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yuradex [85]
4 years ago
13

Question

Mathematics
1 answer:
Ivan4 years ago
8 0

The arc length of AB = 8.37 meters.

Solution:

Given data:

Degree of AB (θ) = 60°

Radius of the circle = 8 m

Let us find the arc length of AB.

Arc length formula:

$\text{Arc length}=2 \pi r\left(\frac{\theta}{360^\circ}\right)

                 $=2 \times 3.14 \times 8 \left(\frac{60^\circ}{360^\circ}\right)

                 $=2 \times 3.14 \times 8 \left(\frac{1}{6}\right)

                 = 8.37 m

The arc length of AB = 8.37 meters.

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Consider the function g defined by g(x) = x(10 – Ax), A > 0. voer g in Without doing any iterations, determine the non-zero f
notka56 [123]

Answer:

The only non-zero fixed point is:  x = 9/A.

The Step-by-step explanation:

A fixed point of a function is a points that is mapped to itself by the function; g(x) = x. Therefore, in order to find the fixed point of the given function we need to solve the following equation:

g(x) = x

x(10 - Ax) = x

10x - Ax² = x

10x - x -Ax² = 0

9x - Ax² = 0

Ax² - 9x = 0

The solutions of this second order equation are:

x = 0 and x = 9/A.

Since we are only asked for the non-zero fixed points, the solution is: 9/A.

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Complete the proof given below.
allochka39001 [22]

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

  • <u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
  • <u>Reflexive property of congruency</u>
  • <u>SSS</u>

Reasons:

The completed two column proof is presented as follows;

Statement  {}                                  Reason

1. ABCD is a parallelogram  {}       1. Given

2. \overline{AB} ≅ \overline{DC} and \overline{BC} ≅ \overline{DA}  {}      2. <u>Opposite sides of a parallelogram</u>

3. \overline{AC} ≅ \overline{CA}    {}                             3. <u>Reflexive property of congruency</u>

4. ΔABC ≅ ΔCDA     {}                   4. <u>SSS</u>

The correct options are therefore;

<u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

brainly.com/question/4218263

brainly.com/question/21390857

8 0
3 years ago
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