All categories

3 years ago

What is the true solution to the equation below? 2 In e^In2x -In e^In10x = In 30

2 answers:

8 0

$The\ domain.\\D:x\in\mathbb{R^+}\\\\2\ln e^{\ln2x}-\ln e^{\ln10x}=\ln30\ \ \ |use\ \log_ab^n=n\log_ab\\\\2\ln2x\ln e-\ln10x\ln e=\ln30\ \ \ \ |use\ \log_aa=1\\\\2\ln2x-\ln10x=\ln30\ \ \ |use\ n\log_ab^n=\log_ab^n\\\\\ln(2x)^2-\ln10x=\ln30\\\\\ln4x^2-\ln10x=\ln30\ \ \ |use\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\ln\dfrac{4x^2}{10x}=\ln30\\\\\ln\dfrac{2x}{5}=\ln30\iff\dfrac{2x}{5}=30\ \ \ \ |\cdot5\\\\2x=150\ \ \ \ |:2\\\\x=75\in D$

Answer: x = 75

andrey2020 [161]3 years ago

6 0

Answer:

Step-by-step explanation:

You might be interested in

Time traveler can take 5 books with him and he has 79 books to choose from how many different ways can the books be selected

AveGali [126]

<u>We are given:</u>

The time-traveller has 79 books, but he can only take 5 books

since we need to find the number of ways he can choose 5 books, we know that the order in which he takes the books does NOT matter

Hence, we will use combination

<u>Finding the number of ways:</u>

Since we will use combination, ₇₉C₅

We know that the formula for combination is (n!) / (r!(n-r)!)

₇₉C₅ = 79! / 5!(74!)

₇₉C₅ = 22,537,515

Therefore, the time traveller can choose 5 books in 22,537,515 different ways

8 0

3 years ago

It's due todayyyyyyy (;ŏ﹏ŏ)

Thepotemich [5.8K]

The correct answer are

Sue interest : 169.6061952

Bill interest: 189.9131472

B. Bill will get more interest then sue

Explain

Sue principal balance p= 2300

Interest for 3 years so t= 3

Interest is compounded yearly n= 1

R= 2.4%

A= 2300(1+2.4/100)^3 = 2300(1+0.024)^3 = 2300 x (1.024)^3 = 2469.6061952

Interest for 3 year is A-p= 2469.6061952 -2300

169.6061952

Bill principle p= 1800

Interest for 3 years t= 3

Interest compounded so n= 1

R= 3.4%

A= 1800(1+3.4/100)^3 = 1800 (1+0.034)^3 = 1800 (1.034)^3 = 1989.9131472

Interest in 3 yrs = 1989.9131472 - 1800 =

189.9131472

For B is below

Hopefully this help you :D

3 0

4 years ago

A truck can be rented from Company A for $120 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent

Jlenok [28]

Answer:

700 miles driven in a day

Step-by-step explanation:

Create an equation to represent the situation, where x is the number of miles.

0.8x + 120 = 0.9x + 50

Solve for x:

120 = 0.1x + 50

70 = 0.1x

700 = x

So, the rental costs will be the same at 700 miles driven in a day.

4 0

3 years ago

Read 2 more answers

One number is 44 times a first number. a third number is 100 more than the first number. if the sum of the three numbers is 5385

svlad2 [7]

I take it that the actual total is 538. If it really is 538538 leave me a note.

Let the first number = x

Let the second # = 44x

Let the third # = 100x

Equation

x + 44x + 100x = 538 Add the left side. All terms are part of the total.

145x = 538 Div By 145

x = 538/145

x = 3.71

Check

First number = 3.71

Second # = 44*3.71 = 163.24

Third number = 100*3.71 = 371

Total these 3 numbers 537.95 The very tiny difference is due to rounding.

5 0

3 years ago

Two buses leave a station at the same time and travel in opposite directions. One bus travels

natima [27]

Answer:

63 miles per hour

54 miles per hour

Step-by-step explanation:

Let the two buses be represented as bus A and bus B.

bus A and bus B leave a station at the same time and travel in opposite directions.

Let the speed of bus A be A miles per hour.

Let the speed of bus B be B miles per hour.

One bus travels 9 miles/hour slower than the other.

Let bus A be the faster bus.

This means that the speed of bus B is B = A - 9

If the two buses are 585 miles apart after 5hours, this means that after 5hours, the total distance travelled by bus A and bus B is 585 miles.

Distance travelled by bus A in 5 hours = speed × time = 5A

Distance travelled by bus B in 5 hours = speed × time = 5B

5A + 5B = 585 - - - - - -1

Substituting B = A - 9 in equation 1

5A + 5(A - 9) = 585

5A + 5A - 45 = 585

10A = 585 + 45 = 630

A = 630/10 = 63 miles per hour

B = A - 9 = 63 - 9 = 54 miles per hour

4 0

3 years ago