21324 questions

Why is the Product Life Cycle such a useful tool to use in business?

The product life cycle is a business marketing tool in which it is able to assess the stages a product goes through in its life. The four stages are 1. Introduction - Where the product is introduced to the market, slow growth 2. Growth - Increase in growth in sales and increase in speed of growth 3. Maturity - Peak in sales at this point, but the increase in speed of growth is slowly declining 4. Decline - sales begin to fall, final stage of the PLC. Therefore using the PLC can help to analyse when a product will have most sales so the operations team can prepare to match demand with supply so there are no shortages in times of high demand and no huge amounts excess inventory, as excess inventory can be  very costly to a business. Another reason as to why it is a useful tool is the stage in which the product will start to make a profit and for how long can be roughly estimated before hand. Therefore these are just two reasons to show the usefullness of the PLC to a business but there are many  many more, along with having its limitations.
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Ameena B.

Answered by Ameena, Business Studies A Level tutor with MyTutor


How to factorise any quadratic expression

Factorising quadratic equations This method is used for the following factorable expression: ax2+bx+c Although this method is particularly useful with quadratic expressions with a≥2, it can be also used when a=1. Given              ax2+bx+c Find SUM=b and PRODUCT=ac Find two numbers p and q, such that p+q=SUM and pq=PRODUCT The smallest number (without considering the sign), say in this case p, goes into the following bracket: (ax+p) The largest number (without considering the sign), say in this case, q, goes into the other bracket: (x+q/a) Hence the factorised form is: (ax+p)(x+q/a) Further algebra could be used to "tidy" the expression Example 6x2 - 13x + 5 SUM = b = -13 and   PRODUCT = ac = 6*5 = 30 So p = -3 and q = -10 , as SUM= -3 -10 = -13   and PRODUCT= (-3)*(-10) = 30 As p is the smallest number, this goes in (ax+p) = (6x-3) And q being the largest, goes into (x+q/a) = (x-10/6) Hence the factorised form is  (6x-3)(x-10/6) or neater (2x-1)(3x-5)  
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Adil P.

Answered by Adil, Maths A Level tutor with MyTutor


How do I integrate ln(x)

This is an integral many people struggle with, but, with a simple trick it becomes a little more straight forward. We will approach this integral using integration by parts. But what are the parts? Well, we can write ln(x) as 1*ln(x). We choose u=ln(x) and dv=1, so du=1/x and v=x So the integral ln(x) becomes:  x*ln(x) – integral(x/x) Which is:  x*ln(x)- x + c Which is our final answer.
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Tom M.

Answered by Tom, Maths A Level tutor with MyTutor


How do you invert a 2x2 matrix?

Take a matrix A=(acbd), where a,b,c,d are numbers. First find the determinant. This is a*d-b*c. Now, rearrange the matrix to become (d-c-ba). Divide this by the determinant, to have A-1=1/(ad-bc)(d-c-ba). This is the inverse of A.
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Yaniv P.

Answered by Yaniv, Further Mathematics A Level tutor with MyTutor


How do you solve the integral of ln(x)

This will use the process of integration by parts. First, notice that ln(x)=ln(x)*1. So, the integral of ln(x) is the integral of ln(x)*1. The process of integration by parts is;  int(v*du/dx)dx=vu - int(dv/dx*u)dx. Set ln(x)=v, 1=du/dx, so int(ln(x)*1)dx = ln(x)*x - int(1/x*x)dx = x*ln(x)-int(1)dx = x*ln(x)-x+constant. And you're done!
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Yaniv P.

Answered by Yaniv, Maths A Level tutor with MyTutor


What are some key differences between sound and light waves?

Sound waves have mass, as they are the longitudinal (along the path of the wave) vibration shockwave of molecule, while light waves do not, as they are the transverse displacement of just energy. Sound waves cannot travel in a vacuum, as they require a medium of massive particle to be transvered, but light wave can, as they are simply a form of energy. In spite of this, the basic properties of waves still apply to both - light and sound can be reflected by objects, they can be refracted in different media, they have wavelength and frequency, and they can interfere to change the magnitude of a wave at any point.
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Yaniv P.

Answered by Yaniv, Physics GCSE tutor with MyTutor


Finding the derivative of a polynomial.

Take any polynomial, eg/ y=x3+1/2x2-3x+9. Then dy/dx=3x,+x-3, in this case. This is because, when deriving in this sense, you take each term in x, multiply it by its index, and reduce that index by 1. In a general sense, for y=(n0)xn+(n1)xn-1+...+(nn-1)xn-(n-1)+(nn),             dy/dx=(n)(n0)xn-1+(n-1)(n1)xn-2+...+(n-(n-1))(nn-1). Multiply the x term by the power, reduce the power by one. This works for all powers, even non-integers.
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Yaniv P.

Answered by Yaniv, Further Mathematics GCSE tutor with MyTutor


Why is tolerance so important to liberals?

The claim that tolerance is important to liberals is not controversial. Voltaire famously declared that “I detest what you say, but will defend to the death your right to say it”. This reflects the idea that liberals are committed to protecting freedom of expression and human rights, regardless of whether another person or group’s moral values conflict with their own. Tolerance is so important to liberals because they are committed to protecting equal individual liberties. For example, liberals want to protect people’s freedom to practise certain religions and follow different moral codes, which requires toleration of points of view that might not be classified as strictly “liberal”. When this tension arises liberals have to weigh up which value is the most significant for a healthy society. It is important for the state to defend human rights and to tolerate different points of view and ways of living. This is the way to achieve a pluralist society which tolerates and protects radically diverse interpretations of the good life. Cultural, moral and political pluralism are necessary for a healthy and free society (J S Mill).
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Kate B.

Answered by Kate, who tutored Politics A Level with MyTutor

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