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3 years ago

Using the properties of exponents and logarithms, find the value of x in 19 + 2 ln x = 25.

2 answers:

8 0

$19+2\ln x=25\ \ \ |-19\\\\2\ln x=6\ \ \ |:2\\\\\ln x=3\iff x=e^3$

$\text{Used de.finition of the logarithm:}\ \ \ \log_ab=c\iff a^c=b$

vivado [14]3 years ago

3 0

Answer:

$x=e^3$

Step-by-step explanation:

The first step is to pass 19 to subtract the other side

$2\cdot ln(x)=25-19$

$2\cdot ln(x)=6$

The second step is to pass the 2 to divide the other side

$ln(x)=\frac{6}{2}$

$ln(x)=3$

The final step is take into account the general form of logarithmic expression.

$ln(a)=b$ -------> $e^b=a$

According to the the previous, if we have $ln(x)=3$ , the value of x would be:

$e^3=x$

$x=e^3$

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How to determine if the columns of a matrix are linearly independent?

astra-53 [7]

Let's consider an arbitrary 2x2 matrix as an example,

$\mathbf A=\begin{bmatrix}\mathbf x&\mathbf y\end{bmatrix}=\begin{bmatrix}x_1&y_1\\x_2&y_2\end{bmatrix}$

The columns of $\mathbf A$ are linearly independent if and only if the column vectors $\mathbf x,\mathbf y$ are linearly independent.

This is the case if the only way we can make a linear combination of $\mathbf x,\mathbf y$ reduce to the zero vector is to multiply the vectors by 0; that is,

$c_1\mathbf x+c_2\mathbf y=\mathbf 0$

only by letting $c_1=c_2=0$ .

A more concrete example: suppose

$\mathbf A=\begin{bmatrix}1&2\\4&8\end{bmatrix}$

Here, $\mathbf x=\begin{bmatrix}1\\4\end{bmatrix}$ and $\amthbf y=\begin{bmatrix}2\\8\end{bmatrix}$ . Notice that we can get the zero vector by taking $c_1=-2$ and $c_2=1$ :

$-2\begin{bmatrix}1\\4\end{bmatrix}+\begin{bmatrix}2\\8\end{bmatrix}=\begin{bmatrix}-2+2\\-8+8\end{bmatrix}=\mathbf 0$

so the columns of $\mathbf A$ are not linearly independent, or linearly dependent.

8 0

3 years ago

Find the midpoint of the segment with the following endpoints. (8,5) and (0, -1)

Karo-lina-s [1.5K]

Answer:

(4,2)

Step-by-step explanation:

$Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(8,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(0,\:-1\right)\\\\=\left(\frac{0+8}{2},\:\frac{-1+5}{2}\right)\\\\= (\frac{8}{2} , \frac{4}{2} )\\\\Simplify\\=\left(4,\:2\right)$

6 0

4 years ago

Which of the following is not part of the Triangle Proportionality Theorem?

natka813 [3]

Answer:

A. AA Similarity Theorem . True

B. Two sides divided proportionally. True

C. A parallel line to one side of a triangle. True

D. A perpendicular line to one side of a triangle. False

Step-by-step explanation:

The Triangle Proportionality Theorem says that if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections.

Now, here the given statements are:

A. AA Similarity Theorem

TRUE, as the angles opposite to equal sides are equal.

And if lines are divided proportionally, both the triangles are Similar by AA similarity theorem.

B. Two sides divided proportionally.

TRUE,as the other two sides of the triangle are divided proportionally by the parallel line.

C. A parallel line to one side of a triangle.

TRUE, as the parallel line divides the other two non- parallel sides in equal proportions.

D. A perpendicular line to one side of a triangle.

FALSE, this part is not required anywhere in the given theorem result.

3 0

3 years ago

Find f(2) given f(x) = -3x^3 + x^2 – 3

aleksley [76]

Answer:

Step-by-step explanation:

f(x) = -3x^3 + x^2 – 3 f(2) means that wherever you see a x, put in a 2.

f(2)= -3(2)^3 + (2)^2 - 3

f(2) = -3*8 + 4 - 3

f(2) = - 24 + 1

f(2) = - 23

6 0

3 years ago

Read 2 more answers

A certain forest covers an area of 1700 km^2. Suppose that each year this area decreases by 3.25%. What will the area be after 6

Olenka [21]

y= 1700 (1- .0325) ^15

= 1700(.9675) ^15

=1700(.60920660)

= 1035.65 km

Hope this helps!

4 0

4 years ago