Lix Lemjay
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I'm a Math tutor.
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Recent Activity

Answered a Question in Science
For this question, we need to refer to the formula of electric force between two charged objects, which is: `F = (k*q_1*q_2)/d^2` where k is the Coulomb's constant that has a value of 9*10^9 N... 
Answered a Question in Math
Addition means putting two or more quantities together. This operation uses the plus sign, +. The numbers to be added are called addend. The result is called sum or total. Consider this example:... 
Answered a Question in Math
To solve, let's assign a variable that represents the age of the triplets this year. Let it be x. Since the triplets are born 2 years after their sister Julie, then Julie is 2 years older than the... 
Answered a Question in Math
To graph a function containing absolute value, we need to consider the property of y=x. `y= {(x if x>0),(0 if x=0), (x if x<0):} ` Applying these properties, the given function f(x) = 2x +... 
Answered a Question in Science
For this problem, a bucket is connected to a rope and spun around in a vertical direction. So, it is moving in a circular motion (see Figure 1 for reference). When the bucket is at the bottom of... 
Answered a Question in Math
Scale factor is the number that we have to multiply to the dimension of a figure to increase or decrease its size. It has a form: `y=c*y_o` where c is the scale factor, y_o is the original... 
Answered a Question in Math
To determine the periodic payment of a mortgage, apply the formula `PMT = (PV(r/n))/([1(1+r/n)^(nt)])` where PMT is the periodic payment, PV is the principal value, r is the annual rate in... 
Answered a Question in Math
To solve, draw a circle that has a radius of 20 yards. This circle represents the circular grass field. At its edge, draw a point representing where the goat is tied (see Figure 1). The goat is... 
Answered a Question in Math
Riemann sum is used to estimate the area under a curve in an interval [a, b]. Its formula is `A ~~ sum_(i=1)^n f(x_i ) Delta x`. To apply this formula, the interval [a, b] is subdivided into... 
Answered a Question in Math
To solve this problem, draw a figure that illustrates the given conditions. For the first time interval (t=5 s), the car is traveling at a constant speed. It means that its speed does not change on... 
Answered a Question in Math
To stretch a function f(x) vertically, we have to multiply the entire function by a constant greater than 1. `g(x) = c*f(x)` So when given the graph of a function f(x), to stretch it vertically,... 
Answered a Question in Math
Let the original function be `y=f(x)` . To stretch this function vertically, multiply it by a constant which is greater than 1. So this function becomes the following: `y_ (n e w) = c*f(x)`... 
Answered a Question in Math
A radical in the form `root(n)(x)` can be simplified using the radical rule: `root(n)(a^n) = a` To apply this rule, consider this example. Example 1: What is the simplified form of `root(3)(x^12)`... 
Answered a Question in Math
One form of the equation of a line is slopeintercept form. It is written as `y = mx + b` where m is the slope of the line. Example 1: What is the slope of the line `y = 3x  8` ? To get the slope... 
Answered a Question in Math
The graph of a quadratic function is a parabola. The vertex form of a quadratic function is: `y=a(x  h)^2 + k` The (h, k) is the vertex of the parabola. The a is the leading coefficient. Its sign... 
Answered a Question in Math
The two numbers that will have a quotient of 16/3 are to be determined. The condition for its dividend is that the number should be less than 1.The given quotient is 16/3, which is greater than 1.... 
Answered a Question in Math
There are different rate problems. These can be word problems that involve motion of an object or person, or they can involve a job completed in a certain amount of time. For rate problems that... 
Answered a Question in Math
Row Reduction is used to convert a `m xx m` matrix into an identity matrix. `[[a,b], [c,d]] rArr [ [1,0], [0,1]]` This can be done by performing row operations. These are: (1) Multiplying a row by... 
Answered a Question in Math
Let the original function be y=f(x). To stretch the graph of this function vertically, multiply it by a constant greater than 1. So the new equation will be: `y_(n e w)= k*f(x)` where k is any real... 
Answered a Question in Math
A vertical line has an equation in the form: `x=a` where a is any real number. In that equation, the value of x is constant. It means that the line has the same x value for any y values. To graph... 
Answered a Question in Math
To solve, draw a pentagon taking into consideration the given conditions which are: length of side AB = 1 length of side BC = 1 length of side CD = 1 length of side DE = 1 length of side EA= 2... 
Answered a Question in Math
When multiplying fractions, there are two ways to perform it. One method is to multiply fractions straight across and reduce resulting fraction to its lowest term. For example: Multiply `5/8` and... 
Answered a Question in Math
On scientific calculators, the inverse trigonometric functions such as `cos^1,` `sin^1` , and `tan^1` are displayed at the top of the buttons cos, sin and tan, respectively. To be able to use... 
Answered a Question in Math
For this problem, a periodic payment has to be made. So to solve this, a formula for annuity should be applied. It says that on the thirteenth year, Gretta wants to retire. Starting from this year... 
Answered a Question in Math
The given trigonometric function is `f(theta) = 6tan(1/3 theta)`. Take note that a tangent function in its basic form `y=tan(x)` has a vertical asymptote at `x=pi/2` and `x = (3pi)/2` on the... 
