Suppose that you have open a saving account with initial deposit of $ 5000, you continue to deposit money into the account at a rate of $ 2000 per year, and the account earns of 3% per year, compounded continuously. Write down an initial value problem that describes your savings account balance b(t). (Hint: change in money-interest+savings). Find your balance at 5 years.

Q: Given the following graph a. Evaluate f (3). f(3) = Number b. Solve for f(x) = 3. n ril H Submit…

A:

Q: Initially an 800 gallon tank contains 400 gallons of water in which is dissolved 50 lbs of salt.…

A:

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given query is to find the antiderivative of the expression.

Q: 2 + 3. The velocity of a particle moving in a straight line is given by v(t) = t² + (a) Find an…

A: The velocity of a particle moving along a straight line is given by vt=t2+3 We have to find the…

Q: Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and…

A:

Q: Give one example to illustrate that vectors satisfy the triangle inequality. Justify your answer

A: Vectors of Triangle Inequality : u+ v≤u + v

Q: 7. (a) Let f(x) = 5x5 + x¹ − 2x³ – 1. Explain why f is continuous on (-∞, ∞). (b) Show that f(x) has…

A: We know a polynomial function is continuous in the whole real number plane. If f(x) be a continuous…

Q: Use the Second Derivative Test to find the location of all local extrema in the interval (-7,5) for…

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x.  f(x)= 4+7ln;…

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

Q: (c) Check that your solutions t substituting the expression 63. xy + 2x + 3x² = 4

A:

Q: Problem 6. A particle is moving on a horizontal line. Its distance from the origin at time t20 is…

A: The  particle is moving to the left if the velocity is negative.

Q: Consider x^6 +7xy^2 = 15065, find dy/dt when x = 5, y = -4 and dx/dt = 2 dy/dt = ?

A:

Q: The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation.…

A:

Q: 18. Using Lagrange multipliers, find the point on the plane x + 2y + 3z = 4 closest to the point…

A:

Q: If t = 3' a) sin t 1. 39463NT 2.0 3. 5. 7. 6. None of these 1 √2 005 (part 2 of 3) 1 1.1 2. 2936 co…

A:

Q: +00 2 e. Se Sexx²dx 0

A:

Q: A formula for calculating the magnitude of an carthquake is M = -log() that uses the common (base…

A:

Q: Find the value or values of c that satisfy the equation C= f(x) = 4x + 4 X [16.16 f(b)-f(a) b-a (Use…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. • Stan(kx)…

A:

Q: Perform the subtraction. E4816-C8416 E4816-C841616 (Simplify your answer.)

A:

Q: S 3 cos³ (x) dx

A: To integrate the given function

Q: Esc [3] Use a first derivative test with a well written conclusion to state the local min and max…

A:

Q: A box with a volume of 8m³ is to be constructed with a gold-plated top, silver-plated bottom, and…

A: Given:         Assuming the box is a cube.         The volume of cube = side³           side3=8…

Q: 3. The area of a circle increases at a rate of 47 cm²/s. How fast is the radius changing when the…

A: We can find the required answer in the below steps using the given data.

Q: 16. Determine lim f(x) if the given function is x→2 f(x) = 2.², 82r, if if x 2 x

A:

Q: If the population of an ant colony in 3 days is known to be 2000 and P'(0) 2. What is the…

A: For Linear Growth we have formula, Pt=P0+ktWhere Pt is population at t days.P0 is initial…

Q: дz дz Given xyz = z + sin(x + y), find and Әх ду

A: The given multivariable function is:xyz=z+sin(x+y)

Q: and flux of F=(x, 7T T ≤t≤ the circulation y) on C: r(t) = (3 cos (t), 3 sin(t)) for is positive,…

A:

Q: its radical so how do u do 409 racial 3

A: To explain how the radical is simplified.

Q: At what point (x, y) is the function f(x) = -4x - 9 closest to the point (3, 1)? Enter an exact…

A: To determine the point on the function which is closest to (3, 1)

Q: Calculate the double integral S fæ cos(2x + y) dA where R is the region: 0 ≤ x ≤ 7,0 ≤ y ≤ 4

A: The given integral is: ∫∫R x cos(2x+y) dA       where R is the region:  0≤x≤π6,   0≤y≤π4

Q: Consider two nonnegative numbers x and y where x + y = 13. What is the minimum value of 2x² + 12y?…

A:

Q: Find the equation of the lines tangent to the curve x² + y² = 4 and parallel to the line x = 3 ?…

A:

Q: (c) Find the value of √a²-x² [₁ 2(x + y) x² + y² giving your answer in terms of a. 1+ -dx dy,

A: The given integral is:∫0a2-x2∫-aa 1+2(x+y)x2+y2 dx dy

Q: solution to evaluate 3 2+1 y-1 ГГГ x + y2 dx dy dz ? Z 3 4 Ⓒ √ ²² - ² - ² + + 2+1 A 6 2 2 В 3 o fl с…

A:

Q: Consider the following. e-10x = 2 (a) Find the exact solution of the exponential equation in terms…

A: As we know that lnem=m lne=m  as lne=1

Q: Use Newton's method to find the slope of the tangent to the curve defined as y = -5x² + 2x-7

A: Let's say the point of contact of the curve and the tangent is at x = a. According to newton's…

Q: Question 1 Evaluate the integral. 2xsinxcosxdx Ax cos 2x - sin 2x + C B-x cos 2x + sin 2x + C C) -x…

A:

Q: Problem 2. f = Is the integral XT dx convergent or divergent? Hint: There is a test that allows you…

A:

Q: and algebraically why the following two transformations are different.. y = 3f (²x-1) +5 y = 3f…

A: The function is given as   y = 3f14x-1+5     and     y = 3f14(x-1)+5

Q: f(x) = x²e-x (a) Find the exact value of the minimum of f for x ≥ 0. f(x) = Find the exact value of…

A:

Q: (2n+1)! b) Ση=1 (3)η

A: Let us consider a series ∑n=1∞un with limn->∞un+1un>1 and also {un} is monotonic increasing…

Q: Question 1 [ a) [ b). Consider the function f(x)=x²+3x+c Find the domain of f(x) in terms of c on…

A:

Q: 5. Find the equation of a parabola with vertex at the origin whose properties are given below. a.…

A:

Q: Convert the general form to standard form of parabola

A:

Q: Find the gradient of the function y at x = 4.

A:

Q: (c) Let F(x, y, z) = x^3i + y^3j + z^3 k i) ∇ · F (ii) ∇ × F

A:

Q: Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find…

A: WE can determine if each of the following vector field is the gradient of a function f(x,y) .

Q: Suppose a product's revenue function is given by R(q) and q is units sold. Find a numeric value for…

A:

Q: dy (y-1)√y²-2y-3 S.

A: