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3 years ago

Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.

Mathematics

1 answer:

Natalija [7]3 years ago

5 0

Answer:

x=3 , x=-3

Step-by-step explanation:

$e^{lnx^2} -9= 0$

Add 9 on both sides

$e^{lnx^2}=9$

To remove base 'e' we take ln on both sides

$ln e^{lnx^2}=ln9$

$lnx^2=ln(9)$

Both sides have ln , so we make the terms equal

$x^2=9$

Take square root on both sides

$x=+-3$

x=3 , x=-3

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9. Determine whether or not the number 257 is prime.

Sladkaya [172]

Answer:

257 is prime.

Step-by-step explanation:

To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.

In this case, √257 = 16.03 so we just need to see if 257 is divisible by <u>2, 3, 5, 7, 11 and 13</u> (the prime numbers that come before 16)

257 is odd, so it is not divisible by 2.

The sum of its digits is 14, therefore, it is not divisible by 3.

257 ends in 7, therefore it's not divisible by 5.

257/ 7 = 36.71 so it's not divisible by 7.

257/ 11 = 23.36 so it's not divisible by 11

Finally 257 / 13= 19.76 so it's not divisible by 13.

Therefore, 257 is prime.

7 0

2 years ago

The sum of two numbers is 30 and their difference is 6

Studentka2010 [4]

I'm going to assume that you are trying to find the two numbers. Based on the information in the problem, we can create the following equations (where $a$ and $b$ are the two numbers):

$a + b = 30$

$a - b = 6$

We have a systems of equations. In this case, it would be easier to use elimination by adding vertically. This produces the result:

$2a = 36$

$a = 18$

To find $b$ , substitute the value for $a$ into one of the earlier equations:

$18 + b = 30$

$b = 12$

The two numbers are 12 and 18.

4 0

2 years ago

The average human gestation period is 270 days with a standard deviation of 9 days. The period is normally distributed. What is

Anna35 [415]

Answer:

Probability that a randomly selected woman's gestation period will be between 261 and 279 days is 0.68.

Step-by-step explanation:

We are given that the average human gestation period is 270 days with a standard deviation of 9 days. The period is normally distributed.

Firstly, Let X = women's gestation period

The z score probability distribution for is given by;

Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = average gestation period = 270 days

$\sigma$ = standard deviation = 9 days

Probability that a randomly selected woman's gestation period will be between 261 and 279 days is given by = P(261 < X < 279) = P(X < 279) - P(X $\leq$ 261)