Answer:
Step-by-step explanation:
This is an exponential equation that is solved by taking the natural log of both sides. The equation is
If we are looking for x when f(x) = 64, then
Take the natural log of both sides:
The rules of logs allows us to bring the x down in front:
Divide both sides by ln(2) to get:
Do this on your calculator to get that x = 6.
You could also have just gone right to your calculator and started raising 2 to consecutive powers starting at like 3 or 4 to eventually get that 2 to the 6th power is equal to 64, but for the basics of solving log equations, you need to know how to do this.
Hey there! I'm happy to help!
First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).
Let's convert this below
A: (1,1)⇒(-1,-1)
B: (5,4)⇒(-5,-4)
C: (7,1)⇒(-7,-1)
D: (3,-2)⇒(-3,2)
Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.
A: (-1,-1)⇒(4,-2)
B: (-5,-4)⇒(0,-5)
C: (-7,-1)⇒(-2,-2)
D: (-3,2)⇒(2,1)
Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)
Now you know how to find the coordinates of translated figures! Have a wonderful day! :D
Answer:
144π or 452.16 units³
Step-by-step explanation:
The formula for volume of a cylinder is 
. We can use the given values for radius and height to find the volume of the cylinder.
<h3>Finding the Volume</h3>
The volume of the cylinder is 144π or 452.16 units³.
The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.
Especially, he has been credited with proving the following five theorems: a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same; the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.
In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.
In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a theorem and is maximum extensively used in the domain of science.
2-1
and interval = [4]
since, function fext is continuous in ginen
interval. And also
+(4) = 42+4
4-1
=
20 = 6667
$(5/4) = ($145/2
stone-1
= 5.833
simle, f(4) > $(5/2), hence Intermediate
Theorem & applies to the indicated
proved.
Now,
= 6
C-1
C-5c +6 = 0
C=2 or c=3
1=
3 or
C= 2, 3
<= 2
Learn more about theorem here brainly.com/question/26594685
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