Question to Solve for x

Topic : Solve for x

Problem : Solve 1 + 2x + x^2 = n^2(1+ 2x/n^2 + x^2/n^4)

Solution :

A Simple Problem on Integration

Topic : Integration

Problem : Integrate x/[3√(5 +2x²)]

Solution :

Upper Bound and Lower Bound of Polynomials

Topic : Polynomials



Question : Find the Upper and Lower Bounds of Polynomial

P(x) = x³ - x² + x - 2



Solution :

Problem to Find the Unknown values of Geometrical Figure

Topic : Square Based Triangle

Question : The Square based pyramid depicted below has averticle height of 13cm. K is the mid point of CD and angle AKL =50 degrees. To the nearest tenth of degree, what is the measure of angle ACK?

Solution :

















Length of Square be x
Tan 50º = 1.19175
= 13 / (x/2)
x = 21.81659041
x = 21.82
Sin 50º = (x/2) / AK
AK = (x/2) / 0.766
AK = 14.24
Tan ∟AKC = AK /(x/2) = 14.24/ 10.91 = 1.31
∟AKC = tanˉ¹(1.31)


∟AKC = 53º

Problem to Find Measurement of Geometrical Figures

Topic : Trapezium

Question : The area of a trapezium shaped field is 960 m^2 , the distance between two parallel sides is 10 m and one of the parallel side is 40m. Find the other parallel side.

Solution :
One of the parallel side a = 40 m, let another parallel side be x, distance between sides (h) = 10 m
The given area of trapezium = 960m^2.
Area of a trapezium = ½ h (a + b)
so 960 = ½ h (a + b) = ½ x 10 x (40 + x)
or 960 = 5( 40 + x)
or 960/5 = 40 + x
or 192 = 40 + x
or 192 – 40 = x
x = 152 m
the other parallel side of the trapezium is 152 m.

Question on Linear Equation

Topic : Word Problem on Linear Equation.

Question : The average of four numbers is 85.If three of the numbers are 76,78 and 81,whats the fourth number

Solution :
76+78+81+x/4=85
235+x/4= 85
235+x = 340
X= 340-235
X= 105
The fourth number is 105.

Question on Personal Finance Concepts

Topic : Jobs and Growth Tax Relief Reconciliation Act

Question : Bernie and Pam Britten are a young married couple beginning careers and establishing a household. They will each make about $50,000 next year and will have accumulated about $40,000 to invest. They now rent an apartment but are considering purchasing a condominium for $100,000. If they do, a down payment of $10,000 will be required.
They have discussed their situation with Lew McCarthy, an investment advisor and personal friend, and he has recommended the following investments:
• The condominium - expected annual increase in market value = 5%.
• Municipal bonds - expected annual yield = 5%.
• High-yield corporate stocks - expected dividend yield = 8%.
• Savings account in a commercial bank-expected annual yield = 3%.
• High-growth common stocks - expected annual increase in market value = 10%; expected dividend yield = 0.1.

Calculate the after-tax yields on the foregoing investments, assuming the Brittens have a 28% marginal tax rate (based on Public Law 108-27, The Jobs and Growth Tax Relief Reconciliation Act of 2003).

Solution :
a)The yield on the Brittens' investment in condominium can be taken as zero since the investment is for personal use and as such no income will be derived out of it. The yield can be realised only on liquidation of the asset.
b) As regards other assets the after tax yields have been worked out as under:
(While arriving at the yield, it has been assumed that the entire 40000 is invested in a particular asset)
Asset Yield Tax After Tax
Municipal bonds 2000 560 1440
High-yield
corporate stocks 3200 896 2304
Savings account 1200 336 864
High-growth
common stocks 4000 1120 2880
c)The yield in respect of High growth common stocks would be realised only if the assets are liquidated.

Hope the explanation will be helpful for you.