Answer:
t = 115
s = 60
g(x) = 10/23x - 10
Step-by-step explanation:
find s first since its easy (it goes up by 10's)
then take a pair from the table that corresponds such as 69 for x and 30 for g(x) and turn them into a fraction:
69/30
do the same for t:
t/50
equal 69/30 to t/50 and solve using cross multiplication:
69/30 = t/50 =
30t = 3450
/30 /30
t = 115
honestly had a little hard time finding the equation but basically I simplified the fraction 30/69 to get 10/23 for slope and then I insert a corresponding x and y value into y= mx+b with the slope value to find b.
Answer:
4 x^3 - 3 x^2
Step-by-step explanation:
Expand the following:
x^2 (4 x - 3)
x^2 (4 x - 3) = x^2×4 x + x^2 (-3):
4 x^2 x - 3 x^2
x^2×4 x = x^(2 + 1)×4:
4 x^(2 + 1) - 3 x^2
2 + 1 = 3:
Answer: 4 x^3 - 3 x^2
Answer:
= 7n - 4
Step-by-step explanation:
The n th term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 3 and d = a₂ - a₁ = 10 - 3 = 7 , thus
= 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4
Answer:
- Question 1a. i)
![x=1.8m](https://tex.z-dn.net/?f=x%3D1.8m)
- Question 1a. ii)
![Volume=27.6m^3](https://tex.z-dn.net/?f=Volume%3D27.6m%5E3)
- Question 1b)
![Volume=65.9m^3](https://tex.z-dn.net/?f=Volume%3D65.9m%5E3)
Explanation:
<u><em>Question 1 a. i) Find the value of x.</em></u>
![tan(\theta )=\dfrac{opposite\text{ }leg}{adjacent\text{ }leg}](https://tex.z-dn.net/?f=tan%28%5Ctheta%20%29%3D%5Cdfrac%7Bopposite%5Ctext%7B%20%7Dleg%7D%7Badjacent%5Ctext%7B%20%7Dleg%7D)
For the smalll triangle you can write:
![tan(\theta )=\dfrac{x}{1m}](https://tex.z-dn.net/?f=tan%28%5Ctheta%20%29%3D%5Cdfrac%7Bx%7D%7B1m%7D)
For tthe big triangle:
![tan(\theta )=\dfrac{x+2.7m}{2.5m}](https://tex.z-dn.net/?f=tan%28%5Ctheta%20%29%3D%5Cdfrac%7Bx%2B2.7m%7D%7B2.5m%7D)
Substitute:
![\dfrac{x}{1m}=\dfrac{x+2.7m}{2.5m}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B1m%7D%3D%5Cdfrac%7Bx%2B2.7m%7D%7B2.5m%7D)
Solve for x:
![2.5x=x+2.7m\\\\2.5x-x=2.7m\\\\1.5x=2.7m\\\\x=2.7m/1.5\\\\x=1.8m](https://tex.z-dn.net/?f=2.5x%3Dx%2B2.7m%5C%5C%5C%5C2.5x-x%3D2.7m%5C%5C%5C%5C1.5x%3D2.7m%5C%5C%5C%5Cx%3D2.7m%2F1.5%5C%5C%5C%5Cx%3D1.8m)
<u><em>Question 1a ii) Find the volume of the frustrum</em></u>
- Find the volume of a cone with height = 2.7m + 1.8m = 4.5m, and radius = 2.5m
Formula:
![Volume=(1/3)\pi \times radius^2\times height](https://tex.z-dn.net/?f=Volume%3D%281%2F3%29%5Cpi%20%5Ctimes%20radius%5E2%5Ctimes%20height)
Substitute:
![Volume=(1/3)\pi \times (2.5m)^2\times 4.5m=9.375\pi m^3](https://tex.z-dn.net/?f=Volume%3D%281%2F3%29%5Cpi%20%5Ctimes%20%282.5m%29%5E2%5Ctimes%204.5m%3D9.375%5Cpi%20m%5E3)
- Find the volume of a cone with heigth = 1.8m and radius = 1m
![Volume=(1/3)\pi \times (1m)^2\times 1.8m=0.6\pi m^3](https://tex.z-dn.net/?f=Volume%3D%281%2F3%29%5Cpi%20%5Ctimes%20%281m%29%5E2%5Ctimes%201.8m%3D0.6%5Cpi%20m%5E3)
- Subtract the volume of the small cone from the volume of the big cone
![Volume\text{ }of\text{ }frustrum=9.375\pi m^3-0.6\pi m^3=8.775\pi m^3\approx 27.6m^3](https://tex.z-dn.net/?f=Volume%5Ctext%7B%20%7Dof%5Ctext%7B%20%7Dfrustrum%3D9.375%5Cpi%20m%5E3-0.6%5Cpi%20m%5E3%3D8.775%5Cpi%20m%5E3%5Capprox%2027.6m%5E3)
<u><em>Question 1b. Calculate the volume of the bin</em></u>
<u>i) Upper frustrum</u>
This is the same frustrum from the equation of above, thus ist volume is 27.6m³.
<u>ii) Lower frustrum</u>
![\dfrac{x}{2.0m}=\dfrac{x+2.4m}{2.5m}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B2.0m%7D%3D%5Cdfrac%7Bx%2B2.4m%7D%7B2.5m%7D)
![2.5x=2(x+2.4m)\\\\2.5x=2x+4.8m\\\\0.5x=4.8m\\\\x=9.6m](https://tex.z-dn.net/?f=2.5x%3D2%28x%2B2.4m%29%5C%5C%5C%5C2.5x%3D2x%2B4.8m%5C%5C%5C%5C0.5x%3D4.8m%5C%5C%5C%5Cx%3D9.6m)
![Volume=(1/3)\pi \times (2.5m)^2\times (9.6m+2.4m)-(2.0m)^2\times (9.6m)](https://tex.z-dn.net/?f=Volume%3D%281%2F3%29%5Cpi%20%5Ctimes%20%282.5m%29%5E2%5Ctimes%20%289.6m%2B2.4m%29-%282.0m%29%5E2%5Ctimes%20%289.6m%29)
![Volume=38.3m^3](https://tex.z-dn.net/?f=Volume%3D38.3m%5E3)
<u>iii) Add the volume of the two frustrums</u>