Jeewana Meegahage
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About
I am an Engineer in profession. I am helping students with their studies as a part time work and it is a hobby of mine.
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Recent Activity

Answered a Question in Math
`tan^(1)x = 1` Take tan on both sides; `tan (tan^(1)x) = tan(1)` x = tan(1) If 1 represent degrees; x = tan(1) = 0.01746 If 1 represent Radians; x = tan(1) = 1.5574 
Answered a Question in Math
Let us say the equation of the line perpendicular to y=2x+5 to be y = ax+b where a and b are unknown that should be discovered. It is given that our line y = ax+b is perpendicular to y = 2x+5. So... 
Answered a Question in Math
From the . or the decimal representation, the left side values increases by the power of 10 which starts from 0. For example: `100 = 1xx10^2+0xx10^1+0xx10^0` So the if the first number to the left... 
Answered a Question in Math
Let us say the coordinates of the point closest to (0,3) are (a,b). The distance (L) between these two points can be given as; `L = sqrt((0a)^2+(3b)^2)` By getting `L^2` `L^2 = a^2+(3+b)^2`... 
Answered a Question in Math
Here we have to know some basics in logarithm before expanding. In the following notations, A,B are non zero positive integers and n is an integer. Log (A*B) = Log(A)+log(B)(1) Log (A/B) =... 
Answered a Question in Math
`2x4(3x+6)=6(2x+1)4` Remove bracket by multiplying; `2x4xx3x24 = 6xx2x64` `2x12x24 = 12x64` `10x24 = 12x10` Take all x parts to one side, and put the numbers on the other side.... 
Answered a Question in Math
For 95% confidence interval we can calculate the true proportion as; `P = barp+1.96sqrt((barp(1barp))/n)` Where; P = true proportion of perry como fans `barp` = Observed proportion of perry como... 
Answered a Question in Math
The center of mass is the unique point at the center of a distribution of mass in space. It has the property that the weighted position vectors relative to this point sum to zero. It is given by;... 
Answered a Question in Math
The center of mass is the unique point at the center of a distribution of mass in space. It has the property that the weighted position vectors relative to this point sum to zero. It is given... 
Answered a Question in Math
The center of mass is the unique point at the center of a distribution of mass in space. It has the property that the weighted position vectors relative to this point sum to zero. It is given... 
Answered a Question in Math
Refer the attached image with calculations. The equation of an arch is a quadratic function. Let us say the equation of the arch is; `y = ax^2+bx+c` Now we draw the arch so that the left most side... 
Answered a Question in Math
Let us say the quadratic function is; `y = ax^2+bx+c` where a,b and c are constants and `a!=0` . It is given that graph passes through (1,4). `4 = a(1)^2+b(1)+c` `4 = ab+c(1)`... 
Answered a Question in Math
`(1+0.1/365)^(365t) = 2` In solving these kind of problems we need to use the logarithm. Take the logarithm on both sides of the equation. `log_(10)((1+0.1/365)^(365t)) = log_10(2)` With logarithms... 
Answered a Question in Math
`(1+0.09/12)^(12t) = 3` In solving these kind of problems we need to use the logarithm. Take the log of both sides of the equation. `log_(10)((1+0.09/12)^(12t)) = log_10(3)` With logarithms we know... 
Answered a Question in Math
Let; 1,2,3,4,5,6 be the numbers of the die in each side and H(head) and T(Tail) be the sides of the coin. When she roll the die and coin the all possible outcomes should be as follows.... 
Answered a Question in Math
Let the two numbers be x and y. Let `x>y` . According to the given data; `xy = 8` (1) `x^2+y^2 = 424` (2) From (1) y = x8 Use the value of y = x8 for (2) `x^2+(x8)^2 = 424`... 
Answered a Question in Math
Charlie's goal of use of water per day = 50 gallons Water consumption for 30 days = `50xx30 ` = 1500 gallons Charlies water bill indication of usage = 1524 gallons 1500 < 1524 Expected usage... 
