Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&... Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)]. Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearly dependent.

Show that Vector_3 can be written as a linear combination of Vector_1,Vector_2 and Vector_4.

Show that T={Vector_1,Vector_2,Vector_4} is linearly independent.

Show that the set of all linear combinations of vectors from S is the same as the set of all linear combinations of vectors from T.

3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz, x2 y 2 ) and the curve r(t) = (sin t,sin t cost, cost) on the interval [ π 4 , 3π 4 ]. Calculate R C F · dr using the definition of the line integral. [5] b) Find a function f : R 3 → R so that F = ∇f. [5] c) Verify your answer from (a) using (b) and the Fundamental Theorem for Line Integrals. [5]

1. Find p and graph the parabola y+12x−2x^2=16

2. Find e, d and determine which conic that has the equation r= 4 / 5 - 4sin(theta)

Please show steps. Thanks a lot.

The demand function for a particular product is given by D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=3x2−7x+110 dollars, where x is the number of units sold. What is the marginal revenue when 44 items are sold? Round your answer to 2 decimal places.

D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√t

thats a suqare root over the numbers

Find a polynomial function P of the lowest possible​ degree, having real​ coefficients, a leading coefficient of​ 1, and with the given zeros. 1+3i​, -1​, and 2?

Find all zeros of the polynomial function. Use the Rational Zero​ Theorem, Descartes's Rule of​ Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root.

f(x)=2x⁴-17x³+13x²+53x+21

The zeros of the function are?

A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $2/unit of Product A and a profit of $6/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?

Solve the following IVP specifically using the Laplace transform method

(d^3)x/d(t^3)+x=e^(-t)u(t)    f(0)=0 f'(0)=0    f''(0)=0

where u(t) is the Heaviside step function

I am stuck on these:

Find or Calculate the derivative of the function.

y = (x^0.3 − 3x − 6)(x⁻¹ + x⁻²)

f(x) = (6.4x − 6)⁻² + (4.3x − 1)⁻²

f(x) =

h(x) = 4^{x2 − x}

r(x) = ln(x + 1) + 3x⁹e^x

Describe the level surfaces of G(x,y, z) = 1 – y^2 – z. Make sure to provide all the following: their equations, types, plots, and a short word description of their geometric shapes.

Find the constants a, b, c, d, e, r0, r1 for the ellipse r =15/(3−2cosθ) and sketch the graph.

1.38.5. One diagonal of a quadrilateral bisects the other if and only if the diagonal also bisects the quadrilateral.

Last year, 292 million music CDs were purchased by 112 million households in the United states.On the average, how many CDs were purchased in each household