Let f open parentheses x close parentheses equals ln open parentheses x squared close parentheses space space space a n d space space space g open parentheses x close parentheses equals square root of e to the power of 3 x end exponent end root. Find f o g open parentheses x close parentheses and its domain?
Answer:
[tex](f\ o\ g)(x) = 3x[/tex]
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
See comment for right presentation of question
Given
[tex]f(x) = ln(x^2)[/tex]
[tex]g(x)=\sqrt{e^{3x}}[/tex]
Solving (a): (f o g)(x)
This is calculated as:
[tex](f\ o\ g)(x) = f(g(x))[/tex]
We have:
[tex]f(x) = ln(x^2)[/tex]
[tex]f(g(x)) = \ln((g(x))^2)[/tex]
Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]
[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]
Evaluate the square
[tex]f(g(x)) = \ln(e^{3x})[/tex]
Using laws of natural logarithm:
[tex]\ln(e^{ax}) = ax[/tex]
So:
[tex]f(g(x)) = \ln(e^{3x})[/tex]
[tex]f(g(x)) = 3x[/tex]
Hence:
[tex](f\ o\ g)(x) = 3x[/tex]
Solving (b): The domain
We have:
[tex]f(g(x)) = 3x[/tex]
The above function has does not have any undefined points and domain constraints.
Hence, the domain is: [tex]-\infty < x < \infty[/tex]
Quincy is having a sale at his store. He is selling a table for $450. If the sales tax is 8.5%, then how much will a customer need to pay in taxes if they buy the table?
Answer:
488.25
Step-by-step explanation:
What is the value of the expression 2[3(4^2+1)]-2^3?
Answer: 94
Step-by-step explanation: use photo math :)
If AB = 4 centimeters, which is closest to BC?
Options
4.7 cm
3.4 cm
2.5 cm
2.1 cm
in my opinion it is 3.4 cm because in any case it is a right triangle,then you can see whith the naked eye that AB is longer
Need help with these questions
Answer:
Area = 31.5 units²
Step-by-step explanation:
Area of the triangle = ½ × base × height
base = 9
height = 7
Substitute
Area = ½ × 9 × 7
Area = ½ × 63
Area = 31.5 units²
Use substitution to find Limit of StartStartFraction cosine (StartFraction pi x Over 4 EndFraction) OverOver x + 1 EndEndFraction as x approaches 3.
ANSWER: C
Answer:
C
Step-by-step explanation:
- square root 2 / 8
[tex]\bold{ \lim_{x \to 3} \frac{cos(\frac{\pi x}{4} )}{x+1} } = \bold{-\frac{\sqrt{2} }{8} }[/tex] , the correct answer is option (C)
What is limit?"A limit is the value that a function approaches as the input approaches some value."
What is substitution in mathematics?"Substitution is the process of replacing an algebraic letter with its value. "
Given: [tex]\lim_{x \to 3} \frac{cos(\frac{\pi x}{4} )}{x+1}[/tex]
By substitution the value of limit,
[tex]\lim_{x \to 3} \frac{cos(\frac{\pi x}{4} )}{x+1}[/tex]
= [tex]\frac{cos(\frac{\pi (3)}{4} )}{(3)+1}[/tex]
= [tex]\frac{cos(\frac{3\pi}{4} )}{4}[/tex]
= [tex]\frac{-\frac{1}{\sqrt{2} } }{4}[/tex]
= [tex]-\frac{1}{4\sqrt{2} }[/tex]
= [tex]\bold{-\frac{\sqrt{2}}{8} }[/tex]
Hence, option (C) is the correct answer.
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h = -16t ^2 + 38t + 5.
Answer:
for rewrite in vertex form is -16(t-19/16)^2 + 441/16
for rewrite in intercept form is h= -16(t-5/2)(t+1/8)
Step-by-step explanation:
The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.25 inches what value is one standard deviation above the mean
Select the reason that supports the following statement.
Answer:
B. Subtraction property of equality
Step-by-step explanation:
If you subtract angle 3