Answers
1/3 ln(x) + ln(2) - ln(3) = 3
Recall that [tex]m\log_b(n)=\log_b(n^m)[/tex], so
ln(x ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
[tex]\log_b(m)+\log_b(n)=\log_b(mn)[/tex]
[tex]\log_b(m)-\log_b(n)=\log_b\left(\dfrac mn\right)[/tex]
Then
ln(2/3 x ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant e. (I'm using exp(x) = e ˣ so I can write it all in one line.)
exp(ln(2/3 x ¹ʹ³)) = exp(3)
Now exp(ln(x)) = x for all x, so this simplifies to
2/3 x ¹ʹ³ = exp(3)
Now solve for x. Multiply both sides by 3/2 :
3/2 × 2/3 x ¹ʹ³ = 3/2 exp(3)
x ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(x ¹ʹ³)³ = (3/2 exp(3))³
x = 3³/2³ exp(3×3)
x = 27/8 exp(9)
which is the same as
x = 27/8 e ⁹
Related Questions
Find the perimeter of quadrilateral ABCD. Round your answer to the nearest hundredth. A(3, 5) B(1, 3) C(3, -1) D(5, 3)
Answers
Answer:
Perimeter = 4(√2 + √5) units
Step-by-step explanation:
Given:
Quadrant of 4 points;
A(3, 5) B(1, 3) C(3, -1) D(5, 3)
Find:
Perimeter
Computation:
Distance = √(x1 - x2)² + (y1 - y2)²
Distance between AB = √(3 - 1)² + (5 - 3)²
Distance between AB = √4 + 4
Distance between AB = 2√2 units
Distance between BC = √(1 - 3)² + (3 + 1)²
Distance between BC = √4 + 16
Distance between BC = 2√5 units
Distance between CD = √(3 - 5)² + (-1 - 3)²
Distance between CD = √4 + 16
Distance between CD = 2√5 units
Distance between DA = √(5 - 3)² + (3 - 5)²
Distance between DA = √4 + 4
Distance between DA = 2√2 units
Perimeter = sum of all sides
Perimeter = 2√2 + 2√5 + 2√2 + 2√5
Perimeter = 4√2 + 4√5
Perimeter = 4(√2 + √5) units
What is the missing value?
54
30%
100%
?
Answers
Answer:
54
Step-by-step explanation:
y divided by the product of 3 and x
Answers
Answer: y/3x
Step-by-step explanation: 3 times x is 3x, so y/3x
The length of a rectangular swimming pool is exactly three times as long
as its width. If the pool has a perimeter of 472m find the width of the pool
Answers
Answer:
59m
Step-by-step explanation:
Length= 3 × ( width)
But perimeter= 2width + 2 Lenght= 472
Let length= X
Width= Y
X= 3Y.........eqn(1)
2X + 2Y= 472........eqn(2)
Substitute X= 3Y in eqn(2)
2(3Y) + 2Y = 472
6Y + 2Y= 472
8Y= 472
Y= 59 m
Hence, the width of the pool is 59 m
I have ¾ of an hour to finish 6 homework assignments. How much time can I spend on each assignment?
Answers
Answer:
7.5 min for each assignment
Step-by-step explanation:
1 hour is 60 minutes, and there are four 15 minute intervals. So, if there are four intervals of 15 minutes that add up to 60, just take three of them and put them over four:
15 ⋅ 15⋅ 15/ 15⋅ 15 ⋅ 15 ⋅ 15= 45 /60
Or we could multiply one hour, or 60 minutes, by 3 /4 .
60 ⋅ 3/ 4 = 60 /1 ⋅ 3 /4 = 60 ⋅ 3/ 4 ⋅ 1 = 180 /4 =45
Three fourths of an hour is 45 minutes.
to find time for each assignment =45/6
7.5 min
im almost done with this hw. plz help!!! give explanation if you actually know the answer so ik u dont just want points....
