CPhill

Re: The first term of a geometric series is 1 and the common ratio is 9. What is the 8th term of the sequence?

Mmmmm....... let's look at this again.

Note that the first few terms of the series are

1, 9 , 81.......

So the first term is just 9^0

And the second term is 9^1

So, the nth term is given by 9^(n-1)

I'll let you take it from there.......

a^2-2a-3=?

I'm assuming you want to factor this...it's just

(a -3) * (a + 1)

We try to !!!!

express the following as a percentage a) 9 over 20 b) 3 out of 25

a) 9 / 20 = x / 100

cross-multiplying, we have

9 * 100 = 20 * x

900 = 20 * x  Divide both sides by 20

45 = x  

So........ 9 / 20 = 45 / 100 = 45%

b) 3 /25 = x /100

cross-multiplying, we have

3 * 100 = 25 * x

300 = 25 * x  Divide both sides by 25

12 = x 

So........ 3 / 25 = 12 / 100 = 12%

the frequency of violet light is 7.5*10^(14) what is its wavelength

The speed of light, c, is equal to the product of the wavelength (lamda), and the frequency, ν.

Then c = λ * v

Therefore

λ = c/ν

λ = 3 x 10⁸ m/sec/(7.5 x 10¹⁴ Hz)

λ = 30 x 10⁷ m/sec/(7.5 x 10¹⁴ Hz)

λ = 4 X 10^-7m

8/9 divided by 5/6

Inverting the second fraction and multiplying, we have

8/9 * 6 /5  =  48 / 45  and reducing, we have   16 / 15

what is 2.4-2v/3=9

Let's subtract 2.4 from both sides   This gives

-2v/3 = 6.6  Multiply both sides by 3

-2v = 19.8

Dividing by -2 gives

v = - 9.9

11ln4x=14 in a decimal

Let's divide both sides by 11 This gives

ln 4x = 14 /11

Writing this in exponential form, we get

e^(14/11) = 4x    dividing both sides by 4, we have

e^(14/11) / 4 = x

so x  ≈ .8926

covert the polar equation to a rectangular equation. r=9csc(θ)

(Let's use theta instead of "x")

Remember....... csc(θ)  = r / y  

So we have

r = 9 (r / y)

Multiply both sides by (y / r)  This gives

r (y / r) = 9 So we have

y = 9

Note that this is just a horizontal line 9 units above the x axis !!

And that's it !!!

2 / 12  =  1 /6 = .1666666 (repeating decimal)