Suppose that the world's current oil reserves, RR, is 1,990 billion barrels. If, on average, the total reserves is decreasing by 22 billion barrels of oil each year, answer the following: Give a linear equation for the total remaining oil reserves, RR, in terms of t,t, the number of years since now. RR =

Q: ) Let T : R? → R? be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps i…

A:

Q: Use Laplace Transform technique to solve the initial value problem y' + 2y = 26 sin 3t , if y(0) = 3

A:

Q: Determine the first four terms of the Fourier Series for the function f(x) = x,0 < x < 2, in a half

A: The given problem is to find the first four terms of the Fourier series of given periodic function.…

Q: п+1 a1 = 0, An ап-1 + 3п + 3, n >1 n

A:

Q: Problem 2 – Use the Laplace Definition to find L {f(t)} f(t) = t5 а. b. f(t) = 3 sin 2t + 4 cos 3t

A: Definition: The Laplace transform of a function ft is denoted and defined by Lft=∫0∞e-stftdt We…

Q: Generate the inverse of the production function below and interpret the result. You can assume x is…

A: Given: The production function, y=x2-0.2x. Here, x is an input of water measured in acre-feet (AF)…

Q: Find the area. a. Inside one leaf of the three-leaved rose = cos30 b. Shared by the circle r=2 and…

A: Given that a) r=cos(3theta) b) r=2 and r= 2 (1 +sin(theta)) c) r=-3cos and r=1-cos( theta) We have…

Q: 92 (a) Determine the roots of fix) -13-20x+ 19 -3x graphically. In addition. determine the first…

A: (A) we are given to use graph to find roots firstly , draw graph we can see that curve intersects on…

Q: Q2: solve the following Linear programming problem using graphical method * Maximize (total profit)…

A: The given linear programming problem is…

Q: 4) Simplify by combining like terms: 3x + 3x + 3x A) 3x3 B) 9x C) 9x2 D) 27x 5) Divide and simplify.

A: Simplify by combining like terms : 3x + 3x + 3x

Q: (b) Prove that for all sets A and B, (AN B)° = A¢ U B°.

A: We have to prove that for all sets A and B, A∩Bc=Ac∪Bc

Q: Sketch the curve x = 3sin?t, y = 4cos²t (0<t s-) by eliminating the parameter, %3D and indicate the…

A: Here we use basic transformation .

Q: Given the region R inside the circle x^2+y^2=4 and above y= sqrt(3) A) Establish that d A exists B)…

A: Double integral over the region.

Q: Let f(x) be a function that passes through five points (-5,–8), (–3,1),(0,–2), (4, –5),(6,7) Find…

A:

Q: Solve the following problem using the method of Lagrange multipliers: Find the marimum and minimum…

A: To find the maximum and minimum values of x−y3, subject to the constraint x2+9y2=9.

Q: Graph each function using radians. y- 4cos 20 2 O *T

A:

Q: .Inside the outer loop of the limason r 1-2 cos e

A: Given that r=1-2cos(theta) We have to find area.

Q: A student borrows ​$1000 at 15​% for 6 months to pay tuition. Find the total amount due using simple…

A:

Q: IA quadrilateral ABCD has coordinates A(1, -1), B(3 ed by a factor of 2 using the origin as a center…

A: Introduction: The factor of Scale (Dilation) In the dilation of a mathematical object, the scale…

Q: Q) find Fourier series on [-n,7] (3) ƒ(x)=cos x COS X (4) ƒ(x)=xsin x (5) ƒ(x)=xcOs x - T < x< 0 (6)…

A: Since you post more than three subparts, as per our guideline we can solve only first three…

Q: 1 Find two equations (using cosine and sine) for the following: A mass on the end of a spring is at…

A: (a) Given that, The mass is hanging 80 cm from the ground, and it pulled down 60 cm and released at…

Q: car travelling along a straight road is clocked at a number of points. Use the following times and…

