Use properties of exponents and logarithms to evaluate the expression as a rational number.

Use Properties Of Exponents And Logarithms To Evaluate The Expression As A Rational Number.

Answers

Answer 1

y= 1/16 is the solution of the equation  where y is [tex]e^{-2ln4}[/tex]

The expression is given to be [tex]e^{-2ln4}[/tex]

The formula is given to be [tex]e^{lnx} =x\\[/tex]

also it is given that ln[tex]e^{x}[/tex]=x

Now to find and evaluate [tex]e^{-2ln4}[/tex]

let y=[tex]e^{-2ln4}[/tex]

taking ln both sides,

ln y = ln[tex]e^{-2ln4}[/tex]

ln y= -2 ln4

ln y= ln 4^-2

Removing ln from both sides,

y = 4^-2

y=1/16

Thus , y= 1/16 is the solution of the equation

#SPJ9


Related Questions

The blueprint specifications for a machined part call for its thickness to be 3.145 in.

with a tolerance of +-0.010 in. Find the limit dimensions of the part?

Answers

The limit dimensions of the part are 3.135 inches and 3.155 inches

How to find the limit dimensions of the part?

The given parameters are

Thickness = 3.145 inches

Tolerance = 0.010 inches

The limit dimensions of the part are calculated as

Limit = Thickness +/- Tolerance

So, we have

Limit = 3.145 inches +/- 0.010 inches

Expand the above expression

So, we have

Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)

Evaluate the sum

Limit = (3.135 inches, 3.155 inches)

Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches

Read more about dimensions at

https://brainly.com/question/19819849

#SPJ1

Consider 2 cylinders. The volume of these two cylinders are. If another cross section is taken at a different height, the areas of the cross sections will be

Answers

The volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.

The formula for the volume of a cylinder is given as:

V=π r² h

Now from the figure,

We have, for the first cylinder the height is 16 units and the radius is 7 units.

Hence,

V = 22/7 × 7² × 16

V = 22/7 × 7 × 7 × 16

V = 2424

Therefore the volume of the two cylinders is 2424. The area of the cross-section will be equal if another cross-section is obtained at a different height.

Learn more about the Volume of a cylinder here:

brainly.com/question/20531647

#SPJ9

The length of a rectangle is nine more than triple the width. If the perimeter is 154 inches, find the dimensions.

Answers

Answer:

Length = 60 inches

Width = 17 inches

Step-by-step explanation:

Let width = w

Length = 3w + 9

Perimeter = 154

Perimeter = 2(length + width)

2(3w + 9 + w) = 154

8w + 18 = 154

8w = 154 - 18

8w = 136

w = 136/8

w = 17 inches

Length = 3w + 9 = 3(17) + 9 = 60 inches

Confused on Math
Solve the Systems
x+2y+2z=-2
2x-y-2z=-5
x+2y+4z=0
x=?
y=?
z=?

Answers

Answer:

Step-by-step explanation:

"Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator."
Can someone please explain the answer to me

Answers

Step-by-step explanation:

[tex] \frac{1}{ {x}^{ \frac{ - 1}{3} } } \times \frac{1}{3x} \\ \frac{1}{ {3x}^{ \frac{2}{3} } } \\ \frac{1}{ 3\sqrt[3]{x {}^{2} } } [/tex]

Can somebody help me if you know what this is

Answers

Answer:The LCM of 15 and 20 is 60.

Step-by-step explanation: I used the internet/gggle

Given [tex]$\triangle RST \cong \triangle XYZ$[/tex]. Points [tex]$P$[/tex] and [tex]$W$[/tex] lie on [tex]$ST$[/tex] and [tex]$YZ$[/tex], respectively. Which of the following statements are true?
A) If [tex]$P$[/tex] is the midpoint of [tex]$\overline {ST}$[/tex] and [tex]$W$[/tex] is the midpoint of [tex]$\overline {YZ},$[/tex] then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

B) If [tex]$\overline {RP}$[/tex] bisects [tex]$\angle SRT$ and [tex]$\overline {XW}$[/tex] bisects [tex]$\angle YXZ$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

C) If [tex]$RP=XW$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

D) If [tex]$\overline {RP}\perp\overline {ST}$[/tex] and [tex]$\overline {XW}\perp\overline{YZ}$[/tex], then [tex]$\triangle RSP\cong \triangle XYW$[/tex].

