Suppose that the exponential growth function is y = 4^x.
If x = 1, then y = 4^1 = 4.
If x = 3, then y = 4^3 = 64.
Let the initial value be 1/2.
The growth function is now y = 1/2 * 4^x.
If x =1, then y = 2 which is half of the y value before adding the 1/2.
If x = 3, then y = 1/2 * 64 = 32.
Answer: 1/2
This is a percent problem which means
You take the amount that has been completed over the total amount. You then multiply it by 100%
30/120*100=25%
The technology I used in helping me solve the problem is using Microsoft Excel. I made one column for the x values which were gathered from the choices, one column for f(x) whose equation is 8^(x-9), and another column for g(x) whose equation is log(3x) + 2.
Inputing these equation to the last two columns yield the values shown in the picture.The 'NUM' means that the equation at that value of x is undefined. From the values, the correct solution would be
(0,0), (9.2,1.5) and (9.6,3.5) to the f(x) equation
(9.6,3.5) to the g(x) equation
Theorem of Pythagoras: a²+b²=c², where a, b is legs and c is hypotenuse.
We've got one leg known, let it be a=sqrt 3,
and the hypotenuse - c=2sqrt3
Putting these into the theorem, we get an equation: (sqrt3)²+b²=(2sqrt3)² . Solving it, we get:
3+b²=4*3
3+b²=12
b²=9
This equation has two possible roots: b=3 and b=-3. Since this is a triangle, there can't be a side with a negative value => b=3.
The answer is a. 3
Step-by-step explanation:
Since
we can get some information from this. First of all
is defined as
. So the adjacent side is 3 and the hypotenuse is 4. Using this we can find the opposite side to find
to calculate csc and cot of theta. So using the Pythagorean Theorem we can solve for the missing side. Also I forget to mention we have to calculate the sign of the adjacent side and the hypotenuse. Since you're given that the angle is in quadrant 2, that means the x-value is going to be negative, and the y-value is going to be negative. And the x really represents the adjacent side and the y represents the opposite. So the adjacent side is what's negative. and the opposite is positive
Pythagorean Theorem:





So now we can calculate
.

Now to calculate the exact value of csc you simply take the inverse. This gives you
. Multiplying both sides by sqrt(7) to rational the denominator gives you
.
Now to calculate cot(theta) you find the inverse of tan. Tan is defined as
. So all you do is take the inverse which is
.
Plug values in

Keep, change, flip

Multiply:

Multiply both sides by sqrt(7)

This is the value of cot(theta)