A:

Q: A parallelogram anc If side of a parallelc of the parallelogram (a) 15 m (c) 1233 m (e) None of…

A: Introduction: A parallelogram is a basic (non-self-intersecting) quadrilateral with two sets of…

Q: Consider the ordinary differential equation dt -x for the range t = 0 to t = a with the initial…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 7. Show that 3-{(; ) ( ) ( )} -1 2 S = 2 1 6 9 is linearly dependent in M22. Write one of the…

A: According to our guidelines I solve only 1 question, so kindly request you to repost the remaining…

Q: The total number of positive integer solution to the equation (x + y + z)(a + b + c + d) = 15 is

A:

Q: Suppose the tenuper a ture at a point (x,y,2) is represen ted by the following: T(2,y,2) = 10e2x* -…

A:

Q: fos 4 csc" xdx

A: If y=f(x), then the variable x is called the input of the function, and the variable y is called the…

Q: 12 A = 4 Find bases for the kernel and image of T(x) = Ax. A basis for the kernel of A is { A basis…

A:

Q: 5. Show the span {(1,0, 1), (–1,2,3), (0, 1, – 1)} is all of R³. 6. Determine whether span {(1,…

A:

Q: 2-Show that the following polynomials from a basis for P2. 1 - 3x + 2x?,1 + x + 4x²,1 – 7x

A:

Q: Suppose that an amount of 10,000 dollars is invested at an annual interest rate of r% compounded…

A:

Q: 1. The graph shows two accounts with the same principal and annual interest rate. Use the graph to…

A:

Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Find a 3 x 3 matrix A such that Az = 10 for all i in R³. A =

A: Given Ax=10x  We have to find 3×3 matrix A  Now

Q: d2y/ dx2 + y = xsinx and show that the solution is  y=c1sinx +c2cos x - x2cos x/4+xsinx/4

A:

Q: 1. A graph of a function f (x) is given as follows. Sketch the graph of f(x) . State all the x and y…

A:

Q: e =5= is Cupve?

A: Algebraic curves are the curves considered in algebraic geometry. A plane algebraic curve is the set…

Q: Among all the numbers between 20000 and 70000, including the numbers 20000 and 70000, how many each…

A: The total number of numbers between 20,000 and 70,000 is 70,000−20,000+1=50,001. First calculate the…

Q: 12. The cables of a suspension bridge are in the shape of a parabola. The towers supporting the…

A:

Q: d. Inside the circle r=4 sine and below the horizontal line r= 3 csce

A:

Q: Consider an Ultimaton game in which the disagreement payoff of each player is c> 0. Which of the…

A: In an ultimaton game we have one player making an offer of how to split a given amount, and the…

Q: Ql: Find out whether each of the following functions is a solution of the ODE. (choose 1) p(x) - 5p"…

A:

Q: Q2. Let a card be selected at random from an ordinary deck of 52 cards. Let A = [ the card is a…

A: Total number of card in a ordinary deck =52. Diamonds, hearts, clubs and spades. Among them diamonds…

Q: pand f(x) =5x as a half-range Fourier sine series in the range 0 < x <A , and sketch the function…

A:

Q: 3- Let {u,v,w} be a basis for a vector space V. Is {u + v,u + w,v + w} a basis for V?

A:

Q: -1 10 1. f(x) dr = 2. f(x) dx = 3. f(x) dx = 4. f(x) dx =

A:

Q: Use the slider to graph the standard position angle, then write the missing radian or degree angle.…

A: Given Degree Measure= 315 degree

Q: 1) If P(x1, Y) and R(x2 y,) lie on the same vertical line, what is the distance between these two…

A: As per our company guidelines we are supposed to answer only the first three questions. Kindly…

Q: 1. The integral of J, \z|dz along any closed path y is 0.

A: As per our guidelines, we suppose to answer only one question in case of multiple questions posted.…