Answers

The triangles ΔRST and ΔXYZ are congruent, then all the same construction make triangles congruent. All the options are correct.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If two triangles are congruent, then the ratio of the corresponding sides will be one.

The triangles ΔRST ≅ ΔXYZ. Points P and W lie on ST and YZ, respectively.

The diagram is given below.

A) If P is the midpoint of ST and W is the midpoint of YZ then ΔRSP ≅ ΔXYW is true.

B) If RP bisects ∠SRT and XW bisects ∠YXZ, then ΔRSP ≅ ΔXYW is true.

C) If RP = XW, then ΔRSP ΔXYW is true.

D) If RP ⊥ ST and XW ⊥ YZ, then ΔRSP ≅ ΔXYW is true.

All the options are correct.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Transitive Property of Equality
If a +5=b+3 and a +5 = 12, then b + 3 =?

Answers

b+3=12

because a+5=b+3 and a+5=12 which means b+3 must be 12 as well

Evaluate 4|-2| - |-3|
5
-5
11

Answers

Answer:

5

Step-by-step explanation:

4(|−2|)−|−3|

=(4)(2)−|−3|

=8−|−3|

=8−3

=5

The sum of three times a number and nine is 12 

Answers

Answer:

1

Step-by-step explanation:

let the number be n

3n + 9 = 12

3n = 12 - 9 = 3

n= 3/3

n= 1

The population of a town increased from 3,250 in 2008 to 4,300 in 2010. Find the
absolute and relative (percent) increase.

Answers

The absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.

Here, we are given that the population of a town increased from 3,250 in 2008 to 4,300 in 2010.

The absolute change can be calculate as-

Final population count - initial population count

= 4,300 - 3,250

= 1,050

Thus, absolute increase = 1,050

Now, the percentage increase can be calculated as follows-

percentage change = absolute change in population/ initial population count × 100

= 1,050/ 3,250 × 100

= 10500/ 325

= 32.3%

Thus, the absolute change in the town's population from 2008 to 2010 is 1,050 and the percentage change is 32.3%.

Learn more about percentage change here-

https://brainly.com/question/11360390

#SPJ9

Which of the following represents "the square of the sum of a number and 4 is 36"?
Ox²+42=36
(x+4)2 = 36
Ox²+4=36

Answers

Answer:

[tex](x + 4)^{2}[/tex] = 36

Step-by-step explanation:

So the "sum of a number and 4" is what gets squared and that together is equal to 36.

Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.

Answers

The length of both UV and ST is [tex]3\sqrt{2}[/tex] and hence they both are congruent.

Here, we are given two lines- UV and ST.

We can find the length of the lines using distance formula. According to distance formula, distance between two points- (x1, y1) and (x2, y2) is given as-

[tex]\sqrt{(x2-x1)^{2} + (y2 - y1)^{2} }[/tex]

Here, for UV,

the two endpoints are- (1,0) and (4,3)

thus, the length of UV will be-

[tex]\sqrt{(4-1)^{2} + (3 - 0)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (3 )^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]3\sqrt{2}[/tex]

Similarly, the two endpoints of ST are- (-2,-1) and (1,-4)

thus, the length of UV will be-

[tex]\sqrt{(1+2)^{2} + (-4 +1)^{2} }[/tex]

= [tex]\sqrt{(3)^{2} + (-3)^{2} }[/tex]

= [tex]\sqrt{9 + 9 }[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]3\sqrt{2}[/tex]

So we can see that UV = ST = [tex]3\sqrt{2}[/tex], which means that both of them are congruent. Hence, option 1 is the correct answer.

Learn more about the distance formula here-

https://brainly.com/question/7243416

#SPJ1

Your question was incomplete. Check for the missing figure below.

name the relationship, corresponding laternate interior alternate exterior same side interior vertical linear

Answers

Answer:

see explanation

Step-by-step explanation:

the relationship between angles a and b

they are alternate interior angles

these angle pairs are on opposite ( alternate) sides of the transversal and are in between ( in the interior of )the parallel lines.

will give brainliest if correct

Answers

The value of f(5) is 4375.

