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Bond [772]
3 years ago
13

prove that if two circles are tangent externally then the common internal tangent bisects a common external tangent.

Mathematics
1 answer:
Scilla [17]3 years ago
5 0

Explanation:

Consider the attached diagram.

Circles A and B have mutual tangents CF and DE that intersect at point F.

We know that the two tangents to a circle from an external point are congruent, so ...

  FE≅ FC

  FD ≅ FC

By the transitive property of congruence, both segments congruent to FC are congruent to each other:

  FD ≅ FE

Therefore, CF is a bisector of DE.

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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round
Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying  \frac{1}{3} with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone :  V=\pi r^{2} \frac{h}{3} = 3.14 \times 9^{2} \times \frac{14}{3} = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying  \frac{4}{3} with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere =  V=\frac{4}{3} \pi r^{3} =  \frac{4}{3} \times 3.14 \times 9^{3} = 3,052.08 cubic inches.

The volume of the half-sphere =  \frac{3,052.08}{2} = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

5 0
3 years ago
Compare the numbers. Use &gt;, =, or &lt;
lesya692 [45]

Answer:

746.982 > 746.963

68.098 < 68.987

589.987 = 589.987

Step-by-step explanation:

4 0
3 years ago
When multiplying two negative numbers, what kind of number does one always get for an answer?
harina [27]

Answer:

a positive number

Step-by-step explanation:

-(-) = +

for example, -1 * -1 = 1

7 0
3 years ago
Read 2 more answers
Pls help extra points and mark brainlist
Stolb23 [73]

Answer:

the answers are a and d

Step-by-step explanation:

x+x+x=3x and you can't add a constant (2) to a variable(3x) so it would just be 3x+2

6 0
3 years ago
q(x)= x 2 −6x+9 x 2 −8x+15 ​ q, left parenthesis, x, right parenthesis, equals, start fraction, x, squared, minus, 8, x, plus, 1
AURORKA [14]

According to the theory of <em>rational</em> functions, there are no <em>vertical</em> asymptotes at the <em>rational</em> function evaluated at x = 3.

<h3>What is the behavior of a functions close to one its vertical asymptotes?</h3>

Herein we know that the <em>rational</em> function is q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15), there are <em>vertical</em> asymptotes for values of x such that the denominator becomes zero. First, we factor both numerator and denominator of the equation to see <em>evitable</em> and <em>non-evitable</em> discontinuities:

q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15)

q(x) = [(x - 3)²] / [(x - 3) · (x - 5)]

q(x) = (x - 3) / (x - 5)

There are one <em>evitable</em> discontinuity and one <em>non-evitable</em> discontinuity. According to the theory of <em>rational</em> functions, there are no <em>vertical</em> asymptotes at the <em>rational</em> function evaluated at x = 3.

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

8 0
1 year ago
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