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3 years ago

Describe the shape resulting from a vertical, horizontal, and angled cross section for each figure

Mathematics

1 answer:

Stolb23 [73]3 years ago

3 0

Problem 22

<h3>Answers:</h3>

vertical: rectangle
horizontal: rectangle
angled: parallelogram

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Explanation:

The vertical and horizontal cross sections are fairly straight forward. They are simply mirror images of the outward showing faces. The angled cross sections are a bit more complicated and there's a lengthy proof involved, but long story short, the angled cutting plane divides the 3D solid such that we have 2 sets of lines that have the same slope (if we consider a 2D view), which leads to 2 sets of parallel sides.

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Problem 23

<h3>Answers:</h3>

vertical: either a triangle or quadrilateral
horizontal: triangle
angled: either a triangle or quadrilateral

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Explanation:

The horizontal cross section is always a triangle because the bottom base face is a triangle. The other two types of cross sections are either triangles or quadrilaterals depending on where the cutting plane is situated. For vertical cross sections that go through the apex point, we get a triangle. For vertical cross sections that do not go through the apex, then we get a quadrilateral. Sometimes a trapezoid is possible here, but not always. It's better to just consider it a quadrilateral to be the most general. A similar situation happens with the angled cuts as well.

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Problem 24

<h3>Answers:</h3>

vertical: triangle, but only if plane is crossing through apex
horizontal: circle
angled: ellipse or parabola

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Explanation:

Imagine you shined a flashlight onto the cone such that the flashlight is perfectly level and flat. It would cast a shadow that is a triangle. This is one way to think of a cross section. If you vertically slice. The horizontal cross sections are always circles due to the circular base of the cone. The angled cross sections are either ellipses or parabolas. For more information, look in your math textbook about conic sections (just ignore the second cone however).

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Problem 25

<h3>Answers:</h3>

vertical: rectangle
horizontal: circle
angled: ellipse

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Explanation:

The horizontal cross sections are circles for similar reasoning as the cone horizontal cross section. However, this time the vertical cross sections are rectangles. The widest possible rectangle is the result of the vertical cutting plane passing through the center of the circular base. Angled cross sections are ellipses. Though some portions of the ellipse may be cut off depending on what the actual angle is.

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Triangle Slmliarity Assignment 2

USPshnik [31]

Answer: SAS

Step-by-step explanation:

There is an angle B or D and the sides being the 26, 21, and 32! (Sorry if I get it wrong)

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2 years ago

What is the slope-intercept form of the equation for the line?

mart [117]

Answer:

(-4, 2) and (4, -5)

m = (-5 - 2)/(4 - (-4)) = -7/8

y = -7/8 * (x - (-4)) + 2

y = -7/8 * (x + 4) + 2

y = -7/8 * x - 3/2

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2 years ago

Find the length and perimeter of a rectangle if its width is 19 m and its area is 475 m?.

Allisa [31]

The length of the rectangle is: 25 m

The perimeter of the rectangle is: 88 m

<h3>What is the Area and Perimeter of a Rectangle?</h3>

Area of a rectangle = (length)(width).

Perimeter of a rectangle = 2(length + width).

Give the following:

Width of rectangle = 19 m

Area of rectangle = 475 m²

Find the Length using the area formula:

475 = (length)(19)

475/19 = length

Length of the rectangle = 25 m

Find the perimeter of the rectangle

Perimeter of the rectangle = 2(25 + 19)

Perimeter of the rectangle = 2(44)

Perimeter of the rectangle = 88 m

Thus, the length of the rectangle is: 25 m

The perimeter of the rectangle is: 88 m

Learn more about the area and perimeter of rectangle on:

brainly.com/question/24571594

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1 year ago

If possible help me in this. I need to find the two odd numbers...

Lelechka [254]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

<h3>Answer: x+2</h3>

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

<h3>Answer: x^2 + (x+2)^2 = 394</h3>

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\$

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

<h3>Answer: Either 13, 15 or -15, -13</h3>

4 0

2 years ago

What composition forms the equation p(x) when given the functions for h(x), f(x), k(x), and g(x)? PLEASE HELP!!!!! thank you!!!!

Flura [38]

Answer: Choice B. k(h(g(f(x))))

For choice B, the functions are k, h, g, f going from left to right.

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Explanation:

We have 4x involved, so we'll need f(x)

This 4x term is inside a cubic, so we'll need g(x) as well.

So far we have

g(x) = x^3

g( f(x) ) = ( f(x) )^3

g( f(x) ) = ( 4x )^3

Then note how we are dividing that result by 2. That's the same as applying the h(x) function

$h(x) = \frac{x}{2}\\\\h(g(f(x))) = \frac{g(f(x))}{2}\\\\h(g(f(x))) = \frac{(4x)^3}{2}\\\\$

And finally, we subtract 1 from this, but that's the same as using k(x)

$k(x) = x-1\\\\k(h(g(f(x)))) = h(g(f(x)))-1\\\\k(h(g(f(x)))) = \frac{(4x)^3}{2}-1\\\\$

This leads to the answer choice B.

To be honest, this notation is a mess considering how many function compositions are going on. It's very easy to get lost. I recommend carefully stepping through the problem and building it up in the way I've done above, or in a similar fashion. The idea is to start from the inside and work your way out. Keep in mind that PEMDAS plays a role.

6 0

2 years ago