# Thread: Can Anyone help me with these questions?

1. ## Can Anyone help me with these questions?

Hi I was wondering if anyone can help me with these questions so I know I got them right.

So can anyone go through these questions with step by step answers

I got these on the internet with no mark schemes and I need answers for all the questions since I self teach.

Thank You

2. ## Re:

#1.
a.
f(x)=x^3+3x^2+5
f'(x)=3x^2+6x
f''(x)=6x+6

#2.

a. (1-2x)^5=1-10x+40x^2-80x^3+80x^4-32x^5

#4.

5^x=17
xln(5)=ln(17)

Divide ln(17) by ln(5)

Thus

x=ln(17)/ln(5)

#5.

b. f(x)=x^3+4x^2+x-6=(x-1)(x+2)(x+3)
c. f(x)=x^3+4x^2+x-6=(x-1)(x+2)(x+3)

Hence

x=1
x=-2
x=-3

This worksheet is a piece of cake. Hopefully this will get you started.

-qbkr21

3. #1.(a)
f'(x)=3x^2-6x
f"(x)=6x-6
(b)see attachment

4. ## Re:

Originally Posted by alinailiescu
#1.(a)
f'(x)=3x^2-6x
f"(x)=6x-6
(b)see attachment
Alinaliescu your differentiation and integration for part A & B are wrong

f(x)=x^3+3x^2+5 NOT f(x)=x^3-3x^2+5

5. Yes, I realized that after I posted the replay. I tried to print out the problems, and the printer didn't work properly.
Anyway, you posted the right solutions.
Thanks

6. ## Re:

I can see how you misread it. The vast majority of these PDF files people attach are very hard to read because of their clarity.

7. #3
Since the points given are the end points of the diameter, the midpoint would be the center of the circle.
((-1+3)/2, (4+6)/2)
thus, (1, 5) is the center.
r=sqrt[(3-1)^2+(6-5)^2]=sqrt(5)
So, the equation is:
(x-1)^2+(y-5)^2=5

8. Thanks so is anyone able to do questions 6-10

9. ## #6

first ,use cos^2(x)=1-sin^2(x) to eliminate cosine function
That would give you:
2(1-sin^2(x))+1=5sinx
2-2sin^2(x)+1-5sinx=0
-2sin^2(x)-5sinx+3=0
This is a quadratic equation in sinx, so using the quadratic formula you have:
sinx=[5+sqrt(25-4*-2*3)]/[-2*2]=[5+7]/(-4)=12/-4=-3(which has no solution for x, since sinx should be between -1 and 1)
or
sinx==[5-sqrt(25-4*-2*3)]/[-2*2]=[5-7]/(-4)=1/2
so x=sin^-1(1/2)
x=pi/6

10. This is a full past paper you are asking others to do.
Surely you can do at least one or two of them.
England exams are not far away.

@alinailiescu

You missed out 5(pi)/6

11. Sorry if it seems your helping me do my past paper so far I have done must of them but I was checking if I got them right.

12. Get someone to check this.

13. Pay attention,
6x^3/3=2x^3 and not 3x^3
So, the answer is -2. (which makes sense since the shaded area is under the x axis,)

14. Anyone for 8 and 9, I finished 10 so don't worry about that.

15. ## Re:

8.a

v=-70
v=70

Do you want to see the work?

8.b

C''=(2800/v^3)

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