Answers
Answer:
D
Step-by-step explanation:
1/12 X 110 = .0833333333 x 110 = 9.16
D. 9
Step-by-step explanation:
110÷12 = 9.1 however just round down to 9
since there are 12 equal pieces of the pie graph you would also count yellow and not exclude it
Write a compound interest function to model the following situation. Then, find the balance after the given number of years. $16,000 invested at a rate of 1.2% compounded monthly;7 years
A. A=16,100 (1.001)^7t; $17,469
B. A=16,100 (1.1)^12t; $6,766,377,209
C. A=16,100(1.001)^12t; $17,510
D. A=16,000(0.001)^12t; $24,150
Answers
Answer:
The answer to this question is:
A = 16,100(1.001)12t; $17,510
Step-by-step explanation:
The model function for compound interest is: [tex](16000[1.001]^{12t})[/tex]
The balance after 7 years will be $17409.
How to calculate the compound interest if it is compounded monthly?Let, P = the principle amount
r = the rate of interest, compounded monthly
t = the time period
Therefore, the amount will be
[tex]= P(1 + \frac{r}{1200})^{12t}[/tex]
Given, the invested amount is $16000.
The rate of interest is 1.2%, compounded monthly.
Total duration of investment is 7 years.
Therefore, the model function of this compound interest is:
= [tex]= (16000[1 + \frac{1.2}{1200}]^{12t})\\= (16000[1 +0.001]^{12t})\\= (16000[1.001]^{12t})\\[/tex]
The amount will be
[tex]= (16000[1.001]^{12t})\\= (16000[1.001]^{84})\\= 17409[/tex]
Therefore, after 7 years, the amount will be $17409.
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Can someone please help me out with this? I can’t figure out exactly what they are saying.
Answers
Answer:
Its English :))))))
Answer:
i would go fro the first one
Step-by-step explanation:
its asking whitch maple have the more absolute deviations
5). Find the surface area.
3.6 yd
7 yd
3 yd
2 yd
Answers
Please Help!!!!!!!!!!
Answers
Answer: Yes, because there are at least two claims
Step-by-step explanation:
Ur welcome 3>
Timothy swam 24 laps . Frank swam 72 laps. How many times as many laps did frank swim than timothy?
Answers
Answer:
3
Step-by-step explanation:
[tex]72[/tex]÷[tex]24=3[/tex]
3/4(1/4x + 8) - (1/2x + 2) = 3/8(4-x) - 1/4x
What is the value of x?
Answers
Step-by-step explanation:
0.75(0.25x+8)-(0.5x+2)=0.375(4-x)-0.25x
0.1875x+6-0.5x-2=1.5-0.375x-0.25x
0.1875x-0.5x+0.375x+0.25x=1.5-6+2
0.3125x=-2.5
x=-2.5/0.3125
x= -8
What is the constant in 24y-8
Answers
Answer:
8 ( 3 − 1 )
Step-by-step explanation:
Please help with this math work!! Solve for x , Assume which appear tangent are tangent
Answers
Answer:
photo is not clear so i can't help u
Answer:
i cant really see the q so sorry but goodluck <3
  help needed pls
Answers
Find the volume of the following figure using unit cubes.
Answers
Answer:
Volume : 94
Step-by-step explanation:
2(4 x 5) = 40
2(3 x 5) = 30
2(3 x 4) = 24
------------------
40 + 30 + 24 = 94
Find the 59th term of the arithmetic sequence 26, 17, 8, ...
Answers
26 - 522 = -496
Answer:
-496
Step-by-step explanation:
it's right :)
Complete the statement. Enter your answer in the box. Use fraction strips or number lines to help.
Answers
Answer:
you did not post a question?
Step-by-step explanation:
Given g(x) = -5x – 4, solve for x when g(x) = 1.
Answers
Answer:
g (1) = -5(1) -4
-5-4
-9............. .......
Step-by-step explanation:
-5(1)-4=-5-4=-9 Answer
hope it helps
what numbers multiply to give 100 and when summed up give 25................................
Answers
Isaiah ran 100 meters on a 200 meter track. He started running on the 19 meter mark. On what Mark did he finish his run
Answers
Answer:
119
Step-by-step explanation:
19+100=119
Housing Price.The file calledsaratoga.JMPcontains data on 1728 houses in Saratoga, NewYork in the year 2006. The dataset includes many features of houses such as the selling price($), total living area (square feet), age (years), value of the land ($1000) the house was buildon, number of bedrooms and bathroom. We want to predict the selling price of a house ($)based on the total living area.(a) Identify the response variable (y): (Choose one.)i. total priceof all houses in the U.S.ii. average priceof houses in the U.S.iii. priceof a house in Saratoga, N.Y.
