Answer:
1) D
2) A
3) C
4) B
5) B
6) C
Step-by-step explanation:
1) V = Bh
V = πr² (h)
V = π (7²)(5)
V = 49π (5)
V = 245π
V ≈ 769.3
2) V = 1/3 Bh
V = 1/3 (12*12)(9)
V = 1/3 (144)(9)
V = 1/3 (1296)
V = 432
3) V = 4/3πr³
V = 4/3 π (4.5³)
V = 4/3 π (91.125)
V = 121.5π
V ≈ 381.51
4) 3 pairs of rectangles
2(16)(5) = 2(80) = 160
2(16)(11) = 2(176) = 352
2(11)(5) = 2(55) = 110
Add together 160 + 352 + 110
622
5) Two triangles 3 rectangles
<em>Triangle</em>
2(1/2)(18)(5) = 18*5 = 90
<em>Rectangles</em>
18*7 = 126
5*7 = 35
18.7*7 = 130.9
Add together 90 + 126 + 35 + 130.9 = 381.9
C) SA = πr² + πrl --> l is the slant height
SA = π (8²) + π (8)(17)
SA = 64π + 136π
SA = 200π
SA ≈ 628
DACBBC
Starting with 60, divide by 5 --> 12
add by 13 --> 25
multiply by 3 --> 75
subtract by 11 --> 64
cube root 64 --> 4
Multiply 60 --> 240
CODE: 240
Answer:
23.19°
Step-by-step explanation:
Given that,
The height of a drone = 12 yards
It has traveled a horizontal of 28 yards
We need to find the angle of depression from the drones current location down to its starting point. It can be calculated as :
![\tan\theta=\dfrac{P}{B}\\\\\theta=\tan^{-1}(\dfrac{P}{B})\\\\=\tan^{-1}(\dfrac{12}{28})\\\\=23.19^{\circ}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7BP%7D%7BB%7D%5C%5C%5C%5C%5Ctheta%3D%5Ctan%5E%7B-1%7D%28%5Cdfrac%7BP%7D%7BB%7D%29%5C%5C%5C%5C%3D%5Ctan%5E%7B-1%7D%28%5Cdfrac%7B12%7D%7B28%7D%29%5C%5C%5C%5C%3D23.19%5E%7B%5Ccirc%7D)
So, the angle of depression is equal to 23.19°.
Since it is one term that is being squared, we can distribute the square.
So, just multiply the current exponent by 2.
6*2 = 12
1*2 = 2
So
![s^{12}t^6](https://tex.z-dn.net/?f=s%5E%7B12%7Dt%5E6)
To model this situation, we are going to use the exponential function:
![f(t)=P(1+ \frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=f%28t%29%3DP%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
where
![P](https://tex.z-dn.net/?f=P)
is the initial number of cars
![r](https://tex.z-dn.net/?f=r)
is the growing rate in decimal form
![n](https://tex.z-dn.net/?f=n)
is number of tames the growing rate is increasing per year
![t](https://tex.z-dn.net/?f=t)
is the time in years
To convert the growing rate to decimal form, we are going to divide the rate by 100%
![r= \frac{12}{100}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B12%7D%7B100%7D%20)
![r=0.12](https://tex.z-dn.net/?f=r%3D0.12)
Since the growing rate is increasing quarterly,
![n=4](https://tex.z-dn.net/?f=n%3D4)
. We also know that the initial number of cars is 920, so
![P=920](https://tex.z-dn.net/?f=P%3D920)
. Lets replace all those values in our function:
![f(t)=920(1+ \frac{0.12}{4} )^{4t}](https://tex.z-dn.net/?f=f%28t%29%3D920%281%2B%20%5Cfrac%7B0.12%7D%7B4%7D%20%29%5E%7B4t%7D)
![f(t)=920(1+0.03)^{4t}](https://tex.z-dn.net/?f=f%28t%29%3D920%281%2B0.03%29%5E%7B4t%7D)
![f(t)=900(1.03)^{4t}](https://tex.z-dn.net/?f=f%28t%29%3D900%281.03%29%5E%7B4t%7D)
We can conclude that:
Rate ---------> The quarterly rate of growth is 0.03 or 3%
Exponent --------> The compound periods multiplied by the number of years is 4t
Coefficient--------> The initial number of cars serviced is 920
Base------> The growth factor is represented by 1.03