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prohojiy [21]
2 years ago
8

3. If 3, x, y, 18, are in arithmetic progression, (A, P) find the value of x and y

Mathematics
1 answer:
Luba_88 [7]2 years ago
5 0

Answer:

Below in bold

Step-by-step explanation:

The sequence is:

3, x, y, 18

If this is an A P then

x - 3 = y - x  

2x - y = 3      (A)  and

y - x = 18 - y

2y - x = 18      (B)

Multiply  (A) by 2:

4x - 2y = 6    (C)

Adding B and C:

3x = 24

x = 8.

and

2y - 8 = 18

2y = 26

y = 13.

So x = 8 and y = 13.

b)   ar + ar^2 = 6ar^3  where a = first term and r = common ratio

Divide by a:

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

r(3r  + 1)(2r  - 1) = 0

So the 2 possible values of r

= -1/3 and 1/2.

i) The common ratio is positive so it must be 1/2.

Second term ar = 8

1/2 a = 8

a = 16.

So the first 6 terms are:

16, 8, 4, 2, 1, 1/2.

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Answer:

10 seconds

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Given that, every 2 seconds the bug will travel a full 1 meter.

To solve this one can simply divide 5m by 0.5 and get 10 seconds.

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What makes (a + 2)(b – 9) = 0 true?
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B would have to equal 9 and a should equal -2 to get 0
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Problems 1-8, name the sets of numbers to which each number belongs.
posledela

The name of the sets of the numbers to which each of the given number belongs is:

  1. 7 = Natural number. Integer. Rational number.
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  3. л = Irrational number.
  4. O = Rational number. Integer.
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<h3>What are sets of numbers?</h3>

These are the various types of number groups that exist for categorizing numbers.

Natural numbers are all positive numbers from 1 to infinity while integers are positive and negative whole numbers. A decimal cannot be an integer as a result.

Rational numbers are discrete which means that they are terminating and eventually stop going while irrational numbers will keep going to infinity and are therefore non-terminating.

Find out more on sets of numbers at brainly.com/question/13081505

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7 0
1 year ago
A line with a slope of -3 that passes through the point (-2, 6)
scZoUnD [109]
I believe the equation is y = -3x + 0
3 0
2 years ago
Factorise 2x^2 - 3x -2 &lt; 0
Galina-37 [17]
Step 1: Factor 2 x^{2} - 3x -2
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite -3x as the sum of x and -4x

2 x^{2} +x-4x-2\ \textless \ 0


Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.

</span>x(2x+1)-2(2x+1)\ \textless \ 0
<span>
Step 3: </span>Factor out the common term 2x+1

(2x+1)(x-2)\ \textless \ 0

Step 4: Solve for x

1. Ask: When will (2x+1)(x-2) equal zero?
2. Answer: When 2x + 1 = 0 or x-2=0
3. <span>Solve each of the 2 equations above:

</span>x=- \frac{1}{2} ,2
<span>
Step 5: </span>From the values of x <span>above, we have these 3 intervals to test.
x = < -1/2
-1/2 < x < 2
x > 2

Step 6: P</span><span>ick a test point for each interval

</span>For the interval x\ \textless \ - \frac{1}{2} &#10;
Lets pick x=-1. Then, 2(-1) ^{2} -3 * -1 -2 \ \textless \  0
After simplifying, we get 3\ \textless \ 0, Which is false. 
Drop this interval.
<span>
For this interval - \frac{1}{2} \ \textless \ x\ \textless \ 2
Lets pick x=0. Then, 2* 0^{2} - 3 * 0-2\ \textless \ 0. After simplifying, we get -2\ \textless \ 0, which is true. Keep this <span>interval.

For the interval </span>x\ \textgreater \ 2

Lets pick x = 3. Then, 2 * 3  ^{2} -3*3-2\ \textless \ 0. After simplifying, we get 7\ \textless \ 0, Which is false. Drop this interval.

.Step 7: Therefore, 
- \frac{1}{2} \ \textless \ x\ \textless \ 2

Done! :)</span>
4 0
3 years ago
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