Let P = (0,0, 0), Q = (1, –1, –2), R = (2,1, 1). Find the area of the triangle PQR. area = Let T = (8,9, 1), U = (-8, –3, 1), V = (-8, –2, –2). Find the area of the triangle TUV. area =

Q: Is there a solution y = y(t) of the differential equation y" + e*y = 0 satisfying lim y(t) = 2021? J...

A: We have a differential equation ,  y'' + ety = 0 First we will find solution of differential equatio...

Q: Let f (z) = zi + (z – 3) - Part (a) Integrate the function f (z)along the curve C given by z t3 +it?...

A: We will use the basic knowledge of complex analysis and integral calculus to answer this question.

Q: What is the principal that will grow to $5600 in six years, eleven months at 3.7% compounded quarter...

A: Compound interest formula A=P1+rnnt where A is accumulated amount P is principal amount r is rate of...

Q: Home work : f ind the a ppro ximate value af the following! 2 ( 8.02) (3.96) + (3.03) 2 - I (5.07) +...

A:

Q: (d) Consider the following system of linear equations 2x1 - 3x2 + x3 - 3x4 + 2x5 = 6 2x1 - 3x2 + 5x3...

A:

Q: Given the integral: 4 dr. Evaluate using Romberg's method. Tolerance = Næ1o 6 %3D 1+x²

A: Use the following formulae, to estimate the integral ∫abfxdx by the Romberg integration method. h=b-...

Q: Differential s of the form

A:

Q: 2. Evaluate. the fallowing.integrals.a.fter.seveoiag.the areler.of.integratiam. dydx Ans..In)/4 C. ....

A:

Q: Select an Answer 1. 3 -9 15 21 1 -3 7 -2 7 -11 -17 Select an Answer 2. -2 -6 -1 -3 1 4 Select an Ans...

A:

Q: Evaluate the definite integral using the Newton-Cotes quadrature formula (Simpson's Rule)

A:

Q: 2y dy = sin dx when y(1) 4 + %3D -

A:

Q: 4. Let X be an ordered set, and A C X . Show that (a) For every x, x has at most one immediate succe...

A:

Q: Double Tower of Hanoi contains 2n disks of n different sizes, with two disks of each size. You must ...

A:

Q: Find the truncation error of the following Maclaurin series given that it is truncated into 3 terms....

A:

Q: Maximise -x2 + 0.4x - y2 + 0.2y using only points within the sphere x² + y < 1 . What is the value o...

A:

Q: liferential equation with variable coefficients, y" + p(t)y/ + q(t)y = 0 (i), %3D can be transformed...

A:

Q: In the following graph, find an Euler cycle if possible. If there is no Euler cycle, find an Euler p...

A: Given :  

Q: Consider the following set: = {tx, y, z] € R³ : x + 2y – z = 0} (a) Show that S is a subspace of R°....

A:

Q: Given the series: Σ k=1 does this series converge or diverge? converges O diverges If the series con...

A: Let us consider the series ∑n=1∞an  The series can be  Convergent Divergent Oscillating 

Q: A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth & Son...

A: Given- A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smoot...

Q: If A = 5i - 2j -3k and B 2i-5j-7k and C=5i- 2j-8k, then the volume of tetrahedron (pyramid) formed b...

A:

Q: a 6) Determine the value(s) of a such that is linearly independent. a +

A: Let us consider the n vectors of order 1x n in Rn  The vectors are said to linearly dependent if the...

Q: A mobile phone company offers a phone plan that allows 600 min of airtime per month. The revenue gen...

A: A quadratic function is defined using the equation: y=ax2+bx+c. The regression analysis is done to d...

Q: 1. Solve the following system of equations using the Gauss elimination method: 2x1 +x2 -x3 = 1 xj+ 2...

A: Multiple : We have given system of equation ,  2x1 + x2 -x3 = 1x1 + 2x2 + x3 = 8-x1 + x2 - x3= -5 By...

