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3 years ago

Solve log (x + 1) = –x2 + 10 by graphing

Mathematics

2 answers:

irga5000 [103]3 years ago

5 0

Answers on edguinity are y1 = –x2 + 10 and y2 = log (x + 1).

Anit [1.1K]3 years ago

3 0

Your answer would be x = 3.0645

CHECK
log (3.0645 + 1) ?=? -(3.0645)2 + 10
log 4.0645 ?=? -9.3912 + 10
0.609 ?=? 0.609

Hope this helps!

So in short your answer is x = 3.0645

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2 years ago

Write an explicit formula for an, the nth term of the sequence 112, -28, 7, ....

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$a_n=112\left(-\frac{1}{4}\right)^{n-1}$

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<u>Geometric Sequences</u>

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

$\displaystyle r=\frac{-28}{112}=-\frac{1}{4}$

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$\displaystyle -28*-\frac{1}{4}=7$

Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:

$a_n=a_1*r^{n-1}$

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3 years ago