1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Wittaler [7]
2 years ago
13

Write the exponential equation in logarithmic form. e^(-3) ≈ .05

Mathematics
1 answer:
vodka [1.7K]2 years ago
7 0

Answer:

  -3 = ln(0.05)

Step-by-step explanation:

Taking the natural log of both sides of the equation gives ...

  -3·ln(e) = ln(0.05)

The natural log of e is 1, so the equation becomes ...

  -3 = ln(0.05)

You might be interested in
What is the equation of a line that contains the point (2.1) and is parallel to
atroni [7]

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes , so

y = 3x + c ← is the partial equation

To find c substitute (2, 1) into the partial equation

1 = 6 + c ⇒ c = 1 - 6 = - 5

y = 3x - 5 ← equation of parallel line → D

3 0
3 years ago
Read 2 more answers
Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie sw
ddd [48]
Stefanie swam 1/3 further in the morning.
4/5 - 7/15
12/15 - 7/15 = 5/15
5/15 = 1/3
4 0
3 years ago
. Given ????(5, −4) and T(−8,12):
damaskus [11]

Answer:

a)y=\dfrac{13x}{16}-\dfrac{129}{16}

b)y = \dfrac{13x}{16}+ \dfrac{37}{2}

Step-by-step explanation:

Given two points: S(5,-4) and T(-8,12)

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: y = mx + c where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

m = \dfrac{y_2 - y_1}{x_2 - x_1}

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

m = \dfrac{12 - (-4)}{(-8) - 5}

m = \dfrac{-16}{13}

to find the perpendicular of this gradient: we'll use:

m_1m_2=-1

both m_1and m_2 denote slopes that are perpendicular to each other. So if m_1 = \dfrac{12 - (-4)}{(-8) - 5}, then we can solve for m_2 for the slop of ther perpendicular!

\left(\dfrac{-16}{13}\right)m_2=-1

m_2=\dfrac{13}{16}:: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope m and the points (x,y). And plug into the equation: (y - y_1) = m(x-x_1)

side note: you can also use the y = mx + c to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

(y - y_1) = m(x-x_1)

we have the slope of the perpendicular to ST i.e m=\dfrac{13}{16}

and the line should pass throught S as well, i.e (5,-4). Plugging all these values in the equation we'll get.

(y - (-4)) = \dfrac{13}{16}(x-5)

y +4 = \dfrac{13x}{16}-\dfrac{65}{16}

y = \dfrac{13x}{16}-\dfrac{65}{16}-4

y=\dfrac{13x}{16}-\dfrac{129}{16}

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for T(-8,12)

(y - y_1) = m(x-x_1)

(y -12) = \dfrac{13}{16}(x+8)

y = \dfrac{13x}{16}+ \dfrac{104}{16}+12

y = \dfrac{13x}{16}+ \dfrac{37}{2}

this is the equation of the line that is perpendicular to ST and passes through T

7 0
3 years ago
What is the pythagorean therum
Nimfa-mama [501]
The Pythagorean theorem is a^2 + b^2 = c^2. You use it when solving for the sides of a triangle.
3 0
3 years ago
Read 2 more answers
The area of a circle is 529 inches. Find the radius.
ruslelena [56]

\sqrt{529}
square root it and divide by pi. square root of 529 is 23. then divided by pi (3.14) is 7.32.
6 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER!
    14·1 answer
  • Somenone help im faling horribly there is two qestion I need help on any one know both
    10·1 answer
  • Which of the following statements are true of a transversal? It is a line. It can be perpendicular to other lines. It intersects
    12·2 answers
  • Negative 5 is fewer than 6 less than a number k
    10·1 answer
  • The length of a rectangle is 4 more than 3 times the width. If the perimeter is 104 meters, what is the width of the rectangle?
    11·1 answer
  • The functions f(x) and g(x) are shown below:
    13·1 answer
  • Suppose that 30% of female students and 25% of male students at a large high school are enrolled in an AP ® class. Independent r
    13·2 answers
  • PLEASE PLEASE I NEED HELP ON THIS QUESTION
    10·2 answers
  • jim is selling greeting cards at a booth at a folk fair. he will be paid $12 plus $2 for each box that he sells how many boxes m
    12·1 answer
  • What is the answer please and thank you
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!