Answer:
Step-by-step explanation:
Given:
Fifth term of a geometric sequence = 
Common ratio (r) = ¼
Required:
Formula for the nth term of the geometric sequence
Solution:
Step 1: find the first term of the sequence
Formula for nth term of a geometric sequence = 
, where:
a = first term
r = common ratio = ¼
Thus, we are given the 5th term to be ¹/16, so n here = 5.
Input all these values into the formula to find a, the first term.
Cross multiply
Divide both sides by 16
Step 2: input the value of a and r to find the nth term formula of the sequence
nth term =
nth term = 
5 to the 4th power would be one way
Answer:
2.
Step-by-step explanation:
For #2, another way to word this question is: For which of the following trig functions is π/2 a solution? Well, go through them one by one. If you plug π/2 into sinθ, you get 1. This means that when x is π/2, y is 1. Try and visualize that. When y is 1, that means you moved off the x-axis; so y = sinθ is NOT one of those functions that cross the x-axis at θ = π/2. Go through the rest of them. For y = cos(π/2), you get 0. At θ = π/2, this function crosses the x-axis. For y = tanθ, your result is undefined, so that doesn't work. Keep going through them. You should see that y = secθ is undefined, y = cscθ returns 1, and y = cotθ returns 0. If you have a calculator that can handle trig functions, just plug π/2 into every one of them and check off the ones that give you zero. Graphically, if the y-value is 0, the function is touching/crossing the x-axis.
Think about what y = secθ really means. It's actually y = 1/(cosθ), right? So what makes a fraction undefined? A fraction is undefined when the denominator is 0 because in mathematics, you can't divide by zero. Calculators give you an error. So the real question here is, when is cosθ = 0? Again, you can use a calculator here, but a unit circle would be more helpful. cosθ = π/2, like we just saw in the previous problem, and it's zero again 180 degrees later at 3π/2. Now read the answer choices.
All multiples of pi? Well, our answer looked like π/2, so you can skip the first two choices and move to the last two. All multiples of π/2? Imagine there's a constant next to π, say Cπ/2 where C is any number. If we put an even number there, 2 will cut that number in half. Imagine C = 4. Then Cπ/2 = 2π. Our two answers were π/2 and 3π/2, so an even multiple won't work for us; we need the odd multiples only. In our answers, π/2 and 3π/2, C = 1 and C = 3. Those are both odd numbers, and that's how you know you only need the "odd multiples of π/2" for question 3.
Answer:
First number is -2.5
Second number 5
Step-by-step explanation:
Four times the first number minus three times the second number is 2.
To represent this statement, 4x -3y =2
Two times the first number increased by three times the second is 10.
To represent thsi statement, 2x+ 3y = 10
4x - 3y = 2
2x + 3y =10
4x - 2x = 2x
2x = -5
x= -2.5
The first number is -2.5
By using Substitution
2x + 3y = 10
2(-2.5) + 3y = 10
-5 + 3y = 10
3y = 10 +5
3y =15
y = 5
The second number is 5
....To check my answer
-5 + 15 = 10
Answer:
Hey! Ok so the height is C.10 ft.
Step-by-step explanation:
So to find the height I have to do
h=Vlw =540 12·4.5=10
So therefore its 10
Hope you have a great day! I'm Eve btw Hoped this helped and consider marking this brainiest!
