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3 years ago

A 450m long field is drawn to a scale 1cm to 90cm.find the lenth of drawing

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

6 0

Answer:

5 cm

Step-by-step explanation:

The length of the drawing will be 450 / 90 = 5 cm.

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A) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given cur

Leno4ka [110]

(a) See the attached sketch. Each shell will have a radius y chosen from the interval [2, 4], a height of x = 2/y, and thickness ∆y. For infinitely many shells, we have ∆y converging to 0, and each super-thin shell contributes an infinitesimal volume of

2π (radius)² (height) = 4πy

Then the volume of the solid is obtained by integrating over [2, 4]:

$\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}$

(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - x (this is the distance between a given x value in the orange shaded region to the axis of revolution) and a height of 8 - x ³ (and this is the distance between the line y = 8 and the curve y = x ³). Then each shell has a volume of

2π (9 - x)² (8 - x ³) = 2π (648 - 144x + 8x ² - 81x ³ + 18x ⁴ - x ⁵)

so that the overall volume of the solid would be

$\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}$

I leave the details of integrating to you.

3 0

3 years ago

A pyramid has a square base with sides of length s. The height of the pyramid is equal to - of the length of a side on the base.

Vera_Pavlovna [14]

<h3>Question:</h3>

A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula represents the volume of the pyramid?

<h3>Answer:</h3>

The formula represents the volume of the pyramid is:

$V=\frac{1}{6}s^3$

<h3>Solution:</h3>

The volume of square pyramid is given by formula:

$V = \frac{1}{3} a^2h$

Where, "h" is the height of pyramid

"a" is the length of side of base

Here given that, pyramid has a square base with sides of length s

Therefore,

a = s

The height of the pyramid is equal to 1/2 of the length of a side on the base

$h = \frac{1}{2} \times s\\\\h = \frac{s}{2}$

Thus the volume of pyramid becomes:

$V = \frac{1}{3} \times s^2 \times \frac{s}{2}\\\\V = \frac{s^3}{6}$

$\boxed{V=\frac{1}{6}s^3}$

Thus the formula represents the volume of the pyramid is $\frac{s^3}{6}$

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4 years ago

How can we get System B from System A? And are they equivalent?

Aliun [14]

What? Where’s the question 11

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=P%3D%5Cfrac%7B11%7D%7B40%7D%2B%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B1%7D%7B20%7D" id="TexFormula1" t

yKpoI14uk [10]

Answer

p = 19/40

Please give brainliest

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3 years ago

A store is located 10 miles from my house, it takes the average female 20 minutes to talk from the store back to her house. Why

grin007 [14]

Answer:

Because she may have been abducted by aliens and there time way is way slower than ours so 20 mins for them is like 15 years for ua, ao you should have her back in 3 years. Lemme get brainliest too

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A 450m long field is drawn to a scale 1cm to 90cm.find the lenth of drawing​

A 450m long field is drawn to a scale 1cm to 90cm.find the lenth of drawing