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a_sh-v [17]
3 years ago
12

What angle relationships are created when parallel lines are intersected by a transversal?

Mathematics
1 answer:
natka813 [3]3 years ago
7 0

Answered by Mimiwhatsup: If two parallel lines are cut by a third line, the third line is called the transversal.

Relationships:

(1) Corresponding angles

(2) Vertically Opposite angles

(3) Alternate interior angles

(4) Alternate exterior angles

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Asap plz<br> What is the reciprocal of 2 3/8? <br> 19/8 <br> 16/3 <br> 8/19 <br> 3/16
Zepler [3.9K]
I think it is 19/8 or 8/19 I am not sure
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2 years ago
The ratio of Sam's money to Buffy's is 1.2. If Sam has $3, how much money does Buffy have? Show your work please
Bad White [126]
If the ratio is 1:2,

sam has three dollars.
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2 years ago
What are the values?
zavuch27 [327]

The average of a set of numbers

Step-by-step explanation:

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3 years ago
Read 2 more answers
Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
What triangle pairs can be mapped to each other using a single tranlation
shepuryov [24]

Answer: I think Figure 4 is the correct one

Step-by-step explanation:

It is not possible to map the triangle MNP and CDE together using just a single translation in Figure 3. With Figure 4, we can use a translation to map the triangle MNP and the triangle CDE. Accordingly, in the diagram, the triangle MNP and the triangle CDE can be translated to each other.

8 0
2 years ago
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