Answered a Question in Math
Flowering bushes need a mixture of 70% soil and 30% vermiculite by volume. So if we simplify this it means to we need 30 buckets of vermiculite to mix with 70 buckets of soil. Vermiculite needed to... 
Answered a Question in Math
slope of a line in XY plane = (change in Y coordinates)/(change in Xcoordinates) If the angle with line and Xaxis is `theta` then the slope can be given as `tantheta`... 
Answered a Question in Math
slope of a line in XY plane = (change in Y coordinates)/(change in Xcoordinates) If the angle with line and Xaxis is `theta` then the slope can be given as `tantheta`... 
Answered a Question in Math
slope of a line in XY plane = (change in Y coordinates)/(change in Xcoordinates) If the angle with line and Xaxis is `theta` then the slope can be given as `tantheta`... 
Answered a Question in Math
slope of a line in XY plane = (change in Y coordinates)/(change in Xcoordinates) If the angle with line and Xaxis is `theta` then the slope can be given as `tantheta` . This angle is... 
Answered a Question in Math
slope of a line in XY plane = (change in Y coordinates)/(change in Xcoordinates) If the angle with line and Xaxis is `theta` then the slope can be given as `tantheta` . This angle is... 
Answered a Question in Math
Slope or gradient of a line in XY plane = (change in Y coordinates)/(change in X coordinates) If the angle of line with Xaxis is `theta` then we can say the slope is `tantheta` . This angle is... 
Answered a Question in Math
See the attached image. Let us say the airplane starts from A. It travels East for 210Km and reach point B. At B it turns 10deg from east to south and goes 100Km when it comes to point C. AC... 
Answered a Question in Math
Here we have to assume that Juan does not work 24 hours. So we assume that Juan works for 'X' hours per day. Further we do not exactly know how many days that Juan works per week. Let us assume... 
Answered a Question in Math
`T_1 = 1+1/2` `T_2 = 1+3/4` `T_3 = 1+7/8` `T_4 = 1+15/16` `T_5 = 1+31/32` Every term has a '1' in its expression. So the nth term will also have '1' as the beginning value. When we consider the... 
Answered a Question in Math
Fraction of blue paint that Mike mixed `= 1/6` Fraction of green paint that Mike Mixed `= 5/8` Total fraction of paint Mike mixed `= 1/6+5/8` Here we need to get a common denominator to add up... 
Answered a Question in Science
`NH_3+H_2O > NH_4^(+)+OH^` Here first of all we need to assume that these reactions will takes place at room temperature(25C) at constant conditions. In this buffer solution; `pOH =... 
Answered a Question in Math
The amount Julia received = 6720$ The sold value of house = 112000$ The commission is the value that Juliet received as a result of selling the house. In this case it is 6720$. So the commission %... 
Answered a Question in Science
momentum(P) = mass(m)*velocity(v) `P = mv` At the first stage; mass of the system(m) = mass of bus+mass of driver+total mass of students `= 2500+75+125xx20` `= 5075kg` Velocity of the bus (v)=... 
Answered a Question in Math
`1.5x+0.8y = 2.3` (1) `0.3x0.2y = 0.1` (2) `(2)xx10` `3x2y =1` `2y = 3x1` (3) `(2)xx10` `15x+8y = 23` `15x+4xx(2y) = 23` (4) Substitute the value of '2y' from (3) to equation... 
Answered a Question in Math
`2xy+2 = 0 ` (1) `4x+y5 = 0` (2) From (1) we can get; `2xy+2 = 0` `y = 2+2x` Substitute the value of 'y' to equation (2); `4x+(2+2x)5 = 0` `6x3 = 0` `x = 1/2` Hence `y = 2+2x = 2+2xx1/2... 
Answered a Question in Math
Let N be the number you want to get the square root. Assume E1 as the initial estimate for `sqrtN` . So the next estimate E2 will be; `E2 = (N/(E1)+E1)/2` Similarly E3 will be; `E3 =... 
Answered a Question in Science
The chemical name of Bleach solution is Sodium Hyhochlorite (`NaClO` ). The chemical notation of Silver nitrate is `AgNO_3` . When these two react with each other disproportionation reaction... 
Answered a Question in Science
`Ba(OH)_2` is a strong base. `Ba(OH)_2 > Ba^(2+)+2OH^` `Na_2CrO_4 ` is a basic salt formed from the reaction of `NaOH` and `H_2CrO_4` `Na_2CrO_4 > 2Na^++CrO_4^(2)` Once these two are... 
Answered a Question in Science
This is a double replacement reaction. During the reaction `Ag` will pair with `Cl` and `Al` will pair with `NO_3^()` . `AgNO_3 > Ag^(+)+NO_3^(1)` `AlCl_3 > Al^(3+)+3Cl^`... 
Answered a Question in Math
The function has no vertical Asymptote means the denominator does not equate to 0 at any value of x. In other words the polynomial should not have real roots. A simple form of this type... 
Answered a Question in Math
Using law of sines `sinA/a = sinB/b = sinC/c` A,B and C are angles and a,b and c are opposite lengths of a triangle as in the image. According to the question we have following data. `A = 83^0 20'... 
Answered a Question in Math
Using law of sines `sinA/a = sinB/b = sinC/c` A,B and C are angles and a,b and c are opposite lengths of a triangle as in the image. According to the question we have following data. `A = 5^040' =... 
Answered a Question in Math
The sine law indicates that in a triangle; `(sinA)/a =(sinB)/b =(sinC)/c` a,b,c are the lengths of the triangle and A,B,C are the opposite angles as shown in image. `(sinA)/a =(sinB)/b` `sin36/8 =... 
Answered a Question in Math
The sine law indicates that in a triangle; `(sinA)/a =(sinB)/b =(sinC)/c` a,b,c are the lengths of the triangle and A,B,C are the opposite angles as shown in image. `(sinA)/a =(sinB)/b` `sin60/9 =... 
Answered a Question in Math
The sine law indicates that in a triangle; `(sinA)/a =(sinB)/b =(sinC)/c` a,b,c are the lengths of the triangle and A,B,C are the opposite angles as shown in image. Angle A `= 15^0 30' = 15.5^0`... 
Answered a Question in Math
The sine law indicates that in a triangle; `(sinA)/a =(sinB)/b =(sinC)/c` a,b,c are the lengths of the triangle and A,B,C are the opposite angles as shown in image. `B = 2^0 45' = 2.75^0` Using... 
Answered a Question in Math
The angle between two vectors u and v is given by; `costheta = (u.v)/(uv)` u.v represent the vector dot product and u and v represents the magnitude of vectors. We know that in unit... 
Answered a Question in Math
The angle between two vectors u and v is given by; `costheta = (u.v)/(uv)` u.v represent the vector dot product and u and v represents the magnitude of vectors. We know that in unit... 
Answered a Question in Science
Water is a major need for all human being. It is a must for them to survive. Man need water to various actions inside the body. Usually a man need to drink about 2.4 liters of water everyday.... 
Answered a Question in Math
Let us the value originally we borrowed is P. Annual interest rate = 10.1% So the interest for 4 years =` Pxx10.1/100xx4` Total amount paid `= P+Pxx10.1/100xx4 = 46200`... 
Answered a Question in Math
I deposit half of my lottery winnings in gold which grows 8% per year. Initial deposit `= 10000/2 = 5000` Value after first year `= 5000xx1.08` Value after two years `= (5000xx1.08)xx1.08 =... 
Answered a Question in Science
The answer is; The net force on the beaker table = 23.5N In this system the weight of beaker and the weight of water are the only forces that acts on the beaker table. The other forces in...
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