2. Caffeine is eliminated from the body at a continuous rate of approximately 17% per hour. A standard cup of coffee contains 150mg of caffeine.  a) Write a formula for the amount of caffeine C in mg as a function of the number t of hours after drinking a cup of coffee.  b) Find the number of hours (to the nearest hour) it makes for half of the caffeine from a cup of coffee to be eliminated from the body.  c) Find the number of hours (to the nearest hour) it takes for only 1.5mg of the caffeine from a cup of coffee to remain in the body.

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Q: 4 Computation Please solve the following questions with details. (1) Evaluate the double integral…

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Q: [0.5 -0.5] 0.5 -0.5 Let A = . Note that the columns of A are orthonormal (why?). 0.5 0.5 0.5 0.5 -3…

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Q: Thingamabob Sales Yaster Inc. is trying to enter the thingamabob market. The research department…

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Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

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Q: (b) Sketch the following function. Write down its equation in unit step function and find its…

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Q: Q5/ Giving the following data: X 0 1 2 3 4 5 f(x) 1 0 1 3 8 16 Evaluate the integral flf(x)]² dx by…

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A: 1 & 5 asked and answered.

Q: 1. Evaluate the following integrals. 2 S.S. Зу xe 4- re3y 4-y dy dx. (a) 0 (b) y+2 1 * √√x² + y² 2…

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Q: 80 jess X e-x sin x dx.

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Q: 3 8. Show that the volume of a cone with height h and radius a equals Ta²h using h iterated…

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Q: What vertexes have the short

A: Given: Graph with 9 vertices To find: Vertex having shortest path

Q: How many thingamabobs should Yaster Inc. produce and sell in order to maximize profit?

A: Given: Price Demand function p(x)=57-1.14x Cost function c(x)=215+11x Revenue function…

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Q: i. Use the bisection method of finding roots of equations xº -x-1=0 use the initial approximations…

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Q: Q2: Find the root of: 2cos(x)-x=0 with xo = 0 using Newton Raphson method (work 4 steps) then find…

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Q: which of the following is a binary operation if a and b are in S

A: To find:  Which of the given is a binary operation if a and b are in S

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Q: [Numerical Integration]. Show manual calculation. The force on a sailboat mast can be represented by…

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Q: 7. So -y dx + x dy x² + y² G₁₁: x² + y² = 1 C₁ traversed in a clockwise direction. (b) Green's…

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Q: (a) Is f continuous at the point (0,0)? Justify your answer. (b) Does the equality lim lim f(x, y) =…

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Q: 7. Which of the following sets of functions is linearly dependent on R0,2? (a) {6, z, sinz} (b) {1,…

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Q: 7) Find all complex solutions to the equation below. Express your answers in both polar and…

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Q: nd the value of y for x=2./ using a 2" order Lagrange polynomial with the appropriate data SI. Y 1…

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Q: 1. The linear span of a set S is the (a) largest subspace contained in S. (c) smallest subspace…

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Q: Simplify and state any restrictions on the variabl y²-2y-B a) 2y²-8y y²–4 y-2 + 2X+1 (x-2)² b)- - 4…

A: First we can simplify these expressions. Then we find the restriction on variable.

Q: System of Linear Equation] Just choose on one of the method below. Show manual calculation. olve the…

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Q: Part 1 - Application Pick one of the two graphs below. Describe a situation which could be modeled…

A: To Explain: A real-life situation that can be represented by one of the given graphs.

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Q: Q2/ The following system of equations is designed to determine concentrations (the c's in g/m³) in a…

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Q: √ x³ e-x sin x dx 0

A: To solve the given integral  ∫0∞x3e-xsinxdx

Q: Solve the problem. -0. -11. -10 Let a , and b = 6 Determine whether b can be written as a linear…

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Q: The Taylor expansion of f for x → 1 is f(x) = 5(x - 1) - 4(x − 1)² + 4(x - 1)³ + o((x - 1)³); then,…

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Q: four vectors ~v1, ~v2, ~v3 and ~v4 be given by ~v1 = (1, 0, 2), ~v2 = (0, 1, −1), ~v3 = (1, 8, −6),…

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Q: 22. Data may have a positive skewness mean long tail of curve to the left. O True O False

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Q: 3 2 - x 9x6 6 5 4 2 = 4x + 5x + 7x + x f(x) = 4x² f(x) = Falls to the left and rises to the right…

A: Given some polynomials, check the end behavior of their graphs. (a) fx=4x3-x2-9x-6

Q: 1. Find the Fourier Sepise of 4x: 0<x< T f(x) {" 1:-π<x<0 on interval-A

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Q: Question 4 Compute the product or state that it is undefined. -5 (3] à do do 38 -245 -18 8 -19 -10 O…

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Q: 5. Identify and sketch the graph of y = x² + 1 in R³.

A: To identify and Sketch: the curve y=x2+1 in ℝ3.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.