Which correctly describes a cross section of the cube below? Check all that apply.

Mathematics

1 answer:

yarga [219]3 years ago

5 0

A cross section parallel to the base is a square measuring 4 cm by 4 cm 

Step-by-step explanation:

Here we have to select the correct statement regarding a cross section of the cube :

A cross section parallel to the base is a square measuring 4 cm by 4 cm :

Since , every side of a cube is same . Any cross section of a cube must be parallel to a square base . Hence, correct statement .

A cross section parallel to the base is a rectangle measuring 4 cm by greater than 4 cm :

Since , every side of a cube is same . Any cross section of a cube must be parallel to a square base . Here, base is rectangle . We don't have a rectangle base in cube . Not correct statement.

A cross section perpendicular to the base through the midpoints of opposite sides is a rectangle measuring 2 cm by 4 cm:

Since , every side of a cube is same . Any cross section of a cube must be parallel to a square base . Here, base should be square not rectangle . So , Not correct statement.

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3. The standard equation of a circle (not centered at the origin) with radius r can be derived from its locus definition: The se

Darya [45]

Answer:

The equation for circle of radius $r$ centered at the point $C: (h,k)$ is:

$(x-h)^2+(y-k)^2=r^2$

Step-by-step explanation:

To derive this equation, we need the formula for the distance between two points in the plane. If the point is given by its cartesian coordinates, we can use the Pythagorean theorem to find what the distance between the points is.

Lets say we have two points, one given by cartesian coordinates P:(x,y) and the other given by cartesian coordiantes C:(h,k)

(see diagram)

We can see that

$\Delta x = x-h\\\Delta y = y-k$

and by the pythagorean theorem we have:

$\Delta s ^2 = \Delta x^2 + \Delta y^2$

Where $\Delta s$ is the distance between the points

Now, combining the last three equations we find:

$\Delta s ^2 = (x-h)^2 + (y-k)^2$

We know that the definition of a circle is the locus of points that are at a distance r from a point called the center of the circle. if we take C:(h,k) as the center of the circle, and $\Delta s =r$ , the last equation becomes: