1. Determine whether the following systems have unique solution, infinitely many solutions or no solutions at all. Those with solutions, determine them. (a) = 2 (mod 18): r = 3 (mod 45). (b) = 1 (mod 18); x = 2 (mod 7).

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

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Q: 2. (a) How many lines of symmetry does a regular octagon have?

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Q: For each condition, give an example of a ring R. Provide a brief explanation for each. (c) integral…

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Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: Relation between cartesian and spherical system  x=ρ sinφ cosθ , y= ρ sinφ sinθ , z= ρ cosφ Where ρ…

Q: Prove that If G Her 3-9 IS is an open set dense in the denx. S nowhere me tric space (sid)

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Q: How did you know to use the number 636 for your x in the hit and trial method and not use another…

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Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…

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Q: Let X = (6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z € N, x+z=y}, where N…

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Q: H.W: Find of and of for the functions: əx 3. f(x, y) = (x² − 1)(y + 2)

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Q: 9. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters)…

A: Given- If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in…

Q: pigeonhole principle

A: Given as, number of lottery tickets = 100 According to question, number of winning tickets = 12 The…

Q: X + y = 6 2x - y = 0 Solves using the substitution method

A: We need to solve the system of equations  x+y=62x-y=0 using substitution method

Q: Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a…

A: The final answer is l = 8

Q: r+∞ If $5 f(x) dx diverges, then so is •+∞ 88 f(x) dx.

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Q: Exercise (1-3): By Charpit method solve the following PDE Question Answer 2 z=ax- (9) 2z+p²+qy+2y² =…

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Q: Calculate the convolution (f+g)(x) of the following functions f(x) and g(x): 0 (x < 0) f(x) = = {²-²…

A: Convolution of two function f(x) and g(x) over infinite range can be given by  f*gx=∫-∞∞ft ×gx-tdt

Q: 2x - 3y = 6 6x - 9y = 10 Use substitution method

A: here We use substituion method

Q: How many positive integers divide 10!. 3 C =

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Answer the followings: 1. Let H = {[a b]: a, b, d € R, ad # 0}. Is H a normal subgroup of GL₂(R)? 2.…

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Q: ✓(3) Prove Green's theorem for F = Y Z + x²y³j y (1,1) i (1,0)

A: Solution of the given problem is below...

Q: D² - 4D + 4)y= e²x sec²x (by Reduction of Order)

A: Solution :

Q: 3. (a) Sketch the region of integration and evaluate the following integral by converting it to…

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Q: Q2: (B) let y = 3sin5x2cos5x show that y + 25y = 0

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Q: I    P    R    T ----------    2000    2%    ½ yrs. 500    ----------    10%    7 mos. 175    1030…

A: According to guidelines I solve first 3 subparts so kindly request you to repost the remaining…

Q: (c) The figure shows two similar prisms, if the volume of Prism I is 40 cm³, find the volume of…

A: To find the volume of prism using formula  Volume V = BH where B is base area and H is height of…

Q: Find the point wise limit of the sequence &{fn} the sequence {fr} Where Sin nx In (x) = √n if tay J…

A: Here we use basic limit property

Q: 1. A quadratic surface has equation 3x-x-x+4x₂+4₁3 +12₂=1. (a) Write this equation in the form x¹ Ax…

A: Given the equation of a quadratic surface, 3x12-x22-x32+4x1x2+4x1x3+12x2x3=1 To write this equation…

Q: 1 4. Given the functions f(x)= -()* and f₂(x)= 10 fi increases rapidly than f₂ fill in the blank…

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Q: Find the value of X(1) for the initial-value problem X d.x dt x(0.5) = 1 2(t+1) using Euler's method…

A: Please see the attachment

Q: find solution using direct integral method for the partial differential equation below: 137 1 12 xz…

A: Here we use basic integral formula to find these

Q: f) Simplify the Boolean algebra product-of-sum expression in part (d), stating the Boolean algebra…

A: Let us simplify the given Boolean expression using Boolean Algebra laws and properties in the next…

Q: 5. Let A be the linear transformation R2 R2 that first reflects vectors across the line y=z, then…

A: see my solution

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

A: if the curve is passing through the point (1,-1) then we have to find the curve if the slope of the…

Q: (MATRICES) Solve the following problems as directed. Show complete solutions and box the final…

A: We can solve this using given information

Q: Assume a 6 month CD purchase for 5,000 pays simple interest at an annual rate of 9.5. How much…

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Q: system of equations using Gauss Jordan method: 342 12 3 231 4 Solve the Assis following

A: We need to solve the given system of equation using Gauss Jorden method.

Q: Ex: S=28a, 106,5c? How many 5-perm. of 5 are there? k=3, r=5 => 35

A: As per the Bartleby guideline, 1 question can be answered. Please repost the second question.

Q: E = {x₁ 13 W bases for P₁ (x) ;) (77) SFEE f = [2x-1, 2x+1s be two ordered (ive P(x) = a₁x+ ac) SETE

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Q: Q1: If the function f(x) define as f: RR such that (x+1, x>2 f(x) = x²-1, x≤2 Show that the function…

A: Given that function f(x)=x+1      x&gt;2x2-1    x≤2To check Differentiability We find Left hand…

Q: Q1: If the function f(x) define as f:R → R such that f(x) = x+1, x>2 x²-1, x≤2 Show that the…

A: O

Q: F C

A: FEBAEFD is  a path  FBCCD is a path FEABFD is a path

Q: 12. Given the differential equation x dx = 0 and one solution y₁ = A (constant), use reduction of…

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Q: Guadalupe is skiing along a circular ski trail that has a radius 3.1 km long. She starts at the…

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Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: Use direct proof to show, "If m + n and n + p are even integers (s and t), where m, n, and pare…

A: To answer the given questions we shall use the following definition  An integer n is said to be even…

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+32) sin(t)dt

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Q: 2. Find solution of the system of equations Az = 0. where 1 1 3 1 6 2 -1 0 1 -1 A -3 2 1 -2 1 4 16 1…

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Q: 3.1 Let S be the set of all bounded continuous functions f: [a, b] → R. Given two points f and g in…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 7. Consider the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy = 0. a) Find an appropriate…

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Q: Hand written plzz how? please explain step by step 6. Assume that there are only three possible…

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