Answer:
36 feet squared
Step-by-step explanation:
Finding the perimeter of an object is adding all of the sides together. If the width of the rug is 6 feet then we know that there are two sides that length. Add those together.
6 feet + 6 feet = 12 feet
You would subtract the number you get from the perimeter.
24 feet - 12 feet = 12 feet
And then divide the number by the number of sides left, 2, to get each of their lengths.
12 feet / 2 feet = 6 feet
To find the area of a rectangle you multiply length times width, which in this case both are 6 feets.
6 feet x 6 feet = 36 feet squared
Answer:
A.
x + 2 + 12
Step-by-step explanation:
Thomas (t) = Andrew (x) * 2 + 12
Answer:
A
Step-by-step explanation:
The two angles in the triangle in the question are 58 degrees and 54 degrees.
Three angles in a triangle add up to 180 degrees
58 + 54 + x = 180
112 + x = 180
subtract 112 on both sides
x = 180 - 112 = 68 degrees
Only option A has a triangle that has the same angles, thus triangles are similar.
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Using the shell method, the volume is
![\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cpi%20%5Cint_0%5E1%20%282-x%29%20%5Ccdot%208x%5E3%20%5C%2C%20dx%20%3D%2016%5Cpi%20%5Cint_0%5E1%20%282x%5E3%20-%20x%5E4%29%20%5C%2C%20dx)
Each cylindrical shell has radius
(the horizontal distance from the axis of revolution to the curve
); has height
(the vertical distance between a point on the
-axis in
and the curve
).
Compute the integral.
![\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}](https://tex.z-dn.net/?f=%5Cdisplaystyle%2016%20%5Cpi%20%5Cint_0%5E1%20%282x%5E3%20-%20x%5E4%29%20%5C%2C%20dx%20%3D%2016%5Cpi%20%5Cleft%28%5Cfrac%7Bx%5E4%7D2%20-%20%5Cfrac%7Bx%5E5%7D5%5Cright%29%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%3D1%7D%20%5C%5C%5C%5C%20~~~~~~~~~~~~~~~~~~~~~~~~~~~~%20%3D%2016%5Cpi%20%5Cleft%28%5Cfrac12%20-%20%5Cfrac15%5Cright%29%20%5C%5C%5C%5C%20~~~~~~~~~~~~~~~~~~~~~~~~~~~~%20%3D%20%5Cfrac%7B24%7D5%5Cpi%20%3D%20%5Cboxed%7B4.8%5Cpi%7D)