On desmos, a graphing calculator, I inputted your numbers, and I got that each side is 11 units long. Therefore, because a hexagon has 6 sides, you would have 6 * 11 = 66 units.
Therefore, your answer is 66.
Hope this helps and have a nice day:)
Answer:
<em>(f-g)(x)=x+14</em>
Step-by-step explanation:
<u>Operations with Functions</u>
Given two functions f(x) and g(x), the following operations are defined:
(f+g)(x)=f(x)+g(x)
(f-g)(x)=f(x)-g(x)
(f*g)(x)=f(x)*g(x)
(f/g)(x)=f(x)/g(x)
We have f(x)=3x+10 and g(x)=2x-4. Use the second formula to find
(f-g)(x)=(3x+10)-(2x-4)
Operating:
(f-g)(x)=3x+10-2x+4
Joining like terms:
(f-g)(x)=x+14
Since you have an equation equal to both x and y, you can either substitute the equation equal to x for x or the equation equal to y for y.
x=y-1
y=4-2x
I would substitute the y in using 4-2x
x=(4-2x)-1
x=3-2x
3x=3
x=1
Then plug in x and solve for y
1=y-1
2=y
Answer:
V = 2000r³/3
Step-by-step explanation:
We know that the base is a circular disk, so it creates a circle on the xy plane. It would be in the form x² + y² = r². In other words x² + y² = (5r)². Let's isolate y in this equation now:
x² + y² = (5r)²,
x² + y² = 25r²,
y² = 25r² - x²,
y = √25r² - x² ---- (1)
Now remember that parallel cross sections perpendicular to the base are squares. Therefore Area = length^2. The length will then be = 2√25r² - x² --- (2). Now we can evaluate the integral from -5r to 5r, of [ 2√25r² - x² ]² dx.
![\int _{-5r}^{5r}\:\left[\:2\sqrt{\left(25r^2\:-\:x^2\right)}\:\right]\:^2\:dx\\=\int _{-5r}^{5r}4\left(25r^2-x^2\right)dx\\\\= 4\cdot \int _{-5r}^{5r}25r^2-x^2dx\\\\= 4\left(\int _{-5r}^{5r}25r^2dx-\int _{-5r}^{5r}x^2dx\right)\\\\= 4\left(250r^3-\frac{250r^3}{3}\right)\\\\= 4\cdot \frac{500r^3}{3}\\\\= \frac{2000r^3}{3}](https://tex.z-dn.net/?f=%5Cint%20_%7B-5r%7D%5E%7B5r%7D%5C%3A%5Cleft%5B%5C%3A2%5Csqrt%7B%5Cleft%2825r%5E2%5C%3A-%5C%3Ax%5E2%5Cright%29%7D%5C%3A%5Cright%5D%5C%3A%5E2%5C%3Adx%5C%5C%3D%5Cint%20_%7B-5r%7D%5E%7B5r%7D4%5Cleft%2825r%5E2-x%5E2%5Cright%29dx%5C%5C%5C%5C%3D%204%5Ccdot%20%5Cint%20_%7B-5r%7D%5E%7B5r%7D25r%5E2-x%5E2dx%5C%5C%5C%5C%3D%204%5Cleft%28%5Cint%20_%7B-5r%7D%5E%7B5r%7D25r%5E2dx-%5Cint%20_%7B-5r%7D%5E%7B5r%7Dx%5E2dx%5Cright%29%5C%5C%5C%5C%3D%204%5Cleft%28250r%5E3-%5Cfrac%7B250r%5E3%7D%7B3%7D%5Cright%29%5C%5C%5C%5C%3D%204%5Ccdot%20%5Cfrac%7B500r%5E3%7D%7B3%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B2000r%5E3%7D%7B3%7D)
As you can see, your exact solution would be, V = 2000r³/3. Hope that helps!
Answer:
Image point → (6, 1)
Step-by-step explanation:
Given point → (-3, 3)
Transformation to be done → 
Transformations to be done,
Step - (1). Translation of the given by 3 units left and 4 units down.
Step - (2). Followed by the rotation counterclockwise 180° about the origin.
Rule for step (1),
(x, y) → (x - 3, y - 4)
By this rule,
(-3, 3) → [(-3 - 3), (3 - 4)]
→ (-6, -1)
Rule for step -2,
(x, y) → (-x, -y)
(-6, -1) → (6, 1)
Therefore, following these two steps coordinates of the image point → (6, 1)