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Vadim26 [7]
2 years ago
12

Let g(x) = log7 (x), find g ¹(0)

Mathematics
1 answer:
klasskru [66]2 years ago
6 0

Step-by-step explanation:

The derivative of log is

\frac{d}{dx} ( log_{a}(x) ) =  \frac{1}{x \:  ln(a) }

You can easily derive this using the Change of base rule, and natural log rules

log_{a}(x)  =  \frac{ log_{e}(x) }{ log_{e}(a) }  =  \frac{ ln(x) }{ ln(a) }

Next, we differentiate with respect to x.

\frac{d}{dx} \frac{ ln(x) }{ ln(a) }  =  \frac{1}{ ln(a) }  \times  \frac{d}{dx}  ln(x)

=  \frac{1}{x ln(a) }

So back to the topic at hand,.

a=7, so we get

\frac{1}{x ln(7) }

We plug in 0, we would get undefined

You might be interested in
7. Jerry has 23 coins in nickels, n, and dimes, d. He
aliya0001 [1]

Answer:

17 nickles !

Step-by-step explanation:

First, identify the variables:

n = amount of nickels

d = amount of dimes

Next, setup the equations based on what you know.  The first equation is:

n + d = 28

For the second equation, we know that a dime is worth 10¢ and a nickel is 5¢, so it should be:

0.05n + 0.10d = 1.95

This a three-step answer:

In one formula (you can use any of them; most people use the simplest one), single out the variable on one side

Apply the first formula into the second formula, and solve it to get the value of one variable

Apply the answer from the second formula into the first formula, and solve it to get the value of the other variable

======

Step One:

n + d = 28

n + d - d = 28 - d

n = 28 - d

Step Two:

0.05n + 0.10d = 1.95

(0.05 * (28 - d)) + 0.10d = 1.95

1.40 - 0.05d + 0.10d = 1.95

1.40 + 0.05d = 1.95

1.40 - 1.40 + 0.05d = 1.95 - 1.40

0.05d = 0.55

d = 11

Step Three:

n = 28 - d

n = 28 - 11

n = 17

======

Your answer should be 17 nickels and 11 dimes.

You can double check by applying the variables into both formulas.

n + d = 28

17 + 11 = 28

28 = 28

0.05n + 0.10d = 1.95

(0.05 * 17) + (0.10 * 11) = 1.95

0.85 + 1.10 = 1.95

1.95 = 1.95

I hope this helped.

7 0
3 years ago
What is the slope of the linear equation below?
spayn [35]

Answer:

-5

Step-by-step explanation:

-5 is the slope because it is the multiplier of x

7 0
2 years ago
What is the sum of the first 70 consecutive odd numbers? Explain.
expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)

The second sum is simply the sum of N ones:

\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N

So, the final result is

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

5 0
2 years ago
Choose the inequality below that x=0 is a solution to.
krok68 [10]

remember: a filled dot means it includes that point and an empty dot means it doesn't


A. has empty dot at 0 so x=0 is not incuded in the solution

B. has filled dot at x=0 so x=0 is a solution

C. has empty dot at 0 so x=0 is not incuded in the solution

D. the line doesn't even go over x=0 so not a solution


answer is B

8 0
3 years ago
What is the square root of 67
Inessa [10]

Every positive number has two square roots.

The square roots of  67  are  8.185... (rounded) and  -8.185... (rounded) .

Both are irrational numbers, so they can't be completely written down
with digits.  No matter how many decimal places I write, it can never be
enough, because these decimals go on forever and never end.

3 0
3 years ago
Read 2 more answers
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