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3 years ago

What is the sum of the geometric sequence 1,-6,36... if there are 6 terms

1 answer:

7 0

$a_1=1;\ a_2=-6;\ a_3=36;\ ...\\\\r=a_2:a_1\to r=-6:1=-6\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\a_1=1;\ r=-6;\ n=6\\\\subtitute\\\\S_6=\dfrac{1(1-(-6)^6)}{1-(-6)}=\dfrac{1-46656}{1+6}=\dfrac{46655}{7}=6665$

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Karina pays $1.92 for pencil erasers. the erasers cost $0.08 each. how many erasers does she buy?

horrorfan [7]

1.92 / 0.08 = 24.....Karina bought 24 erasers

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3 years ago

Look at the picture

Sonbull [250]

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$\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}$

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$\underline{\boldsymbol{\sf{Answer}}}$

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6 0

2 years ago

The roots of the equation x2 - 14x + 48 = 0) are

MrRissso [65]

Answer:

${x}^{2} - 14x + 48 = 0 \\ {x}^{2} - 6x -8 x + 48 = 0 \\ x(x - 6) - 8(x - 6) = 0 \\ (x - 6)(x - 8) = 0 \\ \boxed{ x = 6\: and \: 8}$

4) 6 and 8 is the right answer.

5 0

2 years ago

Identify whether the equation represents an exponential growth or exponential decay function.1. y = 1/4 (1/e)^-2x2. y = (1/e)^4x

zvonat [6]

The general formula for exponential growth and decays is:

$y=y_0e^{kx}$

if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.

Now we need to classify each of the functions:

The function

$y=\frac{1}{4}(\frac{1}{e})^{-2x}$

can be wrtten as:

$\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}$

comparing with the general formula we notice that k=2, therefore this is an exponential growth.

The function

$y=(\frac{1}{e})^{4x}$

can be written as:

$\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}$

comparing with the general formula we notice that k=-4, therefore this is an exponential decay.

The function

$y=2e^{-x}+1$

comparing with the general formula we notice that k=-1, therefore this is an exponential decay.

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1 year ago

osiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equati

sammy [17]

The standard compound interest formula is

Future value after x years with an annual interest of i

=Present Value (1+i)^x [which is an exponential function]

for given present value of $360. interest=0.03 (3%) and a total of x years, above equation reduces to

Future value after x years

=360(1.03^x)

4 0

3 years ago