Problems solved

Question

Problems solved

Problems solved

Problems solved

Problems solved

Answer 1

Emily:

I'm not sure if you mean 4sin²(θ) = 1 or 4*sin(2*θ) = 1

If you are working on 4sin²(θ) = 1 then sin²(θ) = 1/4 so sin(θ) = 1/2 or sin(θ) = -1/2

We know θ = 30º solves sin(θ) = 1/2 and θ = -30º solves sin(θ) = -1/2.

On (-180, 180) θ = 180-30 =150º also solves sin(θ) = 1/2.

Can you figure the other value that will solve sin(θ) = -1/2?

Answer 2

a)

a_o = 3/([+3(0)]= 3

a₁= 3/[1+ 3(1) = 3/4

a₂= 3[(1+ 3(2)] = 3/7

a₃= 3/[1+ 3(3) )= 3/10

a₄= 3/[1+ 3(4)] = 3/13

.

.

.a_n= 3/[1+ 3(n)]= 3/(3n +1)

b)

if n =100

a₁₀₀= 3/[3(100)+ 1] = 3/301

Answer 3

For the sequence 4, 7, 10, 13, ...

a_n = 4 + 3(n - 1)

a_n = 4 + 3n - 3

a_n = 1 + 3n

For the sequence 3/4. 3/7. 3/10, ..

a_n = 3 / (1 + 3n)

What is a₁₀₀?

Answer 4

Answer 5

Hi, Emily,

Here's how to do this kind of question.

What we have here is a probability problem, that is a binomial distribution, namely a set of "trials" where each has the same probability of success, 0,4 in this case.

So, the standard formula is Pr { r successes out of n } = nCr p^r q^(n-r) and nCr = n! / r! (n - r)!

In this case, n = 5, r = 2, p = 0.4 and q = 1 - 0.4 = 0.6

Hence, Pr { 2 successes in n trials } = (5!/2!/3!) (0.4^2) (0.6^3)

= 20/2 (0.16) (0.216)

= 0.3456

= 34.56%

Answer 6

Hi Emily,

The reference angle is the positive acute angle that can represent an angle of any measure.

So, it's the acute angle (<= 90 degrees) in the appropriate quadrant that has the same hypotenuse as the required angle.

Since 195 degrees is in quadrant 3, the reference angle is the acute angle formed by subtracting 180 degrees, that is, 15 degrees.

Answer 7

Emily:

There are 6 letters in fluffy but 3 of those letters are identical (f's)

Use 6!/3! I'll let you simplify this

Answer 8

195° - 180° = ?

Answer 9

Emily:

Notice sin(x+y) = sin(x)*cos(y) + sin(y)*cos(x)

So sin(π/6 + (2*π)/3) = sin(π/6)*cos((2*π)/3) + sin ((2*π)/3)*cos(π/6)

sin (π/6 + (2*π)/3) = sin((5*π)/6).

What is this value equal to?

Answer 10

Mary,

Find the common ratio r.

r = 14.7/15 = 0.98

Since r<1, we can use the formula

S = a₁ / (1-r) r=0.98, what's a₁?