Math Is Fun Forum

Alive

Member

Registered: 2010-08-14

Posts: 92

Are the answers correct?

1)
Solve 2log10(x-3) = 10
2log10(x-3) = 10
log10 (x-3) = 5
x-3 = 10^5 = 100,000
x=100,003

2)
Solve inequation 8^(n-2) > 2048 for n
2^(3n-6) > 2^11
3n - 6 > 11
3n > 17
17/3 < n

3)
If 0<θ<π/2 then sin(π-θ) =
Sin (π-θ) = sinπcosθ-cosπsinθ =
0xcosθ-(-1)sinθ= sinθ

4)
function y=-3cos(2x) has amplitude and period respectively by:
period: pi , Amplitude: 3

5)
Given cos(θ) = 2/3 and 3π/2≤θ≤2π, then tan(θ) =
cos(θ)= 2/3 = sec^2(10)= 9/3 = tan^2(θ)=sec^2(θ)-1=5/4
As(θ) is in 4'th quad. tan(θ) is -ve
= tan(θ) = -√5/2

6)
If tanθ= 7/24 where 0<θ<π/2 then find exact values of sinθ, cosθ and sinθ (π+θ)
Since tanθ = 7/24, the side opposite θ is 7 and the side adjacent to θ is 24. The hypotenuse is: √(7^2 + 24^2) = √625 = 25
Sinθ = 7/25, cosθ = 24/25, sin(π+θ) = -7/25

7)
Solve following equation for x over domain,
2cosx + √3 = 0, 0≤θ≤360°
2cos(x) + sqrt(3) = 0
2cos(x) = -sqrt (3)
cos(x) = -sqrt (3)/2
cos(30deg) = sqrt(3)/2 so 30 degrees is reference angle.
cos(x) is negative in Quad 2 and Quad 3.
So 30 degrees in second and third quadrants.
In Quad 2, 180-30 = 150
In Quad 3, 180+3 = 210

8)
Maximal domain for functions with rule g(x) = loge(x-2) =
x-2>0
x>0

9)
When simplified and expressed with positive powers, (2a^2 b^3)(^-1)/b3
1/(2a^2b^6)

10)
The range and amplitude respectively of function of y=-2sin(x)+2
amp = 2, range of y is 0≤y≤4

11)
And.. Could you please do this for me:
9^2x x 27^x
--------------- =? (Multiple choice: 1, 0, 3^2x, 3^x, 3^-x)
3^7x

Thank you.

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Are the answers correct?

Hi Alive;

I numbered your problems so it is easier to refer to them.

1) Correct.

2) Nice work until you got to the last step! Check that please.

3) I am getting that too.

4) Correct.

6) I like it.

7) That is what I get.

8) I am not getting that. How did you figure your answer?

9) Correct but change that b3 to b^3.

10) Looks good.

11) Answer is 1;

Change the problem to:

Got called away, dinner has arrived!. Be back soon!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Are the answers correct?

lol I gotta go too, Thanks for pointing out my mistake, It really is n>17/3
And thanks a bunch for question 11 :]
Take care!

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Are the answers correct?

Hi Alive;

Glad to help.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.