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Anton [14]
2 years ago
7

20. What is the greatest prime factor of 3^7+6^6 ?

Mathematics
1 answer:
mario62 [17]2 years ago
3 0

Answer:

67

Step-by-step explanation:

3^7 = 2187

6^6 = 46656

46656+2187=48843

Prime factors of 48843: 3, 3, 3, 3, 3, 3, 67

Factor tree:

48843

| \  

16281   3

| \  

5427   3

| \  

1809   3

| \  

603   3

| \  

201   3

| \  

67   3

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X=15

Since 20/4 is 5 and 5•3 is 15
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Step-by-step explanation:

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2 years ago
Show work and explain with formulas.
Musya8 [376]

Answer:

Q6. a₁₁ = 236 196; S₁₁ = 354 292

Q7. 354 292

Q8. a)  Converges, S = 320/3; b) diverges

Step-by-step explanation:

6. Geometric sequence

The first three terms of your sequence are 4, 12, 36.

Each term differs from the previous one by a factor of 3, so it is a geometric sequence.

Each term has the form

aₙ = a₁rⁿ⁻¹

In your sequence, a₁ = 4 and r = 3.

Thus, the formula for the nth term is

aₙ = 4(3)ⁿ⁻¹

The 11th term is

a₁₁ = 4(3)¹¹⁻¹ = 4(3)¹⁰ = 4 × 59 049 = 236 196

The formula for the sum of the first n terms of a geometric series is

Sum = a₁[(1 - rⁿ)/(1 - r)]

For the sum over the first 11 terms,

Sum = 4[(1 - 3¹¹)/(1 - 3)

         = 4(1 - 177 147)/(-2)

         = -2(-177 146)

         = 354 292

7.  Bouncing ball

Mathematically, the ball never stops bouncing. The height of each bounce just gets infinitesimally small.

So , you have an infinite geometric series in which the first term is 40 ft and each successive term is 90 % of the previous term.

The general formula for the nth term is

aₙ = a₁rⁿ⁻¹

with a₁ = 40 ft and r = 0.90.

Since |r| <1, we have a convergent series, and the formula for the sum is

S = a₁/(1-r)

∴ S = 40/(1 - 0.90) = 40/0.10 = 400 ft

The bouncing ball will have travelled 400 ft.

8. Test for convergence

a) 80 + 20 + 5 + 5/4 + ...

r = a₂/a₁ = 20/80 = ¼

r < 1, so the series converges.

S = 80/( 1 - ¼) = 80/¾ = 80 × ⁴/₃ = 320/3

The sum of the series is 320/3.

b) 2/9 + 4/3 + 8 + ...

r = a₂/a₁ = (⁴/₃)/(²/₉) = ⁴/₃ × ⁹/₂ = 2 × 3 = 6.

r > 1, so the series diverges.

6 0
3 years ago
Read 2 more answers
BC and BD are opposite rays. All of the following are true except
SashulF [63]

Answer: B is the answer given that b is the point where they become opposite and they have to be colinear

8 0
3 years ago
Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.
Dmitrij [34]

Answer:

<h2>y = -2x + 1</h2>

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have two points (1, -1) and (2, -3).

Substitute:

m=\dfrac{-3-(-1)}{2-1}=\dfrac{-2}{1}=-2

Put it and the coordinates of the point (1, -1) to the equation of a line:

-1=-2(1)+b

-1=-2+b          <em>add 2 to both sides</em>

1=b\to b=1

Finally:

y=-2x+1

3 0
2 years ago
Read 2 more answers
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