The number of research articles in a prominent journal written by researchers during 1983–2003 can be approximated by U(t) =4.3e0.4t/0.3 + e0.4t thousand articles per year    (0 ≤ t ≤ 20), where t is time in years (t = 0 represents 1983). (a) Find an (approximate) expression for the total number of articles (in thousands) written since 1983 (t = 0). (Round your coefficients to two decimal places.) N(t) =________________________    (b) Roughly how many articles were written from 1983 to 2003? (Round your answer to the nearest whole number.)  ______________________thousand articles

Q: A company plans to enclose three parallel rectangular areas for sorting returned goods. The three ar...

A: Given : Perimeter of the rectangular = 888 yard  Now we find total largest Area = ?

Q:

A:

Q:

A:

Q: 5а? + 36х + 45 dæ а? (г? + 9)

A:

Q: Which one is equal to 2 10 SS zyf(z, y) dz dy -oxoy? O Correlation of X and Y O Covariance of X and ...

A: For the given statement

Q: Briefly explain each step

A: Complete solution = complementary function + particular integral.

Q: If f(w) = e 4 sin w +5 cos w find f'(w). Use exact values. f'(w) =

A: We can make it easier for you

Q: Find each of the following integrals: dx (x2 + 9)2 a. b. esin z cos x dx 0. 15x2 – 14x – 13 - C. dx ...

A: As per our guidelines i can only solve 3 subparts As shown below

Q: Determine whether the given function is periodic. If so, find its fundamental period. (If the functi...

A: To determine - If the given function is periodic or not. Also its fundamental period.

Q: Use the graph of f (z) = = below to find a number 8 such that |f (z) – 0.25| < 0.1 whenever 0< [z – ...

A:

Q: The line y=2 is a line parallel to x-axis. Select one: True False

A: In general, x=a is a line parallel to y axis and y=b is a line parallel to x axis

Q: Find the equation of the tangent line to the graph of the given function at the point with the indic...

A:

Q: Question 5 If f(x) = u - 6u +5du, then what is the y-coordinate of its inflection point?

A: we have given f(x) and we have to find the co-ordinate of its inflection point

Q: (1) Which is the correct formula for finding the derivative of the product of two functions? O (fg)'...

A: PROBLEM SOLVE ON PAPER PLEASE CHECK

Q: Consider a certain system of two first order linear differential equations in two unknowns, x' = Ax,...

A:

Q: As much as possible you are required to use the u-substitution method, but if you think that you hav...

A: Note : As per our guidelines we are allowed to solve one question at a time. Kindly repost the remai...

Q: Find the equation of the plane through (3, -1, 2), (4, 0, 2), and (5, 3, 1).

A: .

Q: What is the result of the fourth iteration of solving a root of the algebraic equation with x0=0 wit...

A: Using Newton raphson method. 

Q:

A:

Q: Solve the optimization problem. Minimize F = 20x² + 20y² with xy2 = 16. %3D F =

A:

Q: E", |r| < 1, Given n=0 1 (a) Find a power series representation for 1+ 2x (b) Integrate the power se...

A:

Q:

A:

Q: As much as possible you are required to use the u-substitution method, but if you think that you hav...

A: Since you have posted multiple question in this question so I have solved first question as per our ...

Q: Find ?f if ?″(?)=2+cos(?),?(0)=1,?(?/2)=−8.f″(x)=2+cos⁡(x),f(0)=1,f(π/2)=−8. ?(?)=

A: To find- f(x)

Q: 3. S dx 1+x2 4. Sx sec?xdx

A:

Q:

A: Using substitution method, integration the function. Put x^3 = t

Q: Compute the definite integrals. Lx cos(x) dx х COS OT – 1 O1 -2 O 2

A: Please refer the attached image for complete solution.

Q: Two non-vertical lines are perpendicular if and only if their slopes are negative reciprocalsof each...

A: Two non vertical lines are perpendicular if and only if their slopes are negative reciprocal

Q:

A: Here is the solution

Q:

A:

Q: Evaluate the following integrations: 5. S sin?x cosxdx 6. Sx tanx?dx 7. cos(rt) dt A sin (nt)

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | 2 sect() dx

A: Note : As per our guidelines we are supposed to answer only one question . Kindly repost other quest...

Q: 6 dx. 1+ 9x2 Calculate

A:

Q: Compute the profit (loss), in dollars, corresponding to the following production levels. P(5,500) =$...

A:

Q:

A:

Q:

A:

Q:

A: In implicit differentiation we differentiate without separating the variable

Q:

A: Here we have to find the area of the shaded region between the big circular equation x2+y2=16 and an...

Q: each of the following integral: x2 a. dx V4-9x2

A: Kindly keep a note in step 1️⃣stating that as per our guidelines we are supposed to answer only 1️⃣q...

Q: Use implicit differentiation to find the slope of the tangent line to x +y² = 4 at (1.6, 1.2) then f...

A:

Q: For the solution of the PDE x*uz + y?u, + x² + 4x + 6y = 0 Which transformation can be used?

A: use special form of charpit auxiliary equation

Q:

A: See the details solution in below

Q: Calculate the derivative of the function. g(x) = (x² – 3x – 1)-7 %3D g'(x) =

A:

Q:

A:

Q: Find the equation of the tangent line of the given funtion at the indicated value of x.  188.f(x)=se...

A:

Q: Suppose that the position of a particle is given by s = {t) = 7t + 6t + 9. (a) Find the velocity at ...

A:

Q:

A: First i have made a substitution so that integral become easy and then solved them.All solution are ...

Q:

A: use partial fraction  ...................(1) ...................(2) take x=1/2 ..............put i...

Q: As much as possible you please use the u-substitution method, but if you think that you have an easi...

A: Since you have posted multiple question in this question so I have solved first question as per our ...

Q: a ødpdød0

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.