Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Dharshi**- Replies: 2

(1) Solve cos2x= -1/2 for x. Give a general formula for all of the solutions. List six specific solutions.

(2) f(x)= (4x^2- x-3)/(2x^2- 11x+5)

a) Find all of the intercepts

b) Find all of the asymptotes.

c) Build a sign chart to define when the graph is above and below x axis.

d) Use this information to build a graph.

3) Solve the exponential equation 7^2x+ 7^(x+1)- 120=0.

I tried all these problems, for pr (1) i got 5pi/6, for (2) got 2,6 for a and b

and for (3) i got the ans as 0.715

Is my ans correct? Am confused with them

**Dharshi**- Replies: 1

Find the foci and vertices for y^2/36+x^2/9=1

I got it as(0,4) and vertices (12,9)

I used the (x-h) and (y-k) form and found the ans.

But, my teacher told it is wrong. Does anybody knows this?

yup!! got it now thanks

**Dharshi**- Replies: 3

If the points (a,2a) (2a,a), (a,a)and enclose a triangle of area 18 sq units, the centroid of the

triangle is

I tried this problem by finding the area, perimeter, side and then atlast the equation of median

and then find the centroid, and got the ans (4,4)

But my teacher says it is wrong

I dont know wat is wrong?? is tere any other method to solve this?

**Dharshi**- Replies: 1

(1) Set up a double integral to find the volume of the solid S in the first octant that is bounded above by

the surface z = 9 - x^2 - y^2 , below by the xy-plane, and on the sides by the planes x=0 and y=x.

(2) a. Evaluate ∫ ∫ ∫ (x^2 + 2z)dxdydz where T is the region bounded by the planes z=0 and

y + z = 4 and the cylinder y = x^2

b. Set up a triple integral in cylindrical coordinates that gives the volume of the solid bounded

above by the hemisphere z = 2 - x^2 - y^2 and below by the paraboloid z = x^2 + y^2

c. Set up a triple integral in spherical coordinates that gives the volume of the solid that lies

outside the cone z = 3x^2 + 3y^2 and inside the hemisphere z = 4 - x^2 - y^2 .

(3) Evaluate ∫∫ sin( y-x)/(y+x) dxdy where Ω is the region in the first quadrant bounded by the line x + y=1

and x + y=2. (Use the Jacobian with u = y - x and v = y + x)

(4) Calculate h(r)·dr C ∫ where h(x, y) = (6xy - y^3 )i + (4y + 3x^2 - 3xy^2 )j and C is the curve consisting of

the line segment from (0, 0) to (2, 4) and the parabola y = x^2 from (2, 4) to (3, 9).

(5) a.Let h(x, y) = 2xy^3 i + 4x^2 y^2 j . Calculate C∫h(r)·dr where C is the boundary of the triangular

region in the first quadrant bounded by the x-axis, the line x=1 and the curve y = x^3 .

b. Let g(x, y) = (2xy + e^x - 3)i + (x^2 - y^2 + sin y)j. Calculate C

∫g(r)·dr where C is the ellipse 4x^2 + 9y^2 = 36

c. Use Green's Theorem to find the area enclosed by the asteroid r(u) = cos^3 ui + sin^3 uj, 0 <= u<= 2pi.

**Dharshi**- Replies: 4

Given P(A)=0.47,P(B)=0.37 , and P(A and B)=0.15 , draw a Venn diagram, fill in the probabilities associated with the various regions, and thus determine:

a) P(A or B) b) P(A' and B') c) P(A/B)

i drew it and found the solution, thanks for ur help

hi i tried with the prob 4 y= 2x^2+10 and line y =4x+16

am getting the ans as 14/3, but in my book it is given as 142/3

How come this comes???

**Dharshi**- Replies: 1

Determine the area of the region bounded by the curve f(x) = 2x^2 + 10, and the line f(x) = 4x + 16, x = -2 and x = 5.

I need the solution step by step does any body knows ??

It is -y^2

s i got that ans

**Dharshi**- Replies: 1

Tim offered to buy hot dogs for his students. Of the 100 students, 52 wanted ketchup, 63 wanted mustard, 25 wanted relish, 24 wanted ketchup and mustard, 11 wanted mustard and relish, 9 wanted ketchup and relish, and 4 wanted all the three condiments. How many students wanted ketchup only

I need the steps

**Dharshi**- Replies: 13

(1) Find the area bounded by the curves f(x) = x^3 and f(x) = √x.

(2) Determine the area of the region bounded by x = -y2 + 10 and x = (y - 2)^2.

(3) Find the area between the curves f(x) = √x and f(x) = x^2.

(4) Determine the area of the region bounded by the curve f(x) = 2x^2 + 10, and the line f(x) = 4x + 16, x = -2 and x = 5.

(5) Find the area bounded by the curve f(x) = x^3 - 6x^2 + 11x 6 and the x-axis

(6) Find the area bounded by the curve y = 8 x^2 and the line y = 2

I tried and getting different answers help me out

**Dharshi**- Replies: 1

Determine the area bounded by the curves f(x) = xe^(-x2), f(x) = x + 2, x = 3 and y-axis

anybody know how to do this?

