Question 4. Use Taylor's Theorem to estimate sin(3) to within 1/60.

Q: Find the orthogonal projection of -14 = -14 onto the subspace W of Rª spanned by and -2 projw(v) = 2…

A: To find The orthogonal projection of v onto the subspace of W of R^4 spanned by the given vectors.

Q: 5. Peter bought kids bicycles for $992 to sell to his bicycle club. He kept 4 of them to himself and…

A: Given: Cost price of all bicycles is $992. He kept 4. Sold remaining at $1104. Profit on each is…

Q: Each pair of polygons is similar. Write a similarity statement and find the scale factor. 4. B C 55…

A:

Q: 1 Question #9) dx x2 + 2x + 10 1 Question #10) x3 – x² – x – 15

A: 9. Given integral isI=∫-∞∞1x2+2x+10dxThe integral is evalauted using Cauchy Residue Theory as shown…

Q: A living room is 7.2 m long and 4.5 m wide. What size would it be on a plan drawn to a scale of…

A: This is a problem of counting.

Q: a. Use the formula for general solution to solve the following equation b. Check for your answer.…

A: The solution is given as

Q: Determine the exponential function given the graph. A y (0, –1) (-1, –5) F(x) = (5) " A - 2 B f(x) =…

A:

Q: A fair die is rolled three times. What is the probability of obtaining at least two 5​'s?

A: Given a fair die rolled three times.

Q: 1. Let f : Z6 → Z6 be such that f(7) = x² + 3. (a) Is f a well defined function? (b) Is f…

A: Please post the multiple sub-parts separately. Here I answered 1st three sub-parts as per our…

Q: Evaluate f(1). F(s)=÷ + 5 7. s7 Round-off to whole number.

A: Let us evaluate f(1) in the next step.

Q: If ||v|| = 6 and ||w|| = 4: What is the smallest possible value of ||v What is the largest possible…

A:

Q: 3. Let C1 be the circle r = 3 cos 0 and C2 the cardioid r = 1+ cos 0. (a) Find all point(s) of…

A: It is given that r1=3cosθ and r2=1+cosθ. We have to find the points of intersection of the curves r1…

Q: ) Find the image of p(t) = 2 – t+ t? ) Show that T is a linear transformation. :) Find the matrix…

A:

Q: ... 4 B = (-1,4) A A = (1,0.25) %3D -4 -3 -2 -1 2 3 4 5 A y= - 4× y=4-x O f(x) =| D y=4•1*

A: We want to find the equation of given curve.

Q: Suppose that the function/ is defined on the intérval as follows. r-2 if-25x<-1 -1 if-1Sx<0 0 if…

A: Given function is f(x) = -2if-2≤x&lt;-1-1if-1≤x&lt;00if0≤x&lt;11if1≤x&lt;2

Q: 4. Evaluate the iterated integral: E dydr. 1/4

A: Double integral

Q: 2. Let X = R² – (0,0) and ~ be defined over X by setting x~y + y = tx for some non-zero t € R. Given…

A: Sol

Q: min flx,,x) = (x, - 1)*+ (n,- 1)² Subrected to 」+Z2コ4 X,ーュ-2 き6 Hint : Convert to standard fom and…

A:

Q: 4. Evaluate the iterated integral: dydr.

A: To Evaluate:∫141∫x2xxydydx

Q: The slope of the surface z ry in the r-direction at the point (2,3) is. slope of this surface in the…

A: The slope of the surface z=xy2 in the x direction at the point (2,3) is =∂Z∂x2,3 . Now ∂z∂x = y2.…

Q: Az + 2xy²)dx + (cos y + 2x²y)dy = 0

A:

Q: 5. = P - p2 Ans: = cet dt 1-P

A:

Q: Problem 4 The helix r(t) = (cos(rt/2), sin(rt/2), t) intersects the sphere x2 + y2 + z2 = 2 in two…

A: We will find tangent vector of helix at point of intersection and the find angle of this tangent…

Q: Oues: Solve:- min flx,,) = (x, - 1)*+ Cn3- 1)? Subrected to n, +22=4 X,ー-2 き6 Hint : Convert to…

A: Given that,minx1, x2fx1, x2=x1-12+x2-12Subjected tox1+x2=4x1-x2-2≥0The minimum of the given function…

Q: A spherical tank of radius 4m is filled with water to a height of 1.2 m. The water is transferred to…

A: Let us find the height of the frustum of the cone in the next steps.

