Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A rectangle is shown on the coordinate grid with vertices
(-4,0),(0,0),(0,2), and
(-4,2). A solid is formed by rotating the rectangle about the
x-axis.
Select all true statements about the revolved solid.
The revolved solid is a cylinder with a base radius of 2 units.
The revolved solid is a cylinder with a base radius of 4 units.
The revolved solid is a cylinder with a height of 2 units.
The revolved solid is a cylinder with a height of 4 units.
The revolved solid is a rectangular prism with a base length of 2 units.
The revolved solid is a rectangular prism with a base length of 4 units.

A rectangle is shown on the coordinate grid with vertices $(-4,0),(0,0),(0,2)$ , and $(-4,2)$ . A solid is formed by rotating the rectangle about the $x$ -axis. $\newline$ Select all true statements about the revolved solid. $\newline$ The revolved solid is a cylinder with a base radius of $2$ units. $\newline$ The revolved solid is a cylinder with a base radius of $4$ units. $\newline$ The revolved solid is a cylinder with a height of $2$ units. $\newline$ The revolved solid is a cylinder with a height of $4$ units. $\newline$ The revolved solid is a rectangular prism with a base length of $2$ units. $\newline$ The revolved solid is a rectangular prism with a base length of $4$ units.

View step-by-step help

View step-by-step help

Write equations of hyperbolas in standard form using properties

Full solution

Q. A rectangle is shown on the coordinate grid with vertices

(-4,0),(0,0),(0,2)

, and

(-4,2)

. A solid is formed by rotating the rectangle about the

x

-axis.

\newline

Select all true statements about the revolved solid.

\newline

The revolved solid is a cylinder with a base radius of

2

units.

\newline

The revolved solid is a cylinder with a base radius of

4

units.

\newline

The revolved solid is a cylinder with a height of

2

units.

\newline

The revolved solid is a cylinder with a height of

4

units.

\newline

The revolved solid is a rectangular prism with a base length of

2

units.

\newline

The revolved solid is a rectangular prism with a base length of

4

units.

Identify Dimensions: Identify the dimensions of the rectangle based on the given vertices. $\newline$ The vertices of the rectangle are $(-4,0)$ , $(0,0)$ , $(0,2)$ , and $(-4,2)$ . The length of the rectangle can be found by the distance between $(-4,0)$ and $(0,0)$ , which is $4$ units. The height of the rectangle can be found by the distance between $(0,0)$ and $(0,2)$ , which is $2$ units.
Characteristics of Solid: Determine the characteristics of the revolved solid. $\newline$ When the rectangle is rotated about the $x$ -axis, the height of the rectangle becomes the diameter of the base of the cylinder, and the length of the rectangle becomes the height of the cylinder.
Analysis: Base Radius: Analyze the first statement: ＂The revolved solid is a cylinder with a base radius of $2$ units.＂ $\newline$ Since the height of the rectangle is $2$ units, and this becomes the diameter of the base of the cylinder upon rotation, the radius of the base is half of the diameter, which is $1$ unit. Therefore, this statement is false.
Analysis: Base Radius: Analyze the second statement: ＂The revolved solid is a cylinder with a base radius of $4$ units.＂ $\newline$ This statement is false because the radius of the base of the cylinder is half of the height of the rectangle, which is $1$ unit, not $4$ units.
Analysis: Height: Analyze the third statement: ＂The revolved solid is a cylinder with a height of $2$ units.＂ $\newline$ This statement is false because the height of the cylinder is the length of the rectangle, which is $4$ units, not $2$ units.
Analysis: Height: Analyze the fourth statement: ＂The revolved solid is a cylinder with a height of $4$ units.＂ $\newline$ This statement is true because the height of the cylinder is the length of the rectangle, which is $4$ units.
Analysis: Cylinder vs Prism: Analyze the fifth statement: ＂The revolved solid is a rectangular prism with a base length of $2$ units.＂ $\newline$ This statement is false because the revolved solid is not a rectangular prism; it is a cylinder.
Analysis: Cylinder vs Prism: Analyze the sixth statement: ＂The revolved solid is a rectangular prism with a base length of $4$ units.＂ $\newline$ This statement is also false because the revolved solid is not a rectangular prism; it is a cylinder.

More problems from Write equations of hyperbolas in standard form using properties

Question

Write the equation in standard form for the hyperbola

x^2 - y^2 = 64

\newline

Posted 2 months ago

Question

What is the center of the hyperbola

4x^2 - y^2 - 100 = 0

\newline

(\_,\_)

Posted 2 months ago

Question

What is the center of the hyperbola

(\frac{x^2}{144}) - (\frac{y^2}{81}) = 1

\newline

Posted 2 months ago

Question

What is the length of the transverse axis of the hyperbola

(\frac{x^2}{64}) - (\frac{y^2}{36}) = 1

\newline

Posted 2 months ago

Question

Write the equation in standard form for the hyperbola

y^2 - x^2 = 81

\newline

Posted 3 months ago

Question

Write the equation in standard form for the hyperbola

x^2 - 4y^2 = 100

\newline

Posted 3 months ago

Question

Write the equation in standard form for the hyperbola

9y^2 - x^2 = 36

\newline

Posted 3 months ago

Question

Write the equation in standard form for the hyperbola

4x^2 - y^2 = 16

\newline

Posted 3 months ago

Question

Write the equation in standard form for the hyperbola

y^2 - 9x^2 = 144

\newline

Posted 3 months ago

Question

y=f(x+3)

is shown. For which value of

x

, rounded to the nearest whole number, must

f(x)=0

Posted 25 days ago