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jolli1 [7]
4 years ago
6

Consider this sequence: -81, -54, -36, -24, … . The sequence is . The common ratio of the sequence is . The sum of the first fiv

e terms of the sequence is .
Mathematics
1 answer:
solong [7]4 years ago
7 0

Answer:

The reason for the decreasing sequence is \frac{2}{3}

the sum of the sequence is -243

Step-by-step explanation:

Note that the numbers are decreasing so we will use the following formula to find the sum:

S∞=\frac{t1}{1-q},

where t1 is equal to the first number of the sequence and q is the reason that gives the following results.

to find q this form is used;  

q= \frac{t2}{t1}= \frac{-54}{-81} =\frac{2}{3}

then we replace in the formula of the sum to find the total

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kotykmax [81]

Hi!

We can see here that this is a composition question.

And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).

To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.

f(x)=\frac{e^7^x+\sqrt{3}}{2}

y=\frac{e^7^x+\sqrt{3}}{2}

x=\frac{e^7^y+\sqrt{3}}{2}

2x=e^7^y+\sqrt{3}

e^7^y=2x-\sqrt{3}

7y=ln(2x-\sqrt{3})

y=\frac{ln(2x-\sqrt{3})}{7}

Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.

g(f(x))

g(\frac{e^7^x+\sqrt{3}}{2})

\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}

2s cancel.

\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}

The natural log and e cancel.

\frac{7x+\sqrt{3}-\sqrt{3}}{7}

\sqrt{3}s cancel.

\frac{7x}{7}

7s cancel.

x

Hope this helps!

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3 years ago
What’s the diameter of this object?
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Answer:

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Step-by-step explanation:

The radius is 1/2 of the diameter.

0.8 * 2 = 1.6

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What is the solution to this equation? 5x - 4 + 3x = 36   A. x = 5   B. x = 16   C. x = 20   D. x = 4
shepuryov [24]

Let's do this in steps, show your work!   | <em>Make sure to ask questions!</em>

#1. Simplify 5x - 4 + 3 to 8x - 4.

<u>8x - 4 = 36.</u>

#2. Add 4 to both sides.

<u>8x = 36 + 4. </u>

#3. Simplify 36 + 4 to 40.

<u>8x = 40.</u>

#4. Divide both sides by 8.

<u>x = 40/8.</u>  <------ <em>It turned into a fraction because it's easier to not divide a decimal. </em>

#5. Simplify 40/8 to 5.  

<u>x = 5. </u>

<h3>Therefore, x = 5.</h3>

<u />

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