How many solutions does this system have? X+ 5y = 0 20y = -4x

Mathematics

1 answer:

AysviL [449]4 years ago

4 0

2 have solutionsof each way if

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PLEASE HELP WILL MARK BRAINLIEST

quester [9]

From the side, area is that of a rectangle added to a trapezoid or triangle, depending on how you slice it
.. rectangle + trapezoid = (4 ft)*(24 ft) +(4 ft +8 ft)*(16 ft)/2 = 192 ft^2
.. rectangle + triangle = (4 ft)*(40 ft) +(1/2)*(4 ft)*(16 ft) = 192 ft^2

The side area is multiplied by the width to find the volume.
.. V = (192 ft^2)*(20 ft) = 3840 ft^3 . . . . . . maximum water volume

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That's a pint or so more than 28,725 gallons.

6 0

4 years ago

Use calculus to find the volume of the following solid S:

Troyanec [42]

S casts a "shadow" on the x-y plane given by the set

$S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}$

Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².

The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is

$\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx$