The eigenvalues of the coefficient matrix A are given. Find a general solution of the indicated system x' = Ax. 2 17 4 x'= -1 10 1 x; λ=6, 6, 6 0 16 x(t) =

Q: 10-8-8-4 191 6 30 O 45 X 10

A: Topic = Functions

Q: (a) Show that the three points define a right triangle. Hint: The difference between two vertices in…

A: Note:as per guidelines we Support only three subparts of the questions.kindly repost next question…

Q: Q2/A/ Prove cot² @ csc 0+1 + 1 = csc0 B/Find the value of c if f(x) is a continuous function at x =…

A: To prove the given trigonometric equation and  To find value of c for which function is continuous…

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to sketch the graph of given function.

Q: x-1 +1 1-z Q1) Find equation of plane normal to line *-¹ == and pass through line 3 2 1 x=y=2.

A: Concept: The standard form of the line is x-x0a=y-y0b=z-z0c Here a, b c represents the normal…

Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

A: A function y=f(x) is continuous in an interval [a,b] if it exists for every x∈[a,b] In other words a…

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

A:

Q: If f '(4) = 0 and f '(x) 0 for 4 < x < 5 then f has a local minimum at x = 4. True False

A: If f '(4) = 0 and f '(x) &lt; 0 for 0 &lt; x &lt; 4 and f '(x) &gt; 0 for 4 &lt; x &lt; 5 then f has…

Q: Solve for m | |m8xy+x)dxdy=3, 0<y<x<1

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Q5: Find the sums of the following (geometric series): 3n-1 - 1 6n-1 n=1

A:

Q: 3. The population of a specific bacteria growing in a Petri dish is modelled by the function t P(t)…

A: Population of bacteria is  P(t)= 12000(3)t/4  a) determine the value of t when P(t) =324000  b) what…

Q: 1 x-3 x2-3x-4 dx

A:

Q: 5. y = log(7x + 3). 4²x¹+8

A:

Q: Question 2. Let f(x, y) = 5xy² + sin(x + y). Find the following: (a) The gradient of f(x, y). (b)…

A: as per company guidelines we solve only first three subparts when multiple parts question being…

Q: A telephone company agrees to put a new exchange for 100 subscribers or less at a uniform charge of…

A: Given the charges per subscriber is 40 pesos for 100 or less, if subscriber is more than 100 then…

Q: 5) a) Find the eccentricity, b) identify the conic, c) give an equation of the directrix & d) Sketch…

A: Concept: We know that a conic section is defined as the locus of a point that moves in such a way…

Q: Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤ x ≤ 2pi

A: Determine the coordinates of the absolute extremes of y = 3sinx(cosx), 0 ≤ x ≤ 2pi

Q: 4. For the function f(x)= 7x - 5 apply the difference quotient simplify your answer. f(x+h)-f(x) h…

A:

Q: Dr. Zeyid T. 1 Y₁ =D²-²-2-[x²] Yp y, = [−1− D² + ···] · [2x +3] : y₁ = -x-2 P How

A:

Q: IF x=t, y=t², 2= 2/3 t3 and r is the position vector, denoted by r=ti + t²j + 3/23 t²³³ k dT @ Find:…

A: Acccording to question,Given equations,x = ty = t2andz = 23t3andr = t i^ + t2 j^ +  23t3 k^

Q: Starting at age 35, you deposit $2000 a year into an IRA account for retirement. Treat the yearly…

A:

Q: A small company of science writers found that its rate of profit (in thousands of dollars) after t…

A: given rate of profit =4t+4t2+2t+2 13To find: Profit in first three years

Q: Suppose an angle a is drawn in standard position. In each case, use the information to determine…

A: We have to find the quadrant for the angle alpha which satisfies the following conditions  a)…

Q: Given the function g(x, y, z) = x²y - 4zex+y, find the slope at P(1,0,1) in the direction of the…

A: Here is the solution

Q: Solve the following differential equations of 1-' 4. (2xy²-2y)dx+(3x²y-4x)dy=0 ( 7

A: The solution is given in the next step.

Q: Given the function f(x) = x² + Draw a sketch of the graph of f. 16 - X x>0

A: Follow the procedure given below.

Q: d²y dx² - y = = x - x - 1

A:

Q: f= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the…

A: Please refer too the image below

Q: 33° 45° 87° 60° 35° 30° Drag each reference angle above to the corresponding angle below. Answers…

A: Given :(1) 93° (2) 215°(3)-150° (4)-60°(5)765°(6) 480°

Q: 3. Find the Laplace transform F(s)=[f(t)](s) where f(t)=- ›-4 4 for 0 < t <2 for t≥ 2.

A:

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections…

A:

Q: Given points P(2,1,3) , Q(1,2,1), R(-1,-2,-2) and S(1,-4,0). Find the shortest distance between…

A: We will use

Q: (f) 2 dy (2y+3) 4x+5 dx y(1) = 3

A:

Q: Show that given R: x € [0,1] ^ y € [0,2] 1133 3x²yexy dy dx = 6 R

A:

Q: Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A:

Q: (6) Solve the following differential equations of 1 -(- ´, ny)dr = 0 y j 21 ...... (y-xy) dx + xdy =…

A:

Q: Given y=(3-ex)/2ex  , determine the behavior as x approaches negative infinity

A:

Q: The number of bachelor's degrees conferred has been increasing steadily in recent decades. The rate…

A: Given: B'(t)=0.621t2-1.213t+15.55

Q: 5) The function A(x) = A₂e-0.0077x models the amount in pounds of a particular radioactive material…

A: Both 5 and 6 has been solved as per the request of the student.

Q: 1. In x x² dx

A: The given integral is: I=∫16lnxx2dx   So, we can also write as; ∫16lnxx2dx=∫16lnx·1x2dx=∫16lnx·x-2dx…

Q: b. 1 1 + In u น - du

A: We can you evaluate the given integral by using the substitution v = ln u

Q: Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

A: This question can be solved using the concept of angle between line and plane.

Q: Q5-Show if the following series are converging or diverge π 1) Σ=1 η 10 Σ=1 (33) 1 της 2) 3) Σ=1

A:

Q: Repeated Irreducible Quadratic Factors: Examples S 1 v4 + 8v² + 16 dv

A:

Q: Evaluate the following integrals C. [x√x + 1dx

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: Here, the given function is: y=f(x)=xx2+4

Q: Starting at age 35, you deposit $2000 a year into an IRA account for retirement. Treat the yearly…

A:

Q: An artist can complete 11 drawings each month. Currently her portfolio contains 50 drawings. How…

A: This question is related to algebraic operations, we will solve it using given information.

Q: Solve the following differential equations of 3x d'y dx² +9y=2e³x +18x+18

A: We need to solve D.E.