Answer:
381.18 cubic units
Step-by-step explanation:
Graph the region:
desmos.com/calculator/iwvreqjz2m
The region is a trapezoid. When we rotate it about x = 1, we get a hollow cylinder shape. We can either use washer method or shell method to find the volume.
If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part. If we use shell method, we only need one integral. So let's use shell method.
Cut a thin, vertical slice of the region. The width of this slice is dx. The height of the slice is y₂ − y₁ = x − 0 = x. The radius of the shell is x − 1.
The volume of the shell is:
dV = 2π (x − 1) (x) dx
dV = 2π (x² − x) dx
The total volume is the sum of all the shells from x=5 to x=7.
V = ∫ dV
V = ∫₅⁷ 2π (x² − x) dx
V = 2π ∫₅⁷ (x² − x) dx
V = 2π (⅓ x³ − ½ x² + C) |₅⁷
V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]
V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]
V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]
V = 2π [⅓ (218) + ½ (-24)]
V = 2π (72⅔ − 12)
V = 121⅓ π
V ≈ 381.18
The volume is approximately 381.18 cubic units.
Answer:
5 to the 15th power.
Step-by-step explanation:
PEMDAS requires us to do parenthesis, then exponents, and then division. Let's do 5³. 5x5x5 is equal to 125. Now, we find 125 to the ninth power. According to my calculations, 125 to the ninth power is equal to 7,450,580,596,923,828,125. Now, we find 5 to the twelfth power, which, according to my calculations, is 244,140,625. Now, we solve. According to my calculations, 7,450,580,596,923,828,125/244,140,625 is equal to 30,517,578,125. 30,517,578,125 is equivalent to 5 to the 15th power. That means that the second option is correct. I hope this helps!
Answer:
The distance is 17
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
Answer:
The file includes the input of your equation, comment if the equation you input is a mistake.
