So exponenetial growth or decay
it goes like this
f(t)=P(1+r)^t
r=rate of decay or grouth
if r>0 then it is grouth by r
if r<0 then it is decay
i
P=initial amount
so
given
f(x)=5500(1.65)^t
f(x)=5500(1+0.65)^t
0.65>0 so it is growing by 65%
Distribute on the left
2x-2+3x=3
Combine like terms
5x-2=3
Add 2 to both sides
5x=5
Divide both sides by 5
x=1
Final answer: x=1
If you can choose and answer more than 1 time pick c
Answer:
g = 2H/(m + r)
Step-by-step explanation:
mg + rg = 2H
g(m + r) = 2H
(g(m + r))/(m + r) = 2H/(m + r)
g = 2H/(m + r)
Answer:
The tree is approximately 91.2 ft tall.
Step-by-step explanation:
Hi there!
We're told:
- angle of elevation = 69 degrees
- there is a point 35 feet from the tree
If we were to draw this out, it would appear to be a right angle triangle. See the picture below.
Now, to solve for the height of the tree, we can use the sine law:
![\frac{a}{ \sin(a) } = \frac{b}{ \sin(b) }](https://tex.z-dn.net/?f=%20%20%5Cfrac%7Ba%7D%7B%20%5Csin%28a%29%20%7D%20%20%3D%20%20%5Cfrac%7Bb%7D%7B%20%5Csin%28b%29%20%7D%20)
where a and b are two sides of a right triangle and A and B are the respective opposite angles
Let the height of the tree = h.
Side h is opposite of the angle measuring 69 degrees:
![\frac{h}{ \sin {69}^{o} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bh%7D%7B%20%5Csin%20%7B69%7D%5E%7Bo%7D%20%7D%20)
Let the angle opposite of the side measuring 35 feet = A.
![\frac{35}{ \sin(a) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B35%7D%7B%20%5Csin%28a%29%20%7D%20)
Because the sum of a triangle's interior angles is 180 degrees, we know that A=180-90-69=21 degrees.
![\frac{35}{ \sin {21}^{o} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B35%7D%7B%20%5Csin%20%7B21%7D%5E%7Bo%7D%20%7D%20)
Use the sine law:
![\frac{h}{ \sin {69}^{o} } = \frac{35}{ \sin {21}^{o} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bh%7D%7B%20%5Csin%20%7B69%7D%5E%7Bo%7D%20%20%7D%20%20%3D%20%20%5Cfrac%7B35%7D%7B%20%5Csin%20%7B21%7D%5E%7Bo%7D%20%20%7D%20)
![h = \frac{35}{ \sin {21}^{o} } \: \sin {69}^{o}](https://tex.z-dn.net/?f=h%20%3D%20%20%5Cfrac%7B35%7D%7B%20%5Csin%20%7B21%7D%5E%7Bo%7D%20%20%7D%20%5C%3A%20%20%5Csin%20%7B69%7D%5E%7Bo%7D%20%20%20)
![h = 91.17812](https://tex.z-dn.net/?f=h%20%3D%2091.17812)
Therefore, the tree is approximately 91.2 ft tall.
I hope this helps!