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.