Q: Given a vector p= (0,1) e R², numerically state a dataset {x}_1 such that li=1 x* = mịn ||x – p||2 =...

A: At first we will define a special dataset {x(i)} which will be such that the Euclidean distance will...

Q: Let F(x) = dt. Find an equation of the tangent line to the curve y = F(x) at the point with x-coordi...

A:

Q: 2. Evaluate. tha fallowing.integrals.a.fler.revening.the erderf.integratiem. S.ing dy.dx. TT Ans.g.2...

A:

Q: 2. (x2 + y?)dx + xydy = 0

A:

Q: Let a = (4, 8, -6) and b = orthogonal to a. (2, 2, –7) be vectors. Decompose the vector b into a com...

A: We are given a=(4,8,-6) and b=(2,2,-7) be the two vectors. We have to decompose the vector b into a ...

Q: Consider the integral // | 2z°dzdyda, where E is the tetrahedron with vertices (0,0,0), (5,0,0), (0,...

A: Evaluation of the triple integral, bounded by tetrahedron  

Q: 3. Call a functionf:N N eventually nondecreasing if the set decr(f) = {n €N|S(n +1) < f(n)} is finit...

A: We will use the basic knowledge of mathematical logic to answer this question. Let ∑ denote the rang...

Q: Evaluate the Legendre symbol () (a) using the reciprocity law 1873 8389 only for the Legendre symbol...

A: As per the question we have to evaluate the Legendre symbol (1873/8389) using : Reciprocity law of ...

Q: 2 Howin show that

A: This is a problem of partial derivative and chain rule.

Q: Assume a; > 0 (i = 1,..., n). Show that 1 +. a1 < (a1a2 ... an)/n. n an

A:

Q: Solve the following system of linear differential equations: y = 6y, - y2 = 2y 1 3y2 a. 4r = k,e + k...

A:

Q: Consider the points A(3,-3,3), B(4, –5, 1), C(-2, –4, 1), and D(6,3,-5). (a) Find the volume of the ...

A:

Q: 1. Determine if the series cos" (-) * (H) en? n=1 is absolutely convergent, conditionally convergent...

A:

Q: Problem 1. Solve the linear system Až = 6, where -- - - A:= 2 -5 and b:=

A:

Q: Try to fit any two moving averages models to the following data and discuss its performance. YEAR 20...

A:

Q: F1 = {all smooth functions f(t) such that f(0) = 1}. %3D %3D Is F1 a subspace of F?

A: In order to solve this problem you need to know the following notions:

Q: Determine whether the relation ? on the set of all people is reflexive, symmetric,  antisymmetric, a...

A: We have to determine whether the relation R on the set defined in the parts (a) and (b), are reflexi...

Q: dy 4 e. + y tan x = y³s dx

A:

Q: Find the distance between u 4 and z 2 The distance between u and z is (Type an exact answer, using r...

A: Let us consider  two vectors u=x1,x2,x3 and v=y1,y2,y3 The distance between the vectors is obtained ...

Q: Determine the b, of the Fourier Series of: f(t) = { -15; -3<t<0 10 ; 0<t< 3

A: Introduction: Suppose, a one cycle a continuous periodic function is defined on the interval -P,P. T...

Q: The solution of which linear inequality is represented by the graph? 4- 2- -4 -6- CLEAR SUBM -6x +5y...

A: Inequality: An inequality is a mathematical expression in which both sides are not equal and we use ...

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main di...

A:

Q: Match the figure with its net. Drag each figure to the box above its net.

A: If the base of a pyramid is a triangle, then it is called a triangular pyramid. If the base of a pyr...

Q: Find L{f(t)}. (Write your answer as a function of s.) (t) = et + 2 L{Rt)} = (s > 1)

A:

Q: Which statement about the distance between 6 and 0 and the distance between the opposite of 6 and 0 ...

A: Distance between two entities is the length between them Distance is a positive scalar quantity Dist...

Q: Find any relative maximum, relative minimum, and saddle points and identify what each point is. (By ...

A: