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Aleks [24]
2 years ago
7

Find the ninth term of the sequence if the second term is 12 and the fourth term is 16/3.

Mathematics
1 answer:
aleksklad [387]2 years ago
6 0

with the assumption this is a geometric sequence and thus it as an "r" common ratio, so we know that the 3rd term must be 12 * r and the 4th term must be 12 * r * r, so let's make a quick table

\begin{array}{rll} term&value\\ \cline{1-2} a_2&12\\ a_3&12\cdot r\\\cline{1-2} a_4&(12\cdot r)r\\ &12r^2\\ &\frac{16}{3}\\\cline{1-2} a_5&12r^3\\ a_6&12r^4\\ a_7&12r^5\\ a_8&12r^6\\ a_9&12r^7 \end{array}\qquad \implies \begin{array}{llll} 12r^2=\cfrac{16}{3}\implies r^2=\cfrac{16}{12\cdot 3}\implies r^2=\cfrac{4}{9}\\\\\\ r=\sqrt{\cfrac{4}{9}}\implies r=\cfrac{\sqrt{4}}{\sqrt{9}}\implies r=\cfrac{2}{3} \end{array} \\\\[-0.35em] ~\dotfill

a_9=12\left( \cfrac{2}{3} \right)^7\implies a_9=12\cdot \cfrac{128}{2187}\implies a_9=\cfrac{512}{729}

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If f(x) = integral of 1/ (sqrt of t^3 +2)dt, then f'1 = ?
mihalych1998 [28]
Differentiating an integral removes the integral.

f(x) = integral of dt/sqrt(t^3 + 2)
f'(x) = 1/sqrt(x^3 + 2)
f'(1) = 1/sqrt(1^3 + 2)
f'(1) = 1/sqrt(3) = sqrt(3)/3.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
4 0
3 years ago
HELP Please <br> I don’t get it lol
weeeeeb [17]

Answer:

bxy and bac

Step-by-step explanation:

since line xy is parallel to ac the triangles are similar

8 0
3 years ago
A farmers field has the dimensions shown. He needs to find the area of the field so that he knows how much he needs to buy .What
kolbaska11 [484]

Answer:

Area of the rectangular Field = 3 8/9 km²

Step-by-step explanation:

Length of the field = 2 1/3 km

Width of the field = 1 2/3 km

Area of a rectangular Field = length × width

= 2 1/3 × 1 2/3

= 7/3 × 5/3

= (7*5)/(3*3)

= 35/9

Area of the rectangular Field = 3 8/9 km²

Perimeter of the rectangular Field = 2(length + width)

= 2(2 1/3 + 1 2/3)

= 2(7/3 + 5/3)

= 2(7+5/3)

= 2(12/3)

=2(4)

= 8 km

Perimeter of the rectangular Field = 8 km

5 0
3 years ago
Determine the discriminant for the quadratic equation -3 = x^2+4x+1 . Based on the discriminant value, how many real number solu
djverab [1.8K]

Answer:

1 real

Step-by-step explanation:

The discriminant is:

b^2-4ac

which comes from the quadratic formula.

The rules are:

If the discriminant is > 0, there are 2 real solutions

If the discriminant is = 0, there is 1 real solution

If the discriminant is < 0, there are 2 imaginary solutions

(there are 2 other situations involving square roots, but these are the most basic ones in Algebra 2 books when you study quadratics)

First, we have to get that quadratic in standard form, which means getting everything on one side of the equals sign and setting it equal to 0:

x^2+4x+4 = 0

where a = 1, b = 4, c = 4

Filling in the discriminant:

4^2-4(1)(4)

gives us

16 - 16 = 0

Therefore, our quadratic has one real solution.  Factor it and see if you'd like, to prove that it is true.

7 0
3 years ago
+ PRINCIPLES OF MATHEMATICS
GREYUIT [131]

Answer:

$9,840

Step-by-step explanation:

Let the money earned from college be 'x'.

Given:

Total money earned from the two jobs = $50,450

Money earned at the store = 1250 + 4(Money earned at college)

∴ Money earned at the store = 1250 +4x

Now, total money earned by Erica is the sum of money earned at store and college. Therefore,

Total money = Money at store + Money at college

50450=1250+4x+x\\5x+1250=50450\\5x=50450-1250\\5x=49200\\x=\frac{49200}{5}=\$9840

Therefore, the money earned by Erica from her job at the college is $9,840.

3 0
3 years ago
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