Answer: x= 12
Step-by-step explanation:
3x+6 = 42
or, 3x = 36
so, x = 12
The answer to the question is 43
Answer:


or

Step-by-step explanation:
We are going to see if the exponential curve is of the form:
, (
).
If you are given the
intercept, then
is easy to find.
It is just the
coordinate of the
intercept is your value for
.
(Why? The
intercept happens when
. Replacing
with 0 gives
. This says when
.)
So
.
So our function so far looks like this:

Now to find
we need another point. We have two more points. So we will find
using one of them and verify for our resulting equation works for the other.
Let's do this.
We are given
is a point on our curve.
So when
,
.


Divide both sides by 8:

Reduce the fraction:

So the equation if it works out for the other point given is:

Let's try it. So the last point given that we need to satisfy is
.
This says when
,
.
Let's replace
with 2 and see what we get for
:






So we are good. We have found an equation satisfying all 3 points given.
The equation is
.
Answer:
Ф = 
Step-by-step explanation:
It is a bit difficult to input the work here, so I uploaded an image
- First we can use the trig identities to change sec²(Ф) to tan²(Ф) + 1
- Then we can combine like terms
- Then we can factor this as a polynomial function
- Then we can set each term equal to zero and solve for Ф
- The first term tan(Ф) - 2 = 0 has no solution because tan(Ф) ≠ -2 anywhere
- The second term tan(Ф) - 1 = 0 has two solutions of
and
so these are the solutions to the problem
Answer:

Step-by-step explanation:
It was given that, florida manatee population is 3,000 and is decreasing by 11% each year.
We want to write a function for this situation.
Since the population is decreasing annually, it is modelled by:

We substitute the give initial population and rate of decrease to get:

This simplifies to:
