Question to Find Factors of a Function

Topic : Functions

Question : Given f(x) = 2x³ - 5x² + 12x - 5 Find all zeros, if

p : ± 1, ± 5

q : ± 1, ± 2

p/q = ± 1/2 , ± 5/2

Solution :

Question on Linear Equation

Topic : Linear Equation

Question : Sue wants to buy a new printer that costs $189. She has $125 saved. She has a job that pays $8 an hour. How many hours must she work to earn enough to buy the printer?

Solution :
The cost of the printer is $189.
She has saved $125.
Also, she is paid $8 an hour to do a job.
We need to find the number of hours she works to buy the printer.
Let us assume “x” to be the number of hours she works to buy the printer.
8x + 125 =189
Now, subtract 125 on either side of the equation.
8x + 125 – 125 = 189 – 125
8x = 64
Divide by 8 on either side of the equation.
8x/8 = 64/8
x = 8
Therefore, the number of hours she works to buy the printer is 8.

Solved variable Saparable form of Differential Equation

Topic : Variable Saparable Form

Question : Solve dy/dx = (x-1)/(y+2)

Solution :
dy/dx = (x-1)/(y+2)
(y+2) dy = (x-1) dx
∫(y+2) dy = ∫(x-1) dx
y²/2 + 2y = x²/2 - x + c1 (c1 is the constant)

Problem on Simple Differentiation

Topic : Simple Differentiation
Problem : Solve y = x² + 4e^x
Solution :
y = x² + 4e^x
dy/dx = d(x²)/dx + 4d(e^x)/dx
dy/dx = 2x + 4e^x

Word Problem on Sine Rule

Topic : Sine Rule

Question : Lookout station B is located 7 miles due east of station A. The bearing of a fire from A is S 8degree50’ W and the bearing from B is S 28degree20’ W. Determine the distance from the fire to B(to the nearest tenth of a mile)

Solution :

Figure is as shown in the figure according the question

From Sine Rule

a / Sin A = b / Sin B = c / Sin C

a = c Sin A / Sin C
a = 7 * Sin (90º + 8º 50’) / Sin (90º - 28º 20’)
a = 7 * Sin (98º 50’) / Sin (19º 30’)
a = 20.72miles

Question on Ratio/Proportionality

Topic : Ratio /Proportionality

Question : Are the ratios 25g: 30g and 40Kg: 48Kg in proportion?

Solution :
25g: 30 g = 25/30 = 5:6
40Kg: 48Kg = 40/48 = 5:6
So 25: 30 = 40:48
Therefore, the ratios are in proportion
25:30: : 40:48.

Question on Linear Equation

Topic : Linear Equation

Question : 9 added to thrice a whole number gives 45. Find the number.

Solution :
Step 1. Let the required number be X.
Step 2 Thrice the whole number is 3X
Step 3 Nine added to 3X is 3X + 9
Step 4 3X + 9 = 45
Step 5 3X = 45 -- 9
Step 6 3X = 36
Step 7 X = 36/3
Step 8 X = 12
The required number is 12