**Dharshi**- Replies: 2

If x~MW(alpha1,beta1,lambda1) and y~MW(alpha2,beta2,lambda2)

and we have aserial system with two components x and y (x and y independent)

if alpha1=0.05, beta1=0.02, annd lambda1=1

if alpha2=0.0005, beta1=0.6, annd lambda1=0.1

MW is Modified Weibull distribution Lia and xei 2003

writ R code to

1)simulte from this system with sample size n=10,20,30,40,50,60,70,80,90,100

2)compute the MLE for each sample size

3)compute the standerd erorr and plot it for each parameters with simple size

do anyone know this how to solve????

**Dharshi**- Replies: 3

(1) For its 2010 tax year, Ilex Corporation has ordinary income of $240,000, a short-term capital loss of $60,000, and a long-term capital gain of $20,000. Calculate Ilex Corporation's tax liability for 2010.

(2) Fisafolia Corporation has gross income from operations of $220,000 and operating expenses of $160,000 for 2010. The corporation also has $20,000 in dividends from publicly traded domestic corporations (ownership in all corporations was less than 20 percent). a. a. Calculate the corporation's dividends received deduction for 2010. b. Assume that instead of $220,000, Fisafolia Corporation has gross income from operations of $135,000. Calculate the corporation's dividends received deduction for 2010.

(3) Beech Corporation, an accrual basis taxpayer, was organized and began business on July 1, 2010. During 2010, the corporation incurred the following expenses: State fees for incorporation $ 500 Legal and accounting fees incident to organization 1,800 Expenses for the sale of stock 2,100 Organizational meeting expenses 750 Assuming that Beech Corporation does not elect to expense but chooses to amortize organizational-expenditures over 15 years, calculate the corporation's deduction for its calendar tax year 2010.

(4) Citradoria Corporation is a regular corporation that contributes $35,000 cash to qualified charitable organizations during 2010. The corporation has net operating income of $140,000 before deducting the contributions, and dividends received from domestic corporations (ownership in all corporations is less than 20 percent) in the amount of $20,000. a. What is the amount of Citradoria Corporation's allowable deduction for charitable contributions for the current year?

b. What may the corporation do with any excess amount of contributions?

(5) Cedar Corporation has an S corporation election in effect. During the 2010 calendar tax year, the corporation had ordinary taxable income of $200,000, and on January 15, 2010, the corporation paid dividends to shareholders in the amount of $120,000. How much taxable income, in total, must the shareholders of the corporation report on their 2010 tax returns? Explain your answer.

(6) Bill and Guilda each own 50 percent of the stock of Radiata Corporation, an S corporation. Guilda's basis in her stock is $25,000. On July 31, 2010, Bill sells his stock, with a basis of $40,000, to Loraine for $50,000. For the 2010 tax year, Radiata Corporation has a loss of $100,375. a. Calculate the amount of the corporation's loss that may be deducted by Bill on his 2010 tax return. b. Calculate the amount of the corporation's loss that may be deducted by Guilda on her 2010 tax return. c. Calculate the amount of the corporation's loss that may be deducted by Loraine on her 2010 tax return.

(7) Grevilla Gerporation is a manufacturing company. The corporation has accumulated earnings of $950,000, and it can establish reasonable needs for $400,000 of that amount. Calculate the amount of the accumulated earnings tax (if any) that Grevilla Corporation is subject to for this year.

(8) Cypress Corporation has regular taxable income of $170,000 (assume annual gross receipts are greater than $5 million) and regular tax liability of $49,550 for 2010. The corporation also has tax preference items amounting to $105,000. Calculate Cypress Corporation's alternative minimum tax liability. Assume Cypress Corporation is not a "small corporation."

No i didnt get any idea but they have asked to solve it using graph theory

**Dharshi**- Replies: 3

Suppose that an airline oers daily non stop flights as follows: there are three flights from New York

to Miami, two flights from Miami to New York, one flight from Miami to Chicago, two flights from

Chicago to Miami, 3 flights from Chicago to New York, 3 flights from New York to Chicago, one

flight from New York to Houston, and one flights from Houston to New York, two

flights from Houston toMiami, and one flight from Miami to Houston.

(a) Draw a graph to represent airline routes, in which each vertex represents a city and an edge joining

two vertices represents the existence of a non stop flight between those two cities.

(b) Find the beta index of the graph you found in part (a).

**Dharshi**- Replies: 1

Use the Handshake Theorem to solve the following problem. Suppose that you arrive

at a gathering of 9 people. Suppose that upon your arrival, you learn two facts: that 36 handshakes

have already taken place and that every person participated in the same number of handshakes, h.

How many hands did each of the 9 people shake? (Find h).

**Dharshi**- Replies: 1

(1) Prove that tan(x/2+pi/4) =sec x+ tanx

(2)Solve cos 2x =-1/2 for x. Give a general formula for all of the solutions. List six specific solutions.

(3) Given the function f(x) = (3x^2+2x+2)/(x+3)

A) Find all x and y intercepts.

B) Find all of the asymptotes.

C) Draw a number line to determine when the graph is above and below the x axis.

**Dharshi**- Replies: 5

How much will you have accumulated over a period of 20 years if, in an IRA which has a 10% interest rate compounded monthly, you annually invest:

a. $1

b. $100

c. $20,000

d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine Parts (b) and (c)?\

We need to use the compound interest formula.Anyone can help me with that?

Thanks i got it

**Dharshi**- Replies: 7

If a number x is twice as large as a number y and if the sum of their squares is 3125, then x and y are, respectively.