Q: Question 3: Obtain the solution set of the set of linear equations given below by using the Gaussian…

A:

Q: Find F(-1). 2e3t sin (2t) – 3e3t cos (2t) COS Round-off to 1 decimal place.

A:

Q: (x – 2)? – In x = 0, [1,2] %3D

A: Ques: use bisection method, to find the solution to the following within 10^−6 for f(x) = (x-2)² -…

Q: (a) classes of X induced by Prove that - is an equivalence relation on X and describe the set X/ ~…

A: This is a problem of relation.

Q: The residue of z cos (÷) at z = 0 is 1. 1/2 -1/2 1/3 4. -1/3 2. 3.

A: Residue of the function at z=0

Q: Area of theregion inside the circle (r=1) and outside the cardiad (r =1+cos).

A: Using polar coordinates the volume of the solid is given by V=∫∫A r drdθ

Q: 5. Find all the zeroes of the function f(x) = - 0.5x + 2.5 x+ 4.5 using False Position Method…

A:

Q: For Item # 8- 10: The function f (t) = t + 4t- 5 shows the number of pieces produced by a…

A:

Q: x3 – 2x2 – 5 = 0, [1,4]

A: With the help of bisection method we find the root of the equation.  In this method we find a…

Q: Evaluate (2x - y) dx + (x + 9y) dy. C: x-axis from (0, 0) to (0, -9) and (0, -9) to (6, -9)

A: Line integration

Q: Use false position methodto find the solution to the following within 10−6

A:

Q: 5s2-2s-19 7. F(s) %3D (s+3)(s-1)²

A: Properties of Inverse Laplace transform…

Q: Solve for the volume of the solid generated by rotating the plane bounded by the equations below…

A:

Q: Consider the number C(n,r) given by n! C(n, r) = (2.1) (n – r) ! -r ! where n and r are integers…

A: Given : Cn, r is given by      Cn, r=n!n-r!·r! where n and r are integers satisfying      n≥2    and…

Q: II. Solve the Inverse by Convolution theorem: -7 ( + 4)(s +2)

A: By the convolution theorem,  The above result can be written in the form ϕt=L-1 {F(s) G(s) }

Q: QFinal the complement of she graphs in fig-1-34 figtit

A:

Q: 2 Find the extremum of z = x ?+ y subject to x + 5y = 4. Set up the Bordered Hessian matrix to…

A: here we can use Lagrange's Multiplier method to solve this question and then we use Hessian matrix…

Q: A curve has an equation of 9x2 + 25y2 = 225. Compute the second eccentricity of the curve. %3D 1.33…

A:

Q: Two similar cones have heights of 4m and 12m. What is their scale factor? What is the ratio of their…

A: Given: Both cone are similar

Q: di t. + 4 i - 5 Si dt = 2 u (t– 2) dt

A:

Q: Reach: Give an example of a linear system that does not have two straight line solutions in the…

A: To find such an example w will build up a linear dynamic system whose equilibrium point is a spiral.…

Q: A B 9. Which figure comes next in the series? A B C D of

A:

Q: 2. Given that cos pv o v+B? 2B (a) Find the Fourier transform of x+b? (b) Use the result from (a) to…

A: Sol

Q: I-y 1. Let f(r, y) Find: Ity+1 (a) f(2, 1) (b) f(1,2) (c) f(a, a) (d) f(y+ 1, y)

A: Use the given function.

Q: Find the area of the shaded region. NOTE: Enter the ezact answer. y = z² +3 y =z 3

A: The area of the shaded region can be found using double integration. Here, the area is bounded by…