Answer:
C
Step-by-step explanation:
The answer is C. If the original equation is 10+20 for one swing, you multiply that by 3 to get the cost of three swings
So, 1 nickel = 5 cents and 1 dime= 10 cents
Answer:
V = 8.06 cubed units
Step-by-step explanation:
You have the following curves:
![y_1=\frac{4}{9}x^2=f(x)\\\\y_2=\frac{13}{9}-x^2=g(x)](https://tex.z-dn.net/?f=y_1%3D%5Cfrac%7B4%7D%7B9%7Dx%5E2%3Df%28x%29%5C%5C%5C%5Cy_2%3D%5Cfrac%7B13%7D%7B9%7D-x%5E2%3Dg%28x%29)
In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:
(1)
To determine the limits of the integral you equal both curves f=g and solve for x:
![f(x)=g(x)\\\\\frac{4}{9}x^2=\frac{13}{9}-x^2\\\\\frac{4}{9}x^2+x^2=\frac{13}{9}\\\\\frac{13}{9}x^2=\frac{13}{9}\\\\x=\pm 1](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29%5C%5C%5C%5C%5Cfrac%7B4%7D%7B9%7Dx%5E2%3D%5Cfrac%7B13%7D%7B9%7D-x%5E2%5C%5C%5C%5C%5Cfrac%7B4%7D%7B9%7Dx%5E2%2Bx%5E2%3D%5Cfrac%7B13%7D%7B9%7D%5C%5C%5C%5C%5Cfrac%7B13%7D%7B9%7Dx%5E2%3D%5Cfrac%7B13%7D%7B9%7D%5C%5C%5C%5Cx%3D%5Cpm%201)
Then, the limits are a = -1 and b = 1
You replace f(x), g(x), a and b in the equation (1):
![V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_%7B-1%7D%5E%7B1%7D%5B%28%5Cfrac%7B13%7D%7B9%7D-x%5E2%29%5E2-%28%5Cfrac%7B4%7D%7B9%7Dx%5E2%29%5E2%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2Bx%5E4-%5Cfrac%7B16%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%20%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2B%5Cfrac%7B65%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5B%5Cfrac%7B169%7D%7B81%7Dx-%5Cfrac%7B26%7D%7B27%7Dx%5E3%2B%5Cfrac%7B65%7D%7B405%7Dx%5E5%5D_%7B-1%7D%5E1%5C%5C%5C%5CV%5Capprox8.06%5C%20cubed%5C%20units)
The volume of the solid of revolution is approximately 8.06 cubed units
Answer:
m = -8/5
Step-by-step explanation:
First determine how much x changes as we go from the first point to the second: -1 to +4. This change (the 'run') is 5 units.
Then find the change in y: -4 - (4) = -8. This change (the 'rise') is -8.
Thus the slope m = rise / run is m = -8/5