Each diagram is made of smaller, identical pieces. Tell how many pieces you would say to model the given percent.

Mathematics

1 answer:

Natasha2012 [34]2 years ago

7 0

<h3>Resolution 12 Shaded in.</h3>

Step-by-step explanation: Imagine a triangle with 16 spots and you need to get 75% of it 16 in all is 100 take away 4 spots you get 12 and 12 from 16 is 75 if you do the math

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Carmen measured a house and made a scale drawing. The scale of the drawing was 9 millimeters = 1 meter. What is the drawing's sc

malfutka [58]

When you write a scale factor, the units have to be the same. In this case, 9mm on the drawing represents 1 meter on the house. Change 1 meter to millimeters (1m = 1000mm).

9 mm on the drawing represents 1000 mm on the house.

The scale factor is 9 to 1000, or, as a fraction, 9/1000.

5 0

2 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

miss Akunina [59]

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)]