What is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

f(1)= 7,

f(n) = 5f(n-1)

f(2) = 5f(1)

     =5*7

f(2)= 35

f(3) =  5f(3-1)

f(3) =  5f(2)

f(3) =  5*35

f(3) = 175

f(4) =  5f(4-1)

f(4) =  5f(3)

f(4) =  5*175

f(4) = 875

f(5) =  5f(5-1)

f(5) =  5f(4)

f(5) =  5*875

f(5) = 4375

Hence, the value of f(5) is 4375.

Learn more about function here:

https://brainly.com/question/12431044

#SPJ1

A can of soda takes an average (mean) of 26 minutes to move through an assembly line. If the standard deviation is 2 minutes and the distribution is normal, what is the probability that the can will take over 29 minutes?

Answers

The probability that a can will take more than 29 minutes is approximately 0.66807

How can the probability of an event be determined in a normal distribution?

The mean time taken by the soda to move through the assembly line = 26 minutes

The standard deviation of the time it takes = 2 minutes

Required: The probability that the can takes more than 29 minutes

Solution: The Z-Score formula is presented as follows;

[tex]Z = \frac{x - \mu}{ \sigma} [/tex]

The Z-Score of a can that takes 29 minutes is given as follows;

[tex]Z = \frac{29 - 6}{ 2} = 1.5[/tex]

Which gives;

Z = 1.5

The probability P(x < Z) obtained online or from the Z-Score table gives;

P(x < 1.5) ≈ 0.93319

Which gives;

The probability that the can will take more than 29 minutes P(x > Z) ≈ 1 - 0.93319 = 0.66807

Learn more about the Z-Score table here:

https://brainly.com/question/25638875

#SPJ1

How many 4/13 pound boxes of cereal can be made from 11,804 pound of cereal?

Answers

The answer is 3,950 boxes

Solve the following proportion for 8/11 = v/6 .
Round your answer to the nearest tenth.

Answers

Answer:

v = 4.4

Step-by-step explanation:

Let's solve your equation step-by-step.

8/11 = v/6

Step 1: Cross-multiply.

8/11 = v/6

(8)*(6)=v*(11)

48=11v

Step 2: Flip the equation.

11v=48

Step 3: Divide both sides by 11.

11v/11 = 48/11

v= 48/11

v = 4.4

A blogger found that the number of visits to her Web site increases 5.6% annually. The Web site had 80,000
visits this year. Write an exponential model to represent this situation. By what percent does the number of
visits increase daily? Explain how you found the daily rate.

Answers

f(t) = 80,00[tex](1+ 0.056)^{t}[/tex] is the exponential function that represents the model. The number of visits increase by 0.015% daily.

Here, we are given that a blogger found that the number of visits to her Web site increases 5.6% annually.

The exponential function is given as-

Final value = initial value [tex](1 + r)^{t}[/tex]

where r = rate of change

and t = time

here, r = 5.6%

r = 0.056

Further, the Web site had 80,000 visits this year ⇒ initial value = 80,000

Thus, we can get the following function-

f(t) = 80,00[tex](1+ 0.056)^{t}[/tex]

where f(t) represents the views after t years.

Now, since we are given that the views increase by 5.6% in 1 year

and 1 year = 365 days

⇒ daily rate = 5.6/365

= 0.015

Thus, the number of visits increase by 0.015% daily.

Learn more about exponentials here-

https://brainly.com/question/2456547

#SPJ9

-5•g(4)-1 If g(x)=1-3/4x

Answers

The value of -5*g(4)-1 is 9.

It is a question of functions.

Here, g is a function of x.

Function

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Let X and Y be any two non-empty sets; mapping from X to Y will be a function only when every element in set X has one end, only one image in set Y.

