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3 years ago

James used base-ten to show that 40 is one-tenth of 400. Explain your reasoning

Mathematics

1 answer:

Elanso [62]3 years ago

3 0

Cause 400 divided by 10 is 40

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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

How do I work this out?

pentagon [3]

1. 1/4(x+3)=12=X+3-12*4/4=X-45/4. Then, x-45/4=0. So, 1. X=45. 2. x+4/3=12=3x-32/3*3=0*3. 3x-32=0. You add 32 to each sides. 3x=32. x=32/3. Therefore, 1. x=45 and 2. x=32/3

8 0

3 years ago

SI TENGO 5 L DE AGUA A 5,7O Y 500ML DE ACEITE A 1,25 ¿CUANTO VALE EL LITRO DE ACEITE Y EL LITRO DE AGUA? REDONDEA A LAS CENTESIM

LuckyWell [14K]

Answer:

use a translation

Step-by-step explanation:

sorry

7 0

3 years ago

Can i get some help. hate homework

omeli [17]

If a sequence is defined recursively by f(0)=2and f(n+1)=-2f(n)+3 for n> 0 then f(2) is equal to what

5 0

3 years ago

A bag has 2 blue 3red and 5 yellow tilas. what is the probability of not picking a red tile

MissTica

Answer:

0.2

Step-by-step explanation:

We have,

Number of blue tiles = 2

Number of red tiles = 3

Number of yellow tiles = 5

Total number of tiles = 2 + 3 + 5 is 10

Now, the probability of picking a blue tile is:

The number of blue tiles divided by the total number of tiles:

2 ÷ 10 = 0.2

4 0

2 years ago

Read 2 more answers