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Schach [20]
3 years ago
12

Can anyone solve these? Thanks.

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
3 0
It won't let me see the picture sorry
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The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep
Alchen [17]
Ooh, fun

geometric sequences can be represented as
a_n=a(r)^{n-1}
so the first 3 terms are
a_1=a
a_2=a(r)
a_2=a(r)^2

the sum is -7/10
\frac{-7}{10}=a+ar+ar^2
and their product is -1/125
\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3

from the 2nd equation we can take the cube root of both sides to get
\frac{-1}{5}=ar
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r
subsituting -1/5 for ar
\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r
which simplifies to
\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for ax^2+bx+c=0
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}
so
for 2r²-5r+2=0
a=2
b=-5
c=2

r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}
r=\frac{5 \pm \sqrt{25-16}}{4}
r=\frac{5 \pm \sqrt{9}}{4}
r=\frac{5 \pm 3}{4}
so
r=\frac{5+3}{4}=\frac{8}{4}=2 or r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}

use them to solve for the value of a
\frac{-1}{5}=ar
\frac{-1}{5r}=a
try for r=2 and 1/2
a=\frac{-1}{10} or a=\frac{-2}{5}


test each
for a=-1/10 and r=2
a+ar+ar²=\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}
it works

for a=-2/5 and r=1/2
a+ar+ar²=\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}
it works


both have the same terms but one is simplified

the 3 numbers are \frac{-2}{5}, \frac{-1}{5}, and \frac{-1}{10}
6 0
3 years ago
Does anybody know where i can watch Naruto shippuden dub online for free no downloads
REY [17]

Answer:

i beliveyou can watch it on 9anime.to but use an addblocker please there is so many ads without it

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Lamar is considering two loans.
Varvara68 [4.7K]

Answer:

a.

Loan I's increase was 0.03 percentage points greater than Loan H's

8 0
3 years ago
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I Need Help Please And This Is Due In 1 Hour
alex41 [277]

So the first one is 1 square meter of ceiling, and it says 1 square meter of cieling is 10.75. <em>So the first one is just that, 10.75</em>

The second one says 10 square meters, so just multiply 10.75, by 10.

In which case you get <em>107.5.</em> So that's the answer.

Third one, it gives you how many ceiling tiles you have. So you divide the 100 tiles by 10.75, which gives you 9.30232558, which becomes <em>9.3</em>

I'm sure you can figure out the last one.

7 0
3 years ago
Si un rectángulo con perímetro de 74 pulgadas tiene un largo de 5 pies más que el ancho,
baherus [9]

Perímetro del rectángulo = 74 pulgadas

Deje que el ancho del rectángulo sea 'x'.

Entonces, la longitud de este rectángulo = x + 5

We know that :

\color{hotpink}\tt \: Perímetro  \: del \:  rectángulo =\color{plum} 2 × (l + b)

Lo que significa :

=\tt 2(x + x + 5) = 74

=\tt 2(2x + 5) = 74

=\tt 4x +10 = 74

=\tt 4x = 74 - 10

=\tt 4x = 64

=\tt x =  \frac{64}{4}

\color{plum} =\tt x = 16

Por lo tanto, el ancho de este rectángulo = 16 pulgadas

Entonces, la longitud de este rectángulo :

=\tt x + 5

= \tt16 + 5

\color{plum} =\tt 21 \: pulgadas

La longitud de este rectángulo = 21 pulgadas

<h2>Por lo tanto :</h2>

● Longitud del rectángulo = <em>21 pulgadas</em>

● Ancho del rectángulo = <em>16 pulgadas</em>

3 0
2 years ago
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