q = 10p because all of them are multiplied by ten
Answer:
The fourth term is -102----------------------------------------------
Explanation:
The term after the nth term is generated by this rule

which means that we first
Step 1) multiply the nth term (

) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence
Let's follow those steps above to generate the first four terms
The first term is

. In short, the first term is 2
The second term is...





So the second term is -6
The third term is...





The third term is 26
Finally, the fourth term is...




The fourth term is -102.
Answer: 125.80 ft
Step-by-step explanation:
Asuming the described situation is as shown in the figure below, we need to find the distance
between the kite and Jacks house, but first we need to find the
,
and then
.
How?
We will use trigonometry, especifically the trigonometric functions sine and cosine:
For
:
(1)
Where
is the opposite side to the angle and
the hypotenuse.
Isolating
:
(2)
For
:
(3)
Where
is the adjacent side to the angle.
Isolating
:
(4)
Finding
:
(5)

(6)
Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house
and the sides are the values calculated in (4) and (6).
So, in this case we will use the <u>Pithagorean theorem</u>:
(7)
Isolating
and writing with the known values:
(8)
(9)
This is the distance between the kite and the house