Solve the following problems. Show your solutions 1. Mang Juan borrowed money to start a business. The bank told him that he has to pay a simple interest of 5% for 6 months on the amount he borrowed. If Mang Juan borrowed

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Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n - n³ + n² + 1 n=1 converges or diver...

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Q: We have lim 1 0, but - n-0 n lim f) 1 lim 1 = 1+0 = f(0). Thus n by Theorem 9.2.1, f is not continuo...

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Q: Find the function y, of t which is the solution of 49y" + 14y'-35y = 0 %3D with initial conditions Y...

A: Introduction: The general solution of a higher order linear homogeneous differential equation is obt...

Q: a) Prove by induction that 2 · 2 + 3· 22 + 4· 23 + .. (n + 1) · 2" = n· 27+1 for all n 2 2.

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Q: Solve the system using matrices (row operations) 24y =-112 = -8 2y - 2z 4л - Зу-42 %3D -3 How many s...

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Q: 19. Evaluate W (1+x, x, x²) (а) —2 (b) —2г (с) 2г (d) 2

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Q: 4.2 True or False: If T : R3 R3 is a linear transformation so that T(e1) = T(e2- e3), then T is not ...

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Q: Evaluate: Σ-Σi-2(2-1) 5-j (i+1)² 14 j=1Zi=2

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Q: 1. lim f(x) = 2. lim f(x) = %3D 3. lim f(x) = 4. lim f(x) = x-2 X-2 5. lim f(x) = %3D

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Q: Let T : R? → R? be the linear transformation which reflects across the line y = -2x and then ()- -3x...

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Q: .(Subtle) Suppose p(x) is continuous on some interval I and a is a number in I. What can be said abo...

A: The complete solutions are given below

Q: Answer in complete solution this Differential Equation: (4D8-16D7+79D6-284D5+448D4-1124D3+531D2+324...

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Q: 1. lim f(x)= x2" 2. lim f(x)= X-2 3. lim f(x) = 4. lim f(x) = x-2 X-2 5. lim f(x) =

A: 1. To find the limit as x→2+ is obtained by looking at the graph.

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A: Let us find the solution of the given vector space problem in the next step.

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Q: For the following differential equations, - Classify whether the equation is ordinary or partial dif...

A: Introduction: When an equation contains derivatives, the equation is referred to as differential equ...

Q: Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduces t...

A: Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduces t...

Q: 2. If y = tan(x +n), find x as a function of y.

A: 2 Given function is y=tanx+π. We have to find the x as a function of y. We know that y=tanx⇒x=tan−1y...

Q: Let a > 1. Find the area of the region bounded by y = /2(x – a) and y x- a. A) B) C) E) 6. A) B) c) ...

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Q: Let R be the divisibility relation (|) on A = {3,5, 6,7, 10, 20, 30}. We know that (A, |) is a poset...

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Q: Let (X,dX) and (Y,dY) be metric spaces. If the sequence (fn) of functions from X to Y converges unif...

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Q: A is a 4 x 5 matrix and rank(A) - 3. Choose from the following options the statement that is true fo...

A: A is a 4×5 matrix with rank (A) = 3 

Q: d waves uniformly in all directions. At a distance of 15.0 m the intensity of the sound is 0.250 W

A: Given as, Distance= 15.0 m, intensity of the sound= 0.250 W/m2.

Q: Match each vector field with its graph. 1. F(x, y) = xi + yi 2. H(x, y) = xi – yj ? v 3. G(r, y) = -...

A: Clearly ,we can see that

Q: 6. Determine whether the following linear transformations are one-to-one. Are they onto? Justify you...

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Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →...

A: The complete solutions is in given below

Q: t(n) = 7t(n-1) - 6 What is the smaller root (the root with smaller value) of the characteristic po...

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Q: A train has one engine and six train cars.  Find the total number of ways an engineer can arrange th...

A: Solution:-

Q: Revenue functions C(q) = q° - 9q + 56q + 5000 and R(q) = - 3q + 2500q, wha narginal cost would be $ ...

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Q: Suppose f is a quadratic function that has roots 8, and f(0) at x = 5 and x = 15. We will - write a ...

A: First we have to sketch graph of fx. Then we proceed further. 

Q: the next three terms. g) -2;-5;-8; _; _; 11 7 h) 2; 2. i) 15; 10; 5;

A: To find- Find the next three terms. g) -2 ; -5 ; -8 ;     ;     ;     h) 2 ; 114 ; 72 ;     ;     ; ...

Q: Read the following carefully, and then answer the questions that follow. We say that two n x n matri...

A: We have to find the value of A100.

Q: solve the following Equations using Euler's Method Equations a. y = 3x5

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Q: A steel company has two mills. Mill 1 costs P70,000 per day to operate, and it can produce 400 tons ...

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Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20 ...

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Q: 3. Find intervals containing solutions to the following equations. а. x – 2-* = 0 b. 2x cos(2x) – (x...

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Q: 15. which are subgroups a. (1, 7, 49, 43) b. (1, 9. 19, 21, 39, 41, 49) e. (RO, RS0, V. H, D) (80. 1...

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for yo...

Q: 5. y = 1- |x|

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Q: a. For any equation containing the variables x and y, the derivative dy/dx can be found by first usi...

A: To find dydx from an implicit function f(x,y)=C, we differentiate it directly term by term and then ...

Q: A is a 4 x 5 matrix and rank(A) - 3. Choose from the following options the statement that is true fo...

A: A is 4×5 matrix with rank A =3.  

Q: let a and b be integers, if 7|(17a+25b) then prove 7|(10a+11b)

A: 7 | (17a+25b)  => There exist some integer k such that       17a+25b = 7k

Q: Let div F = 2(7 – x) and 0 < a, b, c < 13. (a) Find the flux of F out of the rectangular solid 0 < æ...

A: divF=2(7-x) 0≤a,b,c≤13.

Q: Write the first five terms of the sequence, give the exact answer: +oo n 1 Determine whether the seq...

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Q: 5. Here is the graph of y= f( x). (a) Sketch the graph of its inverse on the same grid. (b) Is the i...

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