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3 years ago

convert the following logarithmic equation to the equivalent exponential equation. Use the caret (^) to enter exponents. y=ln x

1 answer:

5 0

1. To solve this problem, you need to remember that an exponential function has the following form:

f(x)=a^x

"a" is the base and "x" is the exponent.

2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:

y=ln x
 e^y=e^(lnx)
 e^y=x

3. Therefore, the answer is:

x=e^y

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The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are

Lynna [10]

A normal distribution with a mean of 74 and a standard deviation of 7.
Mean + 1 SD = 74 + 7 = 81
Less than 81 : 50 % + 34 % = 84 %
Answer:
A ) 84 %

4 0

3 years ago

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The derivative of (x^2 +1)(x^3+ 1) (by definition and basic rule)

dlinn [17]

Answer:

f'(x) = 5x^4 + 2x + 3x^2

Step-by-step explanation:

To find the derivative of this equation we can do two things.

One method is to use the product rule, which states that when f(x) consists of two functions multiplied to each other (meaning f(x) = g(x) * h(x)), the derivative is f'(x) = g'(x)*h(x) + g(x)*h'(x). In simple language, the derivative is found by finding the derivative of x² + 1 and multiplying it with the normal function of x³ + 1, after which you add the product of the nnormal function of x² + 1 and the derivative of x³ + 1.

it might be clearer when I show you:

$f(x) = (x^2 + 1)(x^3 + 1)\\f'(x) = (2x)(x^3 + 1) + (x^2 + 1)(3x^2)\\Simplify:\\f'(x) = 2x^4 + 2x + 3x^4 + 3x^2 = 5x^4 + 3x^2 + 2x\\$

If you are not familiar with this rule you can first write out the function and then use the basic rule:

$f(x) = (x^2 +1)(x^3+1) = x^5 + x^2 + x^3 + 1\\f'(x) = 5x^4 + 2x + 3x^2$

If you need any further help please say so in the comments! I hope this helps! If the steps seem complicated, I suggest you could revise expanding brackets (the first step of the second method) and the basic rules of deriving, but feel free to reach out if you struggle afterwards still

8 0

3 years ago

Clare follows the same workout cycle each time she goes to the gym. First, she runs for 1 3 of an hour. Then, she lifts weights

____ [38]

Answer:

3 times

Step-by-step explanation:

She has 1 1/2 hour to spend in the gym.

1 hr = 60 minute

1/2 of an hour

= 1/2 * 60

= 30 minutes.

In total, she spends 90 minutes in the gym.

If 1/3 of an hour is meant in running, it translates into;

1/3 * 60 = 20 minutes

If 1/6 of an hour is spent in weight-lifting, it translates into;

1/6 * 60 = 10 minutes

In total, she spends,

20 minutes + 10 minutes = 30 minutes for both activities.

To obtain the number of times she would perform both activities, we divide the total amount of time spent in the gym by the amount of time spent for both activities.

= 90 minutes/30 minutes

= 3 times for each cycle.

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3 years ago

You have $110 in your lunch account and plan to spend $2.75 each school day. How many days will it take to spend all of the mone

Westkost [7]

All we have to do here is divide $110 by $2.75

This will give us the amount of days you can buy lunch with $110

110 ÷ 2.75 = 40

Therefore, it will take 40 days to spend all the money in the account

Hope this helps you

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3 years ago

What is the measure of p

xxMikexx [17]

Answer:

Step-by-step explanation:

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3 years ago

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