1) finding the volume of solid whose upper limit is the surface f (x, y) = 4xe^y and which lower limit is the region r. where r is the triangle limited by y = 2x; y = 2; x = 0.

Evaluate or solve the following

A) dy/dx= -(2x²+y²)/(2xy+3y²)

B)dy/dx=(1+y²)/(1+x²)xy

C) (x²+1)dy/dx+2xy=4x² given that when x=3,y=4

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Find the mass and center of mass of the solid E with the given density function ρ.

E is the tetrahedron bounded by the planes

x = 0,

y = 0,

z = 0,

x + y + z = 2;

ρ(x, y, z) = 3y.

PLEASE TYPE!!

Think about where you have noticed circles in your everyday life and find at least 2 examples of circles in your everyday life. For each example, include the following in your post. Be sure to include enough details in your descriptions and explanations so someone who is not familiar with your everyday life will understand them.

1. Describe the circle's use and its measurement (radius or diameter, either an exact value or an approximation is fine).
2. If important, describe the location of the circle (analogous to our finding a circle's center).
3. Explain what you feel is important about the mathematics (measurement and/or location) about the circle.

Find the first four nonzero terms in a power series expansion about x=0 for a general solution to the given differential equation.

(x^2 +5)y"+y=0

convergent or divergent

infinity sigma n = 1 sqrt(n^5+ n^3 -7) / (n^3-n^2+n)

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}.

(a) Prove that U is a subspace of F4.

(b) Find a basis for U and prove that dimU = 2.

(c) Complete the basis for U in (b) to a basis of F4.

(d) Find an explicit isomorphism T : U →F2.

(e) Let T as in part (d). Find a linear map S: F4 →F2 such that S(u) = T(u) for all u ∈ U.

Solve the recurrence relation with the given initial conditions.

b₀ = 0, b₁ = 4, b_n = 2b_{n ? 1} + 2b_{n ? 2} for n ? 2

A city council consists of eight Democrats and eight Republicans. If a committee of six people is? selected, find the probability of selecting four Democrats and two Republicans.

he function

​f(x)equals=0.030.03xplus+500500

represents the rate of flow of money in dollars per year. Assume a​ 10-year period at

88​%

compounded continuously. Find​ (A) the present​ value, and​ (B) the accumulated amount of money flow at

tequals=10.

​(A) The present value is

​$nothing

3. Find the quotient and remainder using long division. x3 + 7x2 − x + 1 x + 8

quotient = ?

remainder = ?

4. Simplify using long division. (Express your answer as a quotient + remainder/divisor.)

f(x) = 8x² − 6x + 3

g(x) = 2x + 1

5.

Find the quotient and remainder using long division.

6.

Use the Remainder Theorem to evaluate P(c).

P(x) = x⁴ + 7x³ − 6x − 12,     c = −1

f(−1) =

7.

Use the Remainder Theorem to evaluate P(c).

P(x) = 9x⁵ − 3x⁴ + 4x³ − 2x² + x − 6,    c = −6

P(−6) =

8.

Consider the following.

P(x) = x³ − 9x² + 27x − 27

Factor the polynomial as a product of linear factors with complex coefficients.

9.

Consider the following.

P(x) = x³ + 2x² − 3x − 10

Factor the polynomial as a product of linear factors with complex coefficients.

10.

The polynomial  P(x) = 5x²(x − 1)³(x + 9) has degree (?). It has zeros 0, 1, and (?). The zero 0 has multiplicity (?), and the zero 1 has multiplicity (?). (answer all (?)

12.

Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)

f(x) = 6x³ + x² − 41x + 30;    x + 3

x =

13.

Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)

f(x) = 3x³ − 17x² + 30x − 16;    x − 1

x =

14.

Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)

2x³ + 7x² − 12x − 42;    2x + 7

x =

15.

A polynomial P is given.

P(x) = x³ + x² + 3x

(a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

(b) Factor P completely.

1) find the are of the region that lies inside of the curve r= 1+ cos theta and outside the curve r=3 cos theta.

2) find the sum"

En=1 3^{1-n}:2^{n+2}

3) find
integration ( 2x^2 +1) e^x^2 dx

4) Does:

E n=12 ((2n)!/(n!)^2) converge or diverge ? justify your answer ( what test?)

1) find all values of theta E [ 0,2 pi], where the curve r= 1- sin theta has a horizontal tangent line

2)find all values of theta E [ 0,2 pi] where the curve r=1- sin theta has a vertical tangent line

3) find the area of the region enclosed by the intersection of the curves"

r= sin theta and r= cos theta

Design a google spreadsheet that will illustrate Riemann summation. Share the unlisted link on the forum. The entries should be (a) function f(x)=x^2 , (b) lower limit x=0, (c) upper limit x=2, (d) n = 4. The result should be three fields: left endpoint, midpoint approximation, right endpoint approximation.