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Nikitich [7]
3 years ago
12

The sum of the first 5 terms of a geometric sequence is 496, and the common ratio is 1/2. what is the first term

Mathematics
1 answer:
CaHeK987 [17]3 years ago
8 0

the answer is 6

have a nice day

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For a sequence an=3/n(n+1) what is the value of a 10
FrozenT [24]

Answer:

\large\boxed{a_{10}=\dfrac{3}{110}}

Step-by-step explanation:

Put <em>n = 10</em> to the equation a_n=\dfrac{3}{n(n+1)}

a_{10}=\dfrac{3}{10(10+1)}=\dfrac{3}{10(11)}=\dfrac{3}{110}

3 0
3 years ago
Read 2 more answers
Two times the sum of a number and 22 is atleast -28<br><br> please hurry
Marta_Voda [28]

Answer:

-6

Step-by-step explanation:

Mark me as brainliest

6 0
3 years ago
in an election an amount of votes was share among parties A,B and C in the ratio of 1:2:4. How many votes party B obtained if pa
spayn [35]

1000

Step-by-step explanation:

Let the share of votes obtained by the parties A, B and C be x, 2x and 4x respectively.

According to the given information:

No of votes obtained by C = 1500 + No of votes obtained by A

\therefore 4x = 150. + x \\\\\therefore 4x - x = 1500\\\\\therefore 3x = 1500\\\\\therefore x = \frac{1500}{3} \\\\\therefore x = 500\\\\\because Votes \:obtained\: by \:B = 2x \\\\\therefore Votes \:obtained\: by \:B = 2\times 500\\\\\purple {\bold {\therefore Votes \:obtained\: by \:B = 1000}} \\\\

7 0
3 years ago
Find the integral using substitution or a formula.
Nadusha1986 [10]
\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx

Derivative of the denominator:
\rm (x^2+2x+5)'=2x+2

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx

and then split the fraction,

\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx

Based on our previous test, we know that a simple substitution will work for the first integral: \rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx

So the first integral changes,

\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx

integrating to a log,

\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2

So we have this going on,

\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx

Bringing all that stuff together as a single square,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx

Making the substitution: \rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx

giving us,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du

simplying a lil bit,

\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du

and hopefully from this point you recognize your arctangent integral,

\rm ln|x^2+2x+5|+\frac52arctan(u)

undo your substitution as a final step,
and include a constant of integration,

\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c

Hope that helps!
Lemme know if any steps were too confusing.

8 0
3 years ago
The expression 36 ÷ 6 • 2 + 1 is equal to _____.<br><br> 2<br> 4<br> 13<br> 18
NeTakaya

Answer:

Step-by-step explanation:

36/6 · 2 + 1

6 ·2 + 1

12 + 1 = 13

answer is 13

7 0
3 years ago
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