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3 years ago

Simplify the expression shown below: ln(e^3 x^4), where x>0

Mathematics

1 answer:

olga2289 [7]3 years ago

5 0

Answer:

Final answer is $3+4\ln(x)$

Step-by-step explanation:

Given expression is $\ln(e^3x^4)$ , where x>0

Now we need to simplify that expression.

Apply formula $\ln(AB)=\ln(A)+\ln(B)$

$=\ln(e^3)+\ln(x^4)$

Apply formula $\ln(x^m)=m\ln(x)$

$=3\ln(e)+4\ln(x)$

Apply formula $\ln(e)=1$

$=3(1)+4\ln(x)$

$=3+4\ln(x)$

Hence final answer is $3+4\ln(x)$

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Christine went shopping and bought each of her eighteight nephews a gift, either a video costing $14.95 or a CD costing $16.8

pogonyaev

So I think you should set up an equation like this: 14.95x+16.88y=131.18 , x+y=8

so x=8-y, plug this into the original equation:
14.95(8-y)+16.88y=131.18
Evaluate: 119.60-14.95y+16.88y=131.18
Combine like terms: 119.60+1.93y=131.18
Subtract 119.60 from both sides. You get: 1.93y=11.58
Divide both sides by 1.93. You get y=6

Plug into second equation: x+y=8 ---> x+6=8 and solve for x. x=2

Christine bought 2 video games and 6 CDs. 14.95(2)+16.88(6)=131.18

4 0

3 years ago

The world's population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion peopl

kkurt [141]

Answer: $f(t) = 4000000000( 1 .019)^t$

Step-by-step explanation:

Here, According to the question, The population of the world is 4 billion (approx).

Again According to the question, The world's population has grown at an average rate of 1.9 percent per year since 1945.

Therefore, after 1975 the growth rate will remains same.

Thus, the population of the world after t years,

$f(t) = 4000000000( 1+\frac{1.9}{100} )^t$ (By the formula $A = P(1+\frac{r}{100})^t$ )

⇒ $f(t) = 4000000000( 1.019 )^t$

Where 1.019 is the growth rate and 4 billion is the initial population.

6 0

3 years ago

PLEASE HELP ME OUT IM FAILING MATH‍♂️ Thx

OleMash [197]

Answer: -1 < x < 1

Step-by-step explanation: Solve for x.

Graph line is down below!

Hope this helps you out! ☺

-Leif-

3 0

3 years ago

The Glitz Jewelry Kit contains round beads in 6 different colors plus 100 star-shaped beads.

Alinara [238K]

Answer:

False, it would actually be 106 beads. If this was a multiplication problem, that would also be false, because 6 times 100 is 600, not 350.

But let's attempt to make this statement true.

First/Last step: Find the missing beads.

The missing beads are 144.

Why?

Because you must add 144 to reach 250, there is no other way but to multiply. In this case, because the key word is, "In all" we are adding.

3 0

2 years ago

PLEASE HELP ME. THANKS!!!

Veronika [31]

Cos(x) = sin(x + 20o) Use the double cos angle formula

Cos(x) = sin(x)*cos(20) + cos(x)*sin(20) Divide through by cos(x). Tanx = sin(x)/cos(x)

1 = tan(x)*cos(20) + sin(20) Subtract sin(20) from both sides.

1 - sin(20) = tan(x)*cos(20) Calculate the value of 1 - sin(20)

0.65798 = tan(x) * 0.939692 Divide by cos(20)

tan(x) = 0.65795/0.939692

tan(x) = 0.70021 Take the inverse of 0.7) = tan(x)

x = tan-1(0.70021)

x = 35 degrees as expected.

Problem Two

The easiest way to do this is to pick random values and try it. The two acute angles are complementary. So 25 and 65 are random enough.

Let A = 25

Let C = 65

Tan(25) = sin(25)/sin(65) ; tan(25) = 0.4663.

sin(25)/sin(65) = 0.4663 Answer

Sin(90 - C) = Sin(A)

Tan(90 - A) = Tan(C)

So the question becomes Cos(A) = Tan(C) / sin(A)

Cos(25) = Tan(65)/Sin(25)

0.906 = ? 5.07 This statement isn't true.

Sin(65) = Cos(25)/Tan(65)

.906 = 0.4226 C is not the correct answer.

D isn't true. The tan does not relate that away. You can find it for yourself.

Cos(A) = Tan(C) You should get 0.906 = 2.14

Sin(C) = Cos(A) / Tan(A) I'll leave you to show this is wrong.

Problem 3

The diagram below is for this problem. Cos(x) = 50/100 = 0.5

x = cos-1(0.5)

x = 60 degrees.

Part 2

Sin(60) = opposite / hypotenuse

opposite = sin(60) * hypotenuse

opposite = 86.61 Be sure and round this to whatever the question says to round it to.

4 0

3 years ago