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dimaraw [331]
3 years ago
13

Jack played the first 3/5 of a basketball game. Then he played the final 1/10 of the game

Mathematics
1 answer:
____ [38]3 years ago
5 0

Answer:

He played 7/10 of the game

Step-by-step explanation:

3/5=6/10

6/10+1/10=7/10

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Three numbers form a geometric progression. If the second term is increased by 2, the progression will become arithmetic and if,
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In this exercise we have to use the knowledge of geometric progression to find three specific numbers, in this way we can say that these numbers correspond to;

0.16\\ -0.64\\ 2.56

Then using the formula of the geometric progression we find that:

a_1*r = a_2\\a_2*r = a_3 = a_1*r^2

now, the differences between the terms must be the same:

a1*r + 2 - a_1 = a_3 - (a_1*r + 2) = a_1*r^2 - (a_1*r + 2)\\a_1*r^2 - 2*a_1*r + a_1 - 4 = 0

and now, when we increase the third term by 9,so we have:

(a_1*r^2 + 9)/(a_1*r + 2) = (a_1*r + 2)/a_1\\(a_1^2*r^2 + 9*a_1)/(a_1*r + 2) = a_1*r + 2\\a_1^2*r^2 + 9*a_1 = (a_1*r + 2)^2 = a_1^2*r^2 + 4*a_1*r + 4\\4*a_1*r - 9*a_1 + 4 = 0\\9*a - 4 = 4*a_1*r\\r = (9*a_1 - 4)/(4*a_1)

Now we use that identity in the first equation :

a_1*(9*a_1 - 4)^2/(4×a_1)^2 - 2*a_1*(9*a_1 - 4)/(4*a_1) + a_1 - 4 = 0\\(81*a_1^2 - 72*a_1 + 16)/(16*a_1) - (9*a_1 - 4)/2 + a_1 - 4 = 0\\81*a_1^2 - 72*a_1 + 16 - 8*a_1*(9*a_1 - 4) + 16*a_1^2 - 64*a_1 = 0\\25a_1^2 - 104a_1 + 16 = 0

The general solution for a quadratic equation is

(-b + \sqrt{(b^2 - 4ac))/(2a)

We have that:

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so, put the numbers in the formula we find:

a_1=4 \\a_1=0.16

See more about geometric progress at brainly.com/question/14320920

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