2. (a) (b) The weight of a radioactive substance remaining after t years is given by -0.04t W=1000x2 grams. 1 Show that t= - log₂ ( 0.04 W 1000 Hence or otherwise, find the time required for the weight to reach (II) 0.001 grams. (I) 20 grams

Q: Using Laplace transform, solve the differential equation below.

A:

Q: a 3d vector field given by V=5xyi+5yj-4zk represents the flow of water out of a system. use gausses…

A:

Q: Assume that T and S are matrix of the same size. Prove or Disprove that (T + S) 2 is a symmetric,…

A: Given   T  and   S are matrix of same size. We have to prove if  T+S is symmetric, skew - symmetric…

Q: Q/Particular Solutions -D- operator method (D²-D² )y=2e*

A:

Q: 1- Find the first derivative of y with respect to x for the following functions: In5 7x a- y = log5…

A:

Q: See the following matrix below: A 2 1 -1 2 0 2 1 B Answer in simplest or reduced fraction form if…

A: The determinant of a 3×3 matrix is calculated using the formula:…

Q: 5. Find the half.. range cosine Fourier Series for.. the function.. X OCX < Z ..£.(x)...= TT-X <x<T…

A: The given problem is to find the half range cosine Fourier series expansion of the given function…

Q: y" — y' = 2x, y (0) = 1, y'(0) = -2

A:

Q: A) Find all real eigenvalues of A, and give algebraic multiplicities, if it exists. B) Find the…

A: This is a problem of Linear Transformation

Q: Find the solution of the system DE: 2x'+y'-2x=1 , x'+y'-3x-3y=2 , where: x(0)=0 , y(0)=0

A: The solution is given as

Q: is not a Field Always because if we take the ideal I =¸ then Z12/ e map y: Z, -→ Z₂ such that y(x) =…

A:

Q: Find the order and degree of e^y" - 3(y¹ ) ² + 2xy = xe^ and write the differential equation in…

A:

Q: 1. Assuming that 80% of the Mars surface is covered with water at an average depth of 3.5 miles and…

A: Follow the steps.

Q: What is the parametric form of a curve equation? Are the curve equations (y-f(x) What is the type of…

A:

Q: 1. Give a geometric description of the set of points in space whose coordinates satisfy the given…

A: Given: Let us consider the given set of points, a) x=-1, z=0 b) x2+y2+z2=25, y=-4 c) x2+y2=4, z=-2

Q: How do you add decimal fractions

A: Fractions in decimal form Math is the representation of fractions in decimal form with denominators…

Q: identify the statement that does not hold in a complete ordered field K and provide a…

A: This is a question of Abstract Algebra.

Q: 8. Determine whether the series converge (a) k+5 Ση (b) k=1 1+2k+k² 1+ 3k + k²

A:

Q: If Ø: R→ S is a ring isomorphism. The Ø preserves O Nilpotent elements Idempotent elements Units O…

A: Let , ϕ : R → S  be a ring homomorphism. We know that , an element x of ring is said to be nilpotent…

Q: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

A:

Q: A relation R is defined on the set of all integers as xRy if x - 4y is greater than 5. Then the…

A: We have given that  , R is a relation defined on a set of all integers as x R y  if  x - 4y greater…

Q: 2. Let f: R → R be the quadratic function defined by f(x) = 3x² - 12x + 15. i) Vertex and Axis of…

A:

Q: 7) There is no proper non-trivial maximal ideals in (Z2₁, because is a maximal ideal in Z2₁, ,0 )…

A: Solution

Q: Consider the differential equation dy -0.6(y - 3), with y(0) = 2. dt In all parts below, round to 4…

A:

Q: 12) evaluate the triple integral. ∫∫∫e (y)dv, where e is bounded by the planes x=0, y=0, z=0, and…

A: A a couple of vital is a exact vital of a characteristic of many actual variables in mathematics…

Q: (d) subspace of R2, or explain why it is not a subspace of R². (i) 1291051 (iis 291051 2012 For each…

A: We solve this problem using the definition of a subspace. The detailed typeset solution in latex is…

Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

A:

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: 1. Find the exponential Fourier Series for the function .f..(t) = 2t .-...<.t.<....... -2 -ja m…

A: We find complex (exponential) F.S.(Fourier series) of  f(t)=e2t (-1&lt;t&lt;1)

Q: Through conversations like these parents and children can begin to find some middle ground. What is…

A: The term statement is used in logic to refer to a meaningful declarative utterance that is true or…

Q: Show that the given set V is closed under addition and multiplication by scalars and is therefore a…

A:

Q: Let E be a vector space. If E= U+V and E=U+W, then there is an isomorphism f: V--W between

A:

Q: 4. Expand .f. (X.).=.03.x. as a half._. ·range Fourier sine.... series in the range FX S.T. 8 ans.:…

A:

Q: Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3 A 92/6 s.u. B 92/4 s.u.…

A:

Q: Consider the two functions 2x+1, for x < 0 1 f(x) = and g(x) = (x - 1). 1-x², for x ≥ 0 2 a) Sketch…

A: Note : Area of a closed bounded region D is given by the double integral  I=∫D∫dA

Q: Try This! Find the area of the given triangle, given that: 3. b = 28.6, c = 44.3 and B = 23.3⁰

A:

Q: A tank originally contains 380 liters of brine holding 450 N of dissolved salt. Eight liters/min of…

A: A tank contain 380 liters of brine and of dissolved salt is  450 N. And, The rate of entering for…

Q: mpotents in Z are {0, 1} elements of Z are non-zero divisors. in Q al Domain sian Integers Z[i] and…

A:

Q: The matrix -| has a singular value decomposition A = UΣVT where U = and What is (Σ)11? Answer: हाज…

A:

Q: 1. (6x-3y+2)dx-(2x-y-1)dy=0

A:

Q: show that the complex Fourier sevies of the function; f.(t) = t. 。st.sl is... jant if (t) = j 2T…

A:

Q: ૦.૫૦૬૫૫) 1.2529636 0.9162907 1.3862944 1.0986123 1.7917595 1.6094379 3.5 1.5 3 2.5 ૫ 5 a. find an…

A: As per the question we are given a data table from which we have to find : The estimated value of…

Q: 1. Evaluate the given integral Q. -L LL²³ . = (2x − z) dz dy dx Зг 2. Give the (upper, lower,…

A: Solution

Q: Find the volume of the region bounded by the sphere x+y+z² =9 and the planes x=0, y=0 and z = 0.

A:

Q: F(s) = 1 (s²+1)(s²+4s+8)

A:

Q: Find the volume of solid generated by revolving the region bounded by the curve y-4/x' and the lines…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Determine if the sequence converges or diverges; if it converges, find the limit.

A:

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

Q: у ху = X Sin x

A: