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hjlf
3 years ago
9

PLZ HELP WITH THIS!!!! IM TIMED AND NEED CORRECT ANSWERS

Mathematics
1 answer:
Georgia [21]3 years ago
4 0

1.   Using the formula for nth term ( = a1 * r^(n-1)

the 5th term = (-2)*(1/4)^4

= -2/256  = -1/128  (answer)

2.   The 4 terms between 1 and  32 are found as follows:-

a1 = 1 and  a6 = 32   so  32/1 = a6/a1

 therefore 32/1 = a1r^5 / a1

so r^5 = 32 and r = 2

so 4 terms are a1r,  a1r^2, a1^r^3 and a1r^4

= 2, 4, 8, 16   (answer)

3.   You need the sum of 10 terms where a1 = -2 and r = 3

S10  = -2 * (3^10 - 1) / (3 - 1)

= -59058

4.  Sum to infinity  = a1 / (1 - r)

a1 = 1 and r = 1/2

so the answer is  1 /  (1 - 1/2)

= 1 / 1/2

= 2   (answer)

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Step-by-step explanation:

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1
Marianna [84]

Answer:

  B. {16, 19, 20}

Step-by-step explanation:

The <em>triangle inequality</em> requires for any sides a, b, c you must have ...

  a + b > c

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  c + a > b

The net result of those requirements are ...

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  • the length of the third side lies between the difference and sum of the other two sides

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If we look at the offered side length choices, we see ...

  A: 8+11 = 19 . . . not > 19; not a triangle

  B: 16+19 = 35 > 20; could be a triangle

  C: 3+4 = 7 . . . not > 8; not a triangle

  D: 5+5 = 10 . . . not > 11; not a triangle

The side lengths {16, 19, 20} could represent the sides of a triangle.

_____

<em>Additional comment</em>

The version of triangle inequality shown above ensures that a triangle will have non-zero area.

The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")

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Read 2 more answers
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