(x) | 4 – x² if 0 <x< 3

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: Find the area enclosed by the curves y = y = 2 1- 9x2 2n B 3 D 6. [+

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Q: Find the radius of convergence, R, of the series. (x + 4)" R Find the interval, I, of convergence of…

A: The given series,        ∑n=1∞n6nx+4n

Q: Evaluate the integral and interpret it as the area of a region. 6x + 7 - x dx 55, 55 - 32 9 9 Sketch…

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Q: Q3) Evaluate triple integral f, (x2 -y²)dz dx dy.

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