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viva [34]
2 years ago
13

Show that b^2 is greater than equal to or less than ac, according as a, b, c are in A.P., G.P.

Mathematics
1 answer:
ValentinkaMS [17]2 years ago
5 0

Answer/Step-by-step explanation  (ac > b² or b² < ac. )

A/c to question, we have to show:-

b² >ac in A.P ........ (1)

b² = ac in G.P .....(2)

b² < ac in H.P. ..... (3)

b = a+c/2 (A.P)

b = √ac ( G.P)

b = 2ac/a+c (H.P)

In A.P :

b² > ac = b² - ac

= (a+c/2)² - ac

= (a²+2ac+c²/4) - ac  = a² + 2ac + c² - 4ac / 4

= a² - 2ac + c² / 4  = ( a - c ) ² / 4 > 0  Hence, b²>ac

In G.P:-

b = √ac

Hence, b² = ac

In H.P :-  b² < ac = ac > b²  = ac - b²  = ac - ( 2ac / a+c)

= ac(a+c) - 2ac / a+c

= a²c + ac² - 2ac / a+c

= ac(2ac - 2) / a+c > 0

Hence, ac > b² or b² < ac.

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7 0
2 years ago
Out of 21 students in Mrs.Clarks class, 3/7 of the class are boys and 4/7 are girls. How many students in the class are girls an
lidiya [134]

Answer:

9 boys and 12 girls

Step-by-step explanation:

if you multiply the denominators by 3, you get "out of" 21. All you need to do after that is multiply the top by 3 as well and it tells you there are 9 boys and 12 girls.

8 0
3 years ago
What is the equation of the line that passes through point P (6, -8) and has a slope of zero?
EleoNora [17]

Answer:

A

Step-by-step explanation:

because it is a straight line locate at x = 6 that pass to every y coordinate, so it pass -8 too.

8 0
3 years ago
If x^3 times x^b equals x^15, which could be a correct value for "b?"
crimeas [40]
B=5
Hope this helps!
Vote me brainliest!
4 0
3 years ago
Hi everyone same as a while ago please help me with this :))) (with solution plzz) Thank you!
solniwko [45]

Answer:

6. 8.2g

7. 3800 ml

8. 560 L

9. 6300 ml

10. 30.48cm

11. 21120 ft

12. 487.48cm

Step-by-step explanation:

820 ÷ 100

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56000 ÷ 100

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12 × 2.54

4 × 5280

16 × 30.48

Please mark me as brainliest

6 0
2 years ago
Read 2 more answers
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