(Простите, пожалуйста, мой английский. Русский не мой родной язык. Надеюсь, у вас есть способ перевести это решение. Если нет, возможно, прилагаемое изображение объяснит достаточно.)
Use the shell method. Each shell has a height of 3 - 3/4 <em>y</em> ², radius <em>y</em>, and thickness ∆<em>y</em>, thus contributing an area of 2<em>π</em> <em>y</em> (3 - 3/4 <em>y</em> ²). The total volume of the solid is going to be the sum of infinitely many such shells with 0 ≤ <em>y</em> ≤ 2, thus given by the integral

Or use the disk method. (In the attachment, assume the height is very small.) Each disk has a radius of √(4/3 <em>x</em>), thus contributing an area of <em>π</em> (√(4/3 <em>x</em>))² = 4<em>π</em>/3 <em>x</em>. The total volume of the solid is the sum of infinitely many such disks with 0 ≤ <em>x</em> ≤ 3, or by the integral

Using either method, the volume is 6<em>π</em> ≈ 18,85. I do not know why your textbook gives a solution of 90,43. Perhaps I've misunderstood what it is you're supposed to calculate? On the other hand, textbooks are known to have typographical errors from time to time...
Answer:
z = 3
Step-by-step explanation:
Similar polygons have the ratio of their corresponding sides equal to each other. There:
9/z = 6/2
Cross multiply
z*6 = 9*2
6z = 18
z = 18/6
z = 3
Answer:
15.5
Step-by-step explanation:
The equation to find area is Length × Width= Area
we have the area and the length, 12.5 × width= 293.75
to find the width, you will have to reverse engineer and divide the area by the length instead.
193.75 ÷ 12.5 =15.5
just to double check, 15.5 × 12.5 = 193.75
the width is 15.5
Answer:
105 11/12
Step-by-step explanation:
With mixed numbers you can also write them as functions so 5 11/12 could also be written as 5+11/12.
Once you have rewritten the mixed number it's simply a matter of addition: 100+5+11/12
Answer:
The height of the trough is about 1.5 ft
Step-by-step explanation:
If each cubic foot of water contains about 7.5 gallons.
Then; 315 gallons is about 
Let h be the height of the trough, then

This implies that;

Divide both sides by 28 to get:


The height of the trough is about 1.5 ft