Answers
Answer:
iii. priceof a house in Saratoga, N.Y.
Step-by-step explanation:
In this question, we take a sample from house prices of 1728 houses in Saratoga, New York.
Since only houses from Saratoga are part of the sample, the response variable will be related only to Saratoga.
In this question:
Sample to find house prices in Saratoga, which is the variable of interest. The correct answer is given by option iii.
What fraction of the whole are the blue piece, the orange piece, the red piece, and the purple piece. How do you know?
Answers
blue: 1/4
Purple: 1/4
Answer:
blue piece is 1/2 because it takes up half of the square, the purple is only 1/4 because it would take 4 purple to fill the big square and the orange is half of the purple so it takes double of pieces so 8 pieces which is 1/8
The point at which two sides of a polygon meet is called a(n).
OA) segment
OB) face
OC) edge
OD) vertex
Answers
Answer:
its called a vertex
Step-by-step explanation:
The line segments that form a polygon are called the sides of a polygon.
A point where two sides meet is a vertex.( in plural form is vertices)
Find the 11 term of the following geometric sequence.
10, 40, 160, 640, ...
Answers
Answer:
099 787 989
Step-by-step explanation:
In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest
tenth of a cm, how long is that leg?
Answers
Answer:
36.5 cm
Step-by-step explanation:
The Adjacent leg is 36.5 cm
What are trigonometric functions?"The trigonometric functions (also called circular functions, angle functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths."
What is hypotenuse, opposite and adjacent side of a right angled triangle?"In a right angled triangle, the hypotenuse is the longest side, an opposite side is the one across from a given angle, and an adjacent side is next to a given angle."
We have
Hypotenuse (AB) = 58 cm
Angle θ = 51 degree
From the figure, by using trigonometric functions
Cos θ = [tex]\frac{BC}{AB}[/tex]
we have to find BC
Cos [tex]51^{0}[/tex] = [tex]\frac{BC}{AB}[/tex]
We have, AB = 58 cm
BC = AB cos [tex]51^{0}[/tex]
⇒BC = 58 . cos [tex]51^{0}[/tex]
⇒BC = 36.50 cm
⇒BC = 36.5 cm
Hence, Adjacent leg is 36.5 cm
Learn more about trigonometric functions here
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If y varies directly as x and x=6 when y = 3 what will y be when x = 10
Answers
Answer:
y = 5
Step-by-step explanation:
What is the value of x?
Answers
Answer: 15
Step-by-step explanation:
x-6/(x-6)+3 = x/x+5
The x in the equation is 15
A circular wheel has a diameter of 42 cm. How far will it roll in 5
revolutions?
Answers
Answer:
3.142
Step-by-step explanation:
Answer:
659.75 cm
Step-by-step explanation:
First, find the circumference with the formula C = 2[tex]\pi[/tex]r
The diameter is 42 cm, so the radius will be 21 cm
Plug in the radius into the equation and solve for C
C = 2[tex]\pi[/tex]r
C = 2[tex]\pi[/tex](21)
C = 131.95
Find how far it will roll by multiplying this by 5
131.95(5)
= 659.75
So, in 5 revolutions, it will roll 659.75 cm
What is the unit rate for the ratio 4/7: 8/21?
Answers
Answer:
The unit rate is 1.5
Step-by-step explanation:
Given
[tex]Ratio = 4/7 : 8/21[/tex]
Required
Determine the unit rate
To do this, we need to express the ratio as:
[tex]Ratio = m : 1[/tex]
Where m is the unit rate
[tex]Ratio = 4/7 : 8/21[/tex]
Express as fraction
[tex]Ratio = \frac{4/7 }{ 8/21}[/tex]
Solve
[tex]Ratio = \frac{4}{7} * \frac{21}{8}[/tex]
[tex]Ratio = 1.5[/tex]
Express as ratio
[tex]Ratio = 1.5 : 1[/tex]
Hence, the unit rate is 1.5