Given that:-

g(x) = 1 - (3/4)x

We have to find the value of  -5*g(4)-1

First we will find g(4),

g(4) = 1 - (3/4)*(4) = 1 - 3 = -2

-5*g(4) - 1 = -5*(-2) - 1 = 10 - 1 = 9

Hence, the value of -5*g(4) - 1  is 9.

To learn more about function, here:-

https://brainly.com/question/12431044

#SPJ1

Which statement about AABC and ADEF is true?

Answers

Answer: D.

hope this helps

9888-1111+4444
...........

Answers

Answer:

the answer is 13,221 ...........

Answer:

13221...........

Step-by-step explanation:

9888-1111=8777

8777+4444=13221

the length of a rectangle is three more than double the width. if the perimeter is 126 inches, find the dimensions.

Answers

The dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.

Leth the width of the revtangle be x.

According to the given question.

The perimeter of the rectangle is 126 inches.

The length of the rectangle is three more than double the width.

⇒ Length of the rectangle  = 3 + 2x

Now, according to the given conditions we can say that

Perimeter of the rectangle = 2( length + width)

⇒ 126 = 2(3 + 2x + x)

⇒ 126  = 2(3 + 3x)

⇒ 63  = 3 + 3x

⇒ 63 - 3 = 3x

⇒ 60 = 3x

⇒ x = 20 inches

Therefore, the length of the rectangle = 3 + 2(20) = 3 + 40 = 43

Hence, the dimensions of the rectangle are 43inches and 20inches if the perimeter of the rectangle is 126 inches.

Find out more information about perimeter here:

https://brainly.com/question/6465134

#SPJ1

Dave and Sandy Hartranft are frequent flyers with a particular . They often from City A to City a of 840 On particular tripthey wirdand the flight takes 2 hoursThe return trip, with the wind behind them, only takes 1 1/2 * t hoursthe wind speed is the same on tripthe wind and find the speed of the plane in still air The wind speed ismph The speed of the plane ismph

Answers

It should be noted that the wind speed is 70km per hour and the plane speed is 490km per hour.

How to illustrate the information?

Based on the information given, the following an be illustrated.

Let P = speed of plane

Let w = speed of wind

The appropriate equation will be:

(P + W) (3/2) = 840 ....... i

(P - W) × 2 = (840 / 2) ...... ii

P + W = 560 .....i

P - W = 420 ......ii

Subtract the equations

2P = 980

P = 980 / 2 = 490

P + W = 560

490 + W = 560

W = 560 - 490

W = 70

Therefore, the wind speed is 70km per hour and the plane speed is 490km per hour.

Learn more about speed on:

brainly.com/question/13943409

#SPJ1

a rectangular room measures 17 feet by 6 feet. find the cost of installing a strip of wallpaper around the room if the wallpaper costs $0.94 foot.

Answers

Answer:

$95.88

Step-by-step explanation:

multiply 6 by 17 and get 102

multiply 102 by 0.94 and get 95.88

List the domain and range of the relation.
{(5,-3), (2.2), (0, -3), (2.1) (5,3)}

Answers

The domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

The domain of a function is the set of inputs that are accepted by the function. The range, also known as the codomain, is the set of all the output values of the function.

Here, we are given a relation with the following set of solutions-  

{(5,-3), (2,2), (0, -3), (2,1) (5,3)}

We know that all x values will form the domain and all the y values will make up the range.

Here the x values are: 5, 2, 0, 2, 5

and the y values are: -3, 2, -3, 1, 3

Thus, the domain of the relation is x = {5, 2, 0, 2, 5} and the range is y = {-3, 2, -3, 1, 3}

Learn more about domain and range here-

https://brainly.com/question/2264373

#SPJ9

Which expression shows another way to write -2/5 divided by 3/2?

Answers

The expression that shows another way to write -2/5 divided by 3/2 will be -2/5 ÷ 3/2.

How to calculate the value?

It should be noted that an expression simply shows the relationship between the variables.

Therefore, the expression that shows another way to write -2/5 divided by 3/2 will be:

= -2/5 ÷ 3/2

= -2/5 × 2/3

= -4/15.

Learn more about expressions on:

brainly.com/question/22048677

#SPJ1

HELLP

Find the coordinates of the point 3/10 of the way from A to B

The coordinates of the point
3/10 of the way from A to B are

Answers

Step-by-step explanation:

this is similar to the complete approach to find the midpoint. just instead of 1/2 we are looking for 3/10 of the distance.

the general approach is

A + (B - A)×factor

factor can be 1/2 or 3/10 or 7/10 or 24/29 or ...

so, we have

(-3, -6) + ((9 - -3)×3/10, (5 - -6)×3/10) =

= (-3, -6) + (12×3/10, 11×3/10) =

= (-3, -6) + (3.6, 3.3) = (0.6, -2.7)

the point 3/10 of the way from A to B is

(0.6, -2.7)

Show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are real and they can not be equal unless a=b=c

Answers

Expanding out the equation, we get

[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]

Considering the discriminant,

[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]

This is always non-negative, meaning the roots are real.

The roots are equal if and only if the discriminant is 0, which is when a=b=c.

Suppose the tangent line to the curve
y = f(x)
at the point
(1, 1)
has the equation
y = 7 − 6x.
If Newton's method is used to locate a solution of the equation
f(x) = 0
and the initial approximation is x1 = 1, find the second approximation x2.

Answers

Answer:

  x2 = 7/6

Step-by-step explanation:

You want the second approximation using Newton's method, given that the first approximation is x1=1 and the function tangent at x=1 is y=7-6x.

Newton's method

Newton's method approximates the function by its tangent line at the point (x, f(x)). That is, the second approximation is the x-intercept of the tangent line y = 7 -6x. That value of x is ...

  0 = 7 -6x

  6x = 7 . . . . . add 6x

  x = 7/6 . . . . divide by 6

The second approximation is x2 = 7/6.

Other Questions
question mode fill in the blank question fill in the blank question. the greek canon established by artists and architects used the principle known as , meaning the correspondence of opposite parts in size, shape, or position. international institutions and domestic compensation: the imf and the politics of capital account liberalization what is heterogeneous Which describes this energy transformation from the turning turbine to electricity?A. mechanical energy into electric energyB. nuclear energy into electric energyC. thermal energy into electric energyD. chemical energy into electric energy in testing inventory at an audit client in the retail industry, you note that some of the inventory is contracted to be held on consignment. as a result, which financial statement assertion is now relevant? you gather some data about the use of a surgical checklist in your operating rooms and have an idea for an improvement. at the next months meeting, you present the idea to your colleagues. how to write 673465 in standerd form Which line from the excerpt supports the conclusion that Odysseus cares for his men?They fell in, soon enough, with Lotus-Eaters,offering the sweet Lotus to our friendsthey longed to stay forever, browsing onI drove them, all three wailing, to the ships, what is the solution to this problem? 2 | x+5 | =4 cornel and deanna resolve their dispute over the subsidence of cornels real property due to deannas excavation for an irrigation pond by having a neutral third party render a binding decision. this is which field is the scientific study of human functioning with the goals of discovering and promoting strengths and virtues that help individuals and communities to thrive? please choose the correct answer from the following choices, and then select the submit answer button. answer choices cognitive psychology positive psychology evolutionary psychology neuroscience Cellular respiration transforms glucose and oxygen into carbon dioxide, water, and energy. c6h12o6 6o2 6co2 ?h2o energy based on the law of conservation of matter, what is the missing coefficient for water? one seventh times the absolute value of the quantity x minus 3 end quantity minus 2 equals 9 5/6=1/3+d omg help mee Which two sentences taken together provide theBEST evidence to support the idea that manynutritious alternatives exist within each of the foodgroups? find the rise and the run do elements in your body occur as free elements? I will Mark Brainlist ...Find the length of p. Please Help its Math question i will Mark Brainlist !! To convert kilograms to pounds, Abby halves the number of kilograms, n, then subtracts 10% from the result of that calculation, whereas Renato subtracts 10% first and then halves theresult. (a) Write an algebraic expression for each method.Abby's expression:Renato's expression:(b) Do the methods give the same answer? what caused native populations to develop distinct and increasingly complex societies by adapting to and transforming their diverse environments?