4257 Maths questions

### solve: x^2 - 11x + 24 =0

This is a trinomial hence this can be solved by factorisation and you have to look at the second and third terms (i.e. -11x and 24). You need to find 2 numbers which add to give -11 and multiply to give 24. This would be -8 and -3. Hence, the quadratic equation becomes (x-8) (x-3) = 0 and as the equation is equal to 0, it shows that (x-8) =0 or (x-3) = 0. Hence the value of x could be either 8 or 3.

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2 days ago

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### Solve the following equation: x^2 + 6x + 8 = 0

There are two ways to solve a quadratic equation such as this. The method we will user here is to convert the equation to look like this: (x + a) * (x + b) = 0 where a and b are constants (i.e. they are equal to a specific number)
Given that the right hand side of both equations is zero, we can conclude that the left hand side of both equations are equal. If we multiply the two brackets in the second equation together, we get the following: x*x + x*b + a*x + a*b = 0This can be simplified to the following: x^2 + (a+b)x + (a*b) = 0
By comparing this to our original equation, we can see that (a+b) =6, and (a*b) = 8.In this case, these are simple equations. We know that 4 + 2 = 6, and 4*2 = 8.This means that the original equation can be written as: (x + 4) * (x + 2) = 0That means that at least one of the two terms within the brackets is equal to zero, so either x = -4 or x = -2.
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3 days ago

Answered by Oliver, who has applied to tutor Maths with MyTutor

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### A projectile is launched upward at 5 m/s, calculate the maximum height and time taken to reach.

The first thing to remember in this case, when using SUVAT, is that V=0, since at the highest point, the velocity of the projectile is 0.Therefore we can input the values:S=?U=5V=0A=-9.8T=?Substituting the values into V=U+AT and S=1/2*(U+V)Tresulting in the values S=1.27 and T=0.51
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3 days ago

Answered by Abbas, who has applied to tutor Maths with MyTutor

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### A 3.6m ladder is resting against a wall at 49 degrees to the ground. If Tom climbs to the top of the ladder, how high off the ground will he be?

This is a simple trigonometry question. Using sin(x)= opposite/ hypotenuse, we get can rearrange to get opposite = sin(x) x hypotenuse. This means that opposite = sin(49) x 3.6 = 2.72m (3 sig. fig.)
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5 days ago

Answered by Janna, who has applied to tutor Maths with MyTutor

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### What is a stationary point (of a function y in terms of x)?

A stationary point is where the rate of change in y over the rate of change in x equates to zero (dy/dx=0). The stationary point may be a maximum, minimum or a point of inflection. Question 2 in the 2017 AQA paper (Pure core 1) is a good applied example (can explain using diagrams and equations).
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5 days ago

Answered by Charlie, Maths tutor with MyTutor

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### Express sqrt(3)*sinx - cosx in the form r*sin(x-a) where r>0 and 0<a<pi/2

First we use a trigonometric identity (given to you in formula booklet) on r*sin(x-a) to express it in a form which is more helpful. We know: r*sin(x-a) = r*(sin(x)cos(a) - cos(x)sin(a)= (r*cos(a))*sin(x) - (r*sin(a))*cos(x)). So we compare this with our original expression of: sqrt(3)*sin(x) - cos(x) . Clearly for these two forms to be equal, we require that r*cos(a) = sqrt(3) [call this eq. 1] and r*sin(a) = 1 [call this eq. 2] . We can then use the basic trigonometric identities (expected to remember): sin2(x) + cos2(x) = 1 and tan(x) = sin(x)/cos(x) to work out the values of r and a. Working out r: If we do [eq.1]2 + [eq.2]2 we get (r2)(cos2(a)) + (r2)(sin2(a)) = 3 + 1 , factorise out the r2 we get: (r2)(cos2(a) + sin2(a) = 4 , this implies r2 = 4 [using trig identity] , which implies r = 2 [important to note we ignore -ve root] . Working out a: If we do [eq. 2]/[eq.1] we get: tan(a) = 1/sqrt(3) [using trig identity] , this implies a = pi/6 [to see this draw our trigonometric "half an equilateral" triangle] . Therefore we conclude that: sqrt(3)*sinx - cosx = 2*sin(x-pi/6)
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6 days ago

Answered by Scott, Maths tutor with MyTutor

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### Find the mean of the following set of numbers: 31, 25, 39, 30, 25

The mean is the average of a set of numbers. To find the mean, add up all the numbers you want to find an average of and divide by how many numbers are in the list. In this example 31 + 25 + 39 + 30 + 25 = 150. There are 5 numbers in the list. To find the mean you divide 150 by 5 (150/5 = 30). Therefore, the mean of this set of numbers is 30.
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6 days ago

Answered by Charlotte, Maths tutor with MyTutor

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### What is the remainder when (3x^3 + 5x^2 + 3) is divided by (x+2)

Put (3x^3 + 5x^2 + 3) under a "bus stop" ready for division.Write it as 3x^3 + 5x^2 + 0x + 3Write (x+2) on the outside of the bus stopconsider what needs to happen to x to get it to 3x^3 --- multiply by 3x^2subtract the multiple of (x+2) that is produced from the original functioncontinue to follow this pattern until you get to the end -- remainder 1
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6 days ago

Answered by Layla, Maths tutor with MyTutor

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### How do you differentiate y = exp(x)sin(x)

y = ex sin(x)
let u = ex and let v = sin(x) du/dx = ex dv/dx = cos(x)
dy/dx = (du/dx)v + (dv/dx)u = exsin(x) + excos(x) = ex(sin(x) + cos(x))
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1 week ago

Answered by Peter, Maths tutor with MyTutor

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### Differentiate y=sin(3x^2 +6)

Here we use our rule for the derivative of the sine function, d\dx(sin(x))=cos(x) and we also apply our chain rule for differentiation as well. So if y = sin(3x^2+6) then we will have that dy\dx=cos(3x^2 +6).d/dx(3x^2 +6)=cos(3x^2 +6).6x=6xcos(3x^2 +6)
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1 week ago

Answered by Ryan, Maths tutor with MyTutor

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