Mathematics Question Thread

[fun_jirachi]

EDIT: I just realised I forgot the dx when writing down the integral of 3x^2 - 2x + 1, but make sure you put that in when writing the integral!

[amelia20181]

how do you do

[amelia20181]

EDIT: I just realised I forgot the dx when writing down the integral of 3x^2 - 2x + 1, but make sure you put that in when writing the integral!

Thanks!

[fun_jirachi]

this is for the first question, i'm working on the second one

[amelia20181]

how do you do

[dermite]

how do you do

form a GP:
a = 0
r = 10%
n = ?
then use sum of a go
s = a(rⁿ-1)/r-1

i dont hve a calculator on me currently, soz, but thatsthe method

[amelia20181]

how do you do this question

[Fergus6748]

how do you do this question

Heya,
So the first question is about primitive functions, first you want to integrate to get the first derivative:
second derivative = 12x +6
first derivative = 6x^2 + 6x + C

So now you have to find out what C is by equating the first derivative with 1 and subbing in x (-1) from the point:

first derivative = 1
first derivative also = 6x^2 + 6x + C
1 = 6(-1)^2 +6(-1) + C
1 = 6 - 6 + C
1 = C
Therefore, first derivative = 6x^2 + 6x + 1

Then find the equation of the curve:
First derivative = 6x^2 + 6x +1
Equation = 2x^3 + 3x^2 + x + C

Then find C again:
-2=2(-1)^3 + 3(-1)^2 + (-1) + C
-2=-2 + 3 - 1 + C
0=2 + C
C=-2
y = 2x^3 + 3x^2 + x - 2

[Fergus6748]

how do you do this question

With the second question, you have to integrate the acceleration equation to find the velocity equation:
Acceleration = 25 e^5t
Velocity = 5e^5t

(a)

Then sub in t = 9:
v = 5e^5(9)
   = 5e^45

(b) Then integrate the velocity equation, to find the displacement equation:

Velocity = 5e^5t
Displacement = e^5t

Then sub in t = 6
x = e^5(6)
   = e^30

(c)
a = 25e^5t
   = 25 (e^5t)
   = 25x
As x = e^5t

(d)
Sub in x = 2 to the acceleration equation
a = 25(2)
   = 50 ms^-2

And that's it

[amelia20181]

how do you do

[Opengangs]

Hint: If it tells us that the blood level decays exponentially, then it's hinting us towards the fact that:

\[ P = Ae^{-kt}\]

We can easily notice that \(A\) is just 150 since at \(t = 0\), the blood alcohol level is \(150\). Could you do the rest from here?

[fun_jirachi]

because it says his blood alcohol level (BAC) decays exponentially, you know that it decays 20%/hr just by reading the question ie. it decays to 80% of its level at the previous hour
a) so after three hours, his BAC will have decayed to approximately 51.2%
to get this answer, you simply take 0.8^3 and convert it to a percentage
the amount that is actually in his bloodstream is about 76.8 mg/dL
if you actually wanted to use calculus/any graphing technique you could look at the graph y=0.8^x, where y = %alcohol still in system and x = time
you'll still get the same answer
b) 20/150= 0.133333333333...
so you calculate when y=0.8^x cuts y=0.133333333...
0.8^x=0.133333333333...
x=log 0.1333333333.../log0.8 (using log laws)
x= approximately 9.030 hrs
you don't actually need calculus to solve this question
hope this helps

[fergo]

Hey there!

Can someone help me with the sum and products of roots? I know the two main formulas are on the formula sheet but I always forget how to do the ones when they manipulate the equations, like when you have to square or times the basic formulas to get the new ones.

I'm trying to just find the other formulas but am having no luck, can anyone help me?!

Thanks!

[fun_jirachi]

Hi there,

Usually, you try and simplify the ones where they manipulate the roots into forms like (a-b)^2 into a+b and ab. Also, it's very common to find that when there is a more complex expression with the only variables being the roots, that there are prior questions that you answer to make the simplification easier. There are no other formulas, its just learning how to simplify algebraic expressions into simpler expressions. If you have any specific examples that could help me better explain this to you, feel free to post them up.
Hope this helps!

[amelia20181]

how do you do this question