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4 years ago

The shapes of the horizontal cross sections of the cone below are all congruent

Mathematics

2 answers:

EastWind [94]4 years ago

7 0

Answer:

B. False

Step-by-step explanation:

We are given the statement,

'The shapes of the horizontal cross-sections of the cone are all congruent'.

Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.

Further, the radius of the circle vary depending on the position form where the cone is cut i.e.

If cut from the top, the circle is approximately equal to a point.

If cut from the middle, the radius of the circle is less than the radius of the cone.

If cut from the bottom, the radius of the circle is equal to the radius of the cone.

Now, 'two figures are congruent if they overlap each other'.

Since, the circles have different radius, they will not overlap each other.

Thus, all the cross-sections of the cone would not be congruent.

Hence, the given statement is false.

Semmy [17]4 years ago

4 0

Answer:

All Circles we get by horizontal cross section are not equal.

Step-by-step explanation:

Given: A cone.

To find: Shape of Horizontal cross section of cone are all congruent or not.

Two shapes are congruent if they are equal in measure or if they overlap each other completely.

Shape of horizontal cross section of cone is CIRCLE.

Two Circles are congruent if they have same radii.

Cross section 1: Horizontal cross section of cone near the base is a large circle almost equal to radius of cone.

Cross section 2: Horizontal cross section of cone near the top is a smallest circle whose radius is almost equal to 'zero'.

Cross section 3: Horizontal Cross section of cone in middle is a circle whose radius is between top's circle and base circle.

Its clear from above that these three cross sections are not congruent as circle don't have same radii.

Therefore, All Circles we get by horizontal cross section are not equal.

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A man bought a TV for £300. He had to pay a deposit of 15%. How much did he pay?

algol [13]

Most of the required information's are already given in the question.
Cost of the Television bought by the man = 300 pounds
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Then
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4 years ago

Given the three topics listed below, discuss a visual, verbal, and algebraic way of connecting the concepts:

AURORKA [14]

Answer:

Lots of connections!

Step-by-step explanation:

I attached some images to make it more clear.

Visual and verbal discussion:

A good starting point is the circle. One can think of a circle as the set of points that are equidistant to a certain point. In that sense, one can define a circle using the distance. At the same time, given a point $(x_{0},y_{0})$ in the plane, we can connect the point with the origin of the coordinates system forming a rectangle triangle! (See 2nd image)

Algebraic discussion:

1. The distance Formula:

Given two points in the plane $(x_{1},y_{1})$ and $(x_{2},y_{2})$ we can find the distance between both points with the distance formula:

$d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

2. Equation of a circle centered at a point $(x_{0},y_{0})$

$r = \sqrt{(x-x{_0}^2) + (y-y_{0})^2}$

3. The Pythagorean Theorem:

Given a triangle of sides $a;b$ and hypotenuse $h$ we have that

$h^2 = a^2 + b^2$

Only by writing this equations we can already see the similarities between all three.

In fact, the most amazing thing about all three is that they are equivalents. That is, we can obtain every single one of them as an immediate result of another.

For instance, as I said before, one can think of a circle as the set of points equidistant to a certain origin or center point. So we could use the distance formula for each point on the circumference and we would obtain always the same value $r$ hence obtaining the equation of a circle.

Also as we discussed, any point on the plane form a rectangle triangle with its coordinates and calculating the distance of said point to the origin of the coordinate system would give us no other thing than the hypotenuse of said triangle!

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3 years ago