Answered a Question in Math
A rational function has holes when common factors exist between the numerator and denominator. To determine the coordinates of a hole, set this common factor equal to zero and solve for x. Then,... 
Answered a Question in Math
Inverse variation is also known as inverse proportion. From the word "inverse", when the value of the variable increases, the other variable decreases. This relationship is described by the... 
Answered a Question in Math
In converting units of measurement to another unit, a conversion factor is used. Examples of conversion factor are: 1 hour = 60 minutes 1 foot = 12 inches These conversions factors should be... 
Answered a Question in Math
When given a simple interest, to compute for its future value, apply the formula `F = P(1 + rt)` where P is the present value, r is the annual rate in decimal form, and t is the number of years.... 
Answered a Question in Math
To multiply functions, we use the notation (f*g*h*...)(x). This means that we take the product of f(x), g(x), h(x), and other functions listed inside the first parenthesis. Consider these... 
Answered a Question in Math
To add functions, we use the notation (f + g + h +....)(x). This means that we have to determine the sum of f(x), g(x), h(x) and the other functions indicated inside the first parenthesis. Consider... 
Answered a Question in Math
`y=2tan^(1)(x)` To find its derivative, apply the derivative formula `d/(dx) tan^(1)=1/(1+x^2).` `y'=2*1/(1+x^2)` `y'=2/(1+x^2)` Therefore, the derivative of the given function is `y' = 2/(1+x^2).` 
Answered a Question in Math
(1) `2p * 3q  4r` To simplify, multiply the numbers and copy the letters. `=6pq  4r` Since the two are unlike terms, they cannot be subtracted. Therefore, the simplified form of the given... 
Answered a Question in Math
(1) `(5x)/(2y^2)*(8x^4)/(5y^2)` To simplify this expression, we have to multiply the fractions straight across. =`(5x*8x^4)/(2y^2*5y^2)` `=(40x*x^4)/(10*y^2*y^2)` To multiply same base, apply the... 
Answered a Question in Science
To solve, the acceleration of the skier along the incline should be determined. To do so, draw the FBD of the skier. (Refer to the attached figure.) The forces acting on the skier are the friction... 
Answered a Question in Math
Let x be the number of electronic digital timers manufactured or sold in a month. (a) To set up the cost function, we need to consider the variable cost and the fixed cost. The variable cost is the... 
Answered a Question in Math
In solving for the length of an arc of a circle, we apply the formula: `s= theta r` where `theta` is the central angle in radians, r is the radius and s is the arc length. In the problem, the given... 
Answered a Question in Math
To determine the bounded region, graph the given equations.(See Figure 1). Then, shade the bounded region. Since the axis of rotation is horizontal, in cylindrical method, the rectangular strip to... 
Answered a Question in Science
To solve using parallelogram method, draw the two vectors on the same initial point. (See Fig.1 in the attachment.) Then, draw another two lines in such a way that a parallelogram is formed. (See... 
Answered a Question in Math
To determine the bounded region, graph the given equations. (Please see attached figure.) On the bounded region, draw a dot to represent its center of mass. To get its coordinates, we have to solve... 
Answered a Question in Math
To determine the bounded region, graph the given equations. See the attached image for the graph I've created. Base on the graph, there are three bounded regions. To get the area of each bounded... 
Answered a Question in Math
Problem #1. Find the points on the curve `y = 2x^3+3x^212x+5` where the tangent line is horizontal. Solution: Take the derivative of the function. `y'=6x^2+6x12` A horizontal line has a slope of... 
Answered a Question in Math
`3^(x+4) = 6^(2x5)` To solve, take the natural logarithm of both sides. `ln (3^(x+4)) = ln (6^(2x5))` To simplify each side, apply the logarithm rule `ln (a^m) =m*ln(a)` . `(x+4)ln(3) = (2x5) ln... 
Answered a Question in Math
The given two points of the exponential function are (1,40) and (3,640). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (1,40), plugin... 
Answered a Question in Math
The given two points of the exponential function are (1,3) and (2,12). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (1,3), plugin x = 1 and... 
Answered a Question in Math
The given two points of the exponential function are (1,2) and (3,50). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (1,2), plugin x=1 and... 
Answered a Question in Math
`sum_(n=1)^oo ((1)^(n+1))/(n+1)` Take note that an alternating series `sum` `a_n = sum (1)^(n+1) b_n` is convergent if the following conditions are satisfied. (i) `b_n` is decreasing,... 
Answered a Question in Math
`sum_(n=0)^oo (1)^(n+1)(n+1)x^n` To determine the interval of convergence, use Ratio Test. The formula of Ratio Test is: `L = lim_(n>oo) a_(n+1)/a_n` Applying this formula, L will be: `L =... 
Answered a Question in Math
`sum _(n=0)^oo (x+1)^n/(n!)` To determine the interval of convergence, use Ratio Test. The formula in Ratio Test is: `L = lim_(n>oo) a_(n+1)/a_n` If L<1, the series is absolutely... 
Answered a Question in Math
`sum_(n=0)^oo x^(5n)/(n!)` To determine the interval of convergence, use Ratio Test. The formula in Ratio Test is: `L= lim_(n>oo) a_(n+1)/a_n` If L <1, the series is absolutely...
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