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3 years ago

Sketch the graph of the function f(x) = x + |x|.

Mathematics

1 answer:

masha68 [24]3 years ago

5 0

Answer:

The absolute value can be graphed using the points around the vertex (0, 0), (-2, 0), (-1, 0), (1, 2), (2, 4).

Step-by-step explanation:

To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0. In this case, x = 0.

Replace the variable x with 0 in the expression.

y = (0) + |0|

PS: The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.

y = 0 + 0

y = 0

The absolute value vertex is (0, 0).

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation: {x|x ∈R}

For each x value, there is one y value. Select few x from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.

Substitute the x value -2 into f(x) = x + |x|. In this case, the point is (-2, 0).

y = 0

Substitute the x value 1 into f(x) = x + |x|. In this case, the point is (1, 2).

y = 2

Substitute the x value 2 into f(x) = x + |x|. In this case, the point is (2, 4).

y = 4

You can find the graph in the attachment.

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The volume of a right cylinder is V = πr2h. If we have an oblique cylinder, like in the figure, what is the volume of a cross-se

olchik [2.2K]

Since you did not attach any picture we cannot say for sure what is the correct answer, but we can discuss the options in order to find the most probable correct answer.

First of all, according to the Cavalieri's principle, an oblique cylinder has the same volume as a right cylinder with the same base surface area and same height.
A cross-section of an oblique cylinder will be a small right cylinder with the same base surface area and a height as small as possible.

I guess the oblique cylinder has height h and it is divided into many (probably 10) cross-sections.

Option A: πr2h
This is exactly the volume of the right cylinder, therefore, unless you are given a cross-section of height h (which would be too easy), this won't be the correct answer.

Option B: 4πr2h
This is 4 times the right cylinder. Again, here the height of the cross-section should be 4h, but it doesn't sound like a possible data (too easy again).

Option C: 1 10 πr2h
Here comes a n issue with the notation: I think the right number you meant to write is (1/10)·πr2h and not 110·πr2h.
If I am right, this means that your oblique cylinder of height h is divided into 10 cross-sections, and therefore the volume of each of these cross-sections will be a tenth of the volume of the oblique cylinder, which means 1/10·πr2h.

Option D: 1 2 πr2h
Here, we have the same notation issue as before. I think you meant (1/2)·πr2h.
Here, your oblique cylinder height h should be divided into only 2 cross-sections. Now, we said the cross-section's height should be the smallest as possible, so an oblique cylinder divided only into two pieces doesn't sound good.

Therefore, the most probable correct answer will be C) (1/10)·πr2h

8 0

3 years ago

Read 2 more answers

10. Solve using substitution. x - 2y = 3 3x + y = -5

nasty-shy [4]

Move all terms that don't contain x to the right side and solve.

x=−5/3−y/3

plz mark me as brainliest :)

5 0

3 years ago

Imaginá que tenés 125 dados cúbicos del mismo tamaño ¿Cuantos dados de altura tiene el cubo de mayor tamaño que podés armar apil

kumpel [21]

Answer:

(i) Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

Step-by-step explanation:

(i) Sabemos por la Geometría Euclídea del Espacio que un cubo es un sólido regular con 6 caras cuadradas y longitudes iguales. Cada dado tiene un volumen de 1 dado cúbico y 125 dados dan un volumen total de 125 dados cúbicos.

El volumen de un cubo está dado por la siguiente fórmula:

$V = L^{3}$

Donde:

$L$ - Longitud de la arista, medida en dados.

$V$ - Volumen del cubo, medido en dados cúbicos.

Ahora, necesitamos despejar la longitud de la arista para calcular la altura máxima posible:

$L = \sqrt[3]{V}$

Dado que $V = 125\,dados^{3}$ , encontramos que la altura del cubo de mayor tamaño sería:

$L =\sqrt[3]{125\,dados^{3}}$

$L = 5\,dados$

Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) El área cuadrada formada por cubos está determinada por la siguiente fórmula:

$A = L^{2}$

Donde:

$L$ - Longitud de arista, medida en dados.

$A$ - Área, medida en dados cuadrados.

Puesto que la longitud de arista se basa en un conjunto discreto, esto es, el número de dados disponibles, debemos encontrar el valor máximo de $L$ tal que no supere 125 y de un área entera. Es decir:

$L \leq 125\,dados$

Si cada cubo tiene un área de 1 dado cuadrado, entonces un cuadrado conformado por 125 dados tiene un área total de 125 dados cuadrados. Entonces:

$L^{2}< 125\,dados^{2}$

Esto nos lleva a decir que:

$L < 11.180\,dados$

Entonces, la longitud máxima del cuadrado con la mayor cantidad de cubos posible es de 11 dados. El número total requerido de cubos es el cuadrado de esa cifra, es decir:

$n = (11\,dados)^{2}$