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erik [133]
3 years ago
14

Find the slope using the formula. (3,-2) and (3, 6)

Mathematics
1 answer:
dangina [55]3 years ago
6 0

Answer:

m = undef

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (3, -2)

Point (3, 6)

<u>Step 2: Find slope </u><em><u>m</u></em>

  1. Substitute:                    m=\frac{6+2}{3-3}
  2. Add/Subtract:               m=\frac{8}{0}
  3. Divide:                          m = undef

When we divide anything by zero, we will get undefined. Therefore, this would be a vertical line.

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Answer:

A. -4

Step-by-step explanation:

Slope is rise over run, or y2-y1 / x2-x1.

\frac{y2-y1}{x2-x1} = \frac{-4-8}{2--1} =\frac{-12}{3} = -4

<u>The slope is A. -4.</u>

Let's see--does that make sense? A slope of four would be pretty steep, and that matches the graph. It also should be negative because the line goes down and to the right, not up and to the right, so -4 makes sense!

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Step-by-step explanation:

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A cone has radius 9 and a height 12. A frustum of this cone has height 4.
Anettt [7]

Answer:

Part A)

The lower base has a radius of 9 units, and the upper base has a radius of 6 units.

Part B)

5 units.

Part C)

75π or about 235.62 square units.

Step-by-step explanation:

Please refer to the figure below.

The cone has a radius of 9 units and a total height of 12 units.

A frustum of the cone has a height of 4 units.

Part A)

The lower radius of the frustum will simply be 9 units.

For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:

\displaystyle \frac{12}{8}=\frac{9}{x}

Solve for <em>x.</em> Simplify:

\displaystyle \frac{3}{2}=\frac{9}{x}

Cross-multiply:

18=3x\Rightarrow x=6

The upper base has a radius of 6 units.

Part B)

We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:

SH^2=12^2+9^2

Simplify:

SH^2=225\Rightarrow SH=15\text{ units}

Now, find the slant height of the upper cone:

(SH_\text{cone})^2=8^2+6^2=100

So:

SH_\text{cone}=10

Then the slant height of the frustum will be the cone subtracted from the total. Thus:

SH_{\text{frustum}}=15-10=5\text{ units}

Part C)

We can first find the lateral area of the entire cone. The lateral area is given by:

LA=\pi r\ell

The lateral area of the entire cone will be:

LA=\pi (9)(15)=135\pi

The lateral area of the upper cone will be:

LA_\text{cone}=\pi(6)(10)=60\pi

Then the lateral area of the frustum is:

LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2

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