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Readme [11.4K]
3 years ago
5

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

Mathematics
2 answers:
Klio2033 [76]3 years ago
7 0

Answer:

dy/dx = [1/ln(10)][(2x+6)/(x^2 +6x)]

Step-by-step explanation:

See attachment

WARRIOR [948]3 years ago
3 0

Answer:

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

Step-by-step explanation:

given

y = \log_{10}{(x^2+6x)}

using the property of log \log_ab=\frac{log_cb}{log_ca}, and if c =e,\log_ab=\frac{ln{b}}{ln{a}}, we can rewrite our function as:

y = \dfrac{\ln{\left (x^{2} + 6 x \right )}}{\ln{\left (10 \right )}}

now we can easily differentiate:

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{d}{dx}(\ln{(x^{2} + 6x)})\right)

\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{2x+6}{x^{2} + 6x}\right)

\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}

This is our answer!

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Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 4
Studentka2010 [4]
81 cards 43x2=86  86-5=81
3 0
3 years ago
The students at Woodward Elementary voted for a school mascot. The falcon won with 58 of the votes and the eagle came second wit
Anuta_ua [19.1K]

Answer:

67 students voted for the eagle

Step-by-step explanation:

The students at Woodward Elementary voted for a school mascot. The falcon won with 5/8 of the votes and the eagle came second with 1/3 of the remaining votes. If 536 students voted for a mascot, how many students voted for the eagle

Total students who voted = 536

Falcon won with 5/8 of the votes

5/8 of 536

=5/8 × 536

= 2,680/8

= 335 votes

Falcons won with 335 votes

Remaining votes = Total votes - falcons votes

= 536 - 335

= 201 votes

There are 201 votes remaining

Eagle came second with 1/3 of the remaining votes

1/3 of the remaining votes

= 1/3 × 201

= 201/3

= 67 votes

67 students voted for the eagle

5 0
2 years ago
Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he
sweet [91]

\huge{\boxed{\text{42 ounces}}}

25% is equal to \frac{1}{4}, so multiplying it by 4 gets 100%.  This means we can multiply 10.5 by 4 to get 100% of the fiber the koala ate that day.

10.5*4=\boxed{42}

7 0
3 years ago
Read 2 more answers
Please help! Please let me know if you need a better picture.
Dmitriy789 [7]

Answer:

-2

Step-by-step explanation:

First you should write out the entire word equation into one you may recongnize:

7x - 12 = -3x - 32

After this, solve for x:

7x + 3x = 12 - 32

<u>10x</u> = <u>-20</u>

10      10

x = -2

the number is -2

5 0
3 years ago
What is the common difference between successive terms in the sequence​
Lelechka [254]

9,2.5,-4,-10.5,-17

Let's find the difference between two consecutive terms

2.5 - 9 = -6.5

-4 - 2.5 = -6.5

-10.5 - (-4) = -6.5

-17 -(-10.5) = -6.5

We can see that the common difference is -6.5

-6.5 is the common difference between successive terms in the sequence 9,2.5,-4,-10.5,-17

the common difference is negative because we subtract 6.5 to get the next term.

4 0
3 years ago
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