Solve by factoring. m^2+8m+7=0 A. 8,7 B. -7,1 C. -7,-1 D. 7,1

Solve ln 2 + ln x = 5. Round to the nearest thousandth, if possible.

azamat

Answer:

The value of x nearest to thousandths is, 74.207

Step-by-step explanation:

Solve : $\ln 2 + \ln x = 5$

$\ln$ represents the logarithmic function with base e.

Using logarithmic properties:

$\ln (mn) = \ln m + \ln n$

$\ln x = a$ , then $x = e^a$

$\ln 2 + \ln x = 5$

Apply the logarithmic properties; we have

$\ln 2x = 5$

then;

$2x = e^5$

or

$2x=148.41315910258$

Divide both sides by 2 we get;

$x = 74.2065796$

Therefore, the value of x nearest to thousandths is, 74.207

3 0

2 years ago

What is the volume of a cone when the radius is 6 and the height is 13

lidiya [134]

Answer:

<h2>489.84 units³</h2>

Step-by-step explanation:

Given,

Radius ( r ) = 6

Height ( h ) = 13

Volume of cone = ?

Now, Let's find the volume of cone:

$= \pi \: {r}^{2} \frac{h}{3}$

plug the values

$= 3.14 \times {6}^{2} \times \frac{13}{3}$

Evaluate the power

$= 3.14 \times 36 \times \frac{13}{3}$

Calculate

$489.84$ units³

Hope this helps..

Best regards!!

6 0

2 years ago

Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

8 0

2 years ago

Read 2 more answers

Write an algebraic expression for the phrase five less than the product of six and N

GenaCL600 [577]

Answer:

6N - 5

Step-by-step explanation:

five less than the product of six and N: <em>6N</em>

five less than the product of six and N: <em>6N </em><em>- 5</em>

Answer: 6N - 5

6 0

3 years ago

How many more games will it take until tom and will have scored the same number of points

erma4kov [3.2K]

Answer:

<em>Both players will need to play 7 more games to have the same score.</em>

Step-by-step explanation:

Will makes 18 points per game and Tom makes 21 points per game. Will has a total of 483 points and Tom has 462 points.

We have to calculate the number of games Tom and Will need to play for them to have the same number of points. Since Tom makes more points per game, we're sure it will eventually happen.

Let's call x to the number of games that both players will play. Will will have a number of points equal to:

W = 483 + 18x

And Tom will have:

T = 462 + 21x

For both number of games to be equal, the equation to solve is:

483 + 18x= 462 + 21x

Move 18x to the right side and 462 to the left side:

483 - 462 = 21x - 18x

Operating:

21 = 3x

x = 21 / 3 = 7

Thus, both players will need to play 7 more games to have the same score.

8 0

2 years ago