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2 years ago

Find the volume of the prism.

Mathematics

1 answer:

Gemiola [76]2 years ago

4 0

Answer:

Step-by-step explanation:

The volume of the triangular prism, this is an isosceles triangular prism is

V=1/2 * a*b*h

V=1/2 x10x8x14=560 cm^3

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A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

Steps for graphing -x^2-4x-3

sdas [7]

Answer:

Step-by-step explanation:

There are several ways to do this. The first, which I personally think is the quickest way without having to do too much math or rearranging the equation is to simply pick random points for x and solve for y.

For instance, you might try -2 for x.

- ( - 2)^2 - 4 ( - 2) - 3

= - 4 + 8 - 3

= 1

So one of your points would be (-2, 1)

Then you might choose, say, -3 for x. And after that, -1 for x. If you want to graph even more points after those (the more points, the more accurate your graph), choose -4 and 0 for x. Simply put it into the equation and find y. Then graph.

3 0

3 years ago

Which system of linear inequalities is graphed?

SIZIF [17.4K]

Answer:

A) {x < −2

{y ≤ −x − 2

Step-by-step explanation:

The first step is to treat these inequalities as Slope-Intercept equations, then graph them according to what you know about the rate of changes [slopes] of the lines. Then insert the inequality symbols later and figure out which line they get, based on their symbols:

Dashed Line → >, <

Solid Line → ≥, ≤

$x < -2$ is the vertical line with a less than sign, so it gets the dashed line, whereas the other line has a less than or equal to sign, so this line gets the solid line.