Answer:
(a) 8.15
(b) 12.92
Step-by-step explanation:
Given: P = $3000, r = 0.085
![A = Pe^{rt}](https://tex.z-dn.net/?f=A%20%3D%20Pe%5E%7Brt%7D)
Where
A is the Amount
P is the Principal
r is the rate
t is the time
(a) For the amount to double, A = 2 × P
A = 2 × $3000
A = $6000
![6000 = 3000e^{0.085t}](https://tex.z-dn.net/?f=6000%20%3D%203000e%5E%7B0.085t%7D)
![\frac{6000}{3000} = e^{0.085t}](https://tex.z-dn.net/?f=%5Cfrac%7B6000%7D%7B3000%7D%20%3D%20e%5E%7B0.085t%7D)
![2 = e^{0.085t}](https://tex.z-dn.net/?f=2%20%3D%20e%5E%7B0.085t%7D)
Take
of both sides
![log_{e}2 = log_{e}e^{0.085t}](https://tex.z-dn.net/?f=log_%7Be%7D2%20%3D%20log_%7Be%7De%5E%7B0.085t%7D)
But ![log_{e}e = 1](https://tex.z-dn.net/?f=log_%7Be%7De%20%3D%201)
∴ ![ln2 = 0.085t](https://tex.z-dn.net/?f=ln2%20%3D%200.085t)
![t = \frac{ln2}{0.085}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bln2%7D%7B0.085%7D)
![t = \frac{0.693}{0.085}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B0.693%7D%7B0.085%7D)
t = 8.15
(b) For the amount to double, A = 3 × P
A = 3 × $3000
A = $9000
![9000 = 3000e^{0.085t}](https://tex.z-dn.net/?f=9000%20%3D%203000e%5E%7B0.085t%7D)
![\frac{9000}{3000} = e^{0.085t}](https://tex.z-dn.net/?f=%5Cfrac%7B9000%7D%7B3000%7D%20%3D%20e%5E%7B0.085t%7D)
![3 = e^{0.085t}](https://tex.z-dn.net/?f=3%20%3D%20e%5E%7B0.085t%7D)
Take
of both sides
![log_{e}3 = log_{e}e^{0.085t}](https://tex.z-dn.net/?f=log_%7Be%7D3%20%3D%20log_%7Be%7De%5E%7B0.085t%7D)
But ![log_{e}e = 1](https://tex.z-dn.net/?f=log_%7Be%7De%20%3D%201)
∴ ![ln3 = 0.085t](https://tex.z-dn.net/?f=ln3%20%3D%200.085t)
![t = \frac{ln3}{0.085}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bln3%7D%7B0.085%7D)
![t = \frac{1.0986}{0.085}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B1.0986%7D%7B0.085%7D)
t = 12.92
First covert the feet to meters.
1 meter = 3.3 feet.
Divide the total number of feet by 3.3 to get total number of meters:
198 / 3.3 = 60 meters per second.
Multiply meters per second by 15 seconds:
60 x 15 = 900 meters in 15 seconds.
Answer:
13/20
Step-by-step explanation:
0.65 = 65/100
both are multiples of 5, so simplify:
65/100 = 13/20
-Chetan K
Answer:
See below.
Step-by-step explanation:
To find the surface area, find the area of the square base and add it to the area of each triangle face. Find the area of the base by multiplying base length by base length. Find the area of each triangle face by multiplying 1/2 * b*h.
Example:
For a base which is 12 by 12. The area is 12 x 12 = 144.
For the triangle face, the area is 1/2 * 12 * 15 = 90. Since there are 4 faces, the total area is 4 * 90 = 360.
Together the surface area is 360 + 144 = 504.