Answer:
The volume of the solid is 19.
unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
![V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5Ea_b%20%7B%5Cleft%28%20%5Bf%28x%29%5D%5E2%20-%20%5Bg%28x%29%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx)
Where;
a = 1, and b = 2, we have;
g(x) = 1
![V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5E%7B2%7D_1%20%7B%5Cleft%28%20%5Bx%5E3%5D%5E2%20-%20%5B1%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx%20%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bx%5E7%7D%7B7%7D%20%2B%20x%20%5Cright%5D_1%5E%7B2%7D%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7B2%5E7%7D%7B7%7D%20%2B2%20-%5Cleft%28%20%5Cdfrac%7B1%5E7%7D%7B7%7D%20%2B%201%5Cright%29%5Cright%5D%20%3D19%5Cdfrac%7B1%7D%7B7%7D)
The volume of the solid, V = 
unit³ = 19. unit³
Answer: 4 years after the original investment, it is approximately $1,093.
Step-by-step explanation:
Hi, to answer this question we have to apply the simple interest formula:
I = p x r x t
Where:
I = interest
P = Principal Amount
r = Interest Rate (decimal form)
t= years
Replacing with the values given
I = 1000x (2.25/100) x t
- It will triple in approximately 3 years. FALSE
I = 1000x (2.25/100) x 3 =67.5
1000+67.5 = 1067.5
- It will no longer grow after several years: False, it will grow because it has a growth rate.
- 4 years after the original investment, it is approximately $1,093. TRUE
I = 1000x (2.25/100) x 4 =90
1000+90 = $1090
- It will double in approximately 10 years.
I = 1000x (2.25/100) x 10 =225
1000+90 = $1225
Feel free to ask for more if needed or if you did not understand something.
Answer:
4/5
Step-by-step explanation:
slope is 4/5
y = mx + b
m = slope
