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3 years ago

Which logarithmic equation is equivalent to the exponential equation below? E^a=60

Mathematics

1 answer:

Gala2k [10]3 years ago

8 0

Answer:

Step-by-step explanation:

e is the base of the natural log system.

take the natural log of both sides.

ln(e^a) = ln(60) The power can come down

a ln(e) = ln(60) The natural log of e = 1

a * 1 = ln (60)

a = ln(60)

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A programmer wants to display how the shape of a rectangle with a fixed perimeter of 300 inches can be changed by varying the re

stiv31 [10]

If the rectangle has a fixed width of 300, it means that

$2(l+w)=300 \iff l+w=150 \iff w=150-l$

where $w$ and $l$ are width and length, respetively.

So given the length $l$ , the are would be

$l\times w = l\times (150-l)=-l^2+150l$

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3 years ago

Complete the recursive formula of the geometric sequence 16\,,\,3.2\,,\,0.64\,,\,0.128,...16,3.2,0.64,0.128,

Nastasia [14]

Answer:

$a_{n+1}=0.2a_n$ for all n>0, $a_1=16$

Step-by-step explanation:

Let $\{a_n\}=\{16,3.2,0.64,0.128,\cdots \}$ be the sequence described.

A geometric sequence has the following property: there exists some r (the ratio of the sequence) such that $\frac{a_{n+1}}{a_n}=r$ forr all n>0.

To find r, note that

$\frac{3.2}{16}=\frac{32}{10(16)}=\frac{2}{10}=\frac{1}{5}=0.2$

Similarly

$\frac{0.64}{3.2}=\frac{64}{10(32)}=\frac{1}{5}=0.2$

$\frac{0.128}{0.64}=\frac{1}{5}=0.2$

Thus $a_{n+1}=r a_n=\frac{a_n}{5}=0.2a_n$ for all n>0, and $a_1=16$

3 0

3 years ago

Solve the equation: -9h - 6 +12h + 40 =22

Anettt [7]

h = -4

Hope this helps! :)

~Zane

3 0

2 years ago

The cost of printing a catalog of the products that your company distributes is a flat rate of $52 plus $0.20 per copy. Let C re

Delvig [45]

Answer:

1045384620173418506891046 number of copies

Step-by-step explanation:

10464929103984753671930600 ×55215278300

5 0

3 years ago

Read 2 more answers

(9, 19) (2, 16)<br> Write the coordinates as decimals or integers.

9966 [12]

Answer:

In decimal 0.428571428

Step-by-step explanation:

The slope = (y2 - y1)/(x2 - x1) y2 = 16, y1 = 19x2=2 and x1=9

The slope = (16 - 19)/(2 -9)

The slope = (-3)/(-7)

The slope = 0.428571428

So in decimal form the coordinates are going to be written as 0.428571428

Slope is the steepness of a line, it is the difference between the y coordinates divided by the difference in x coordinates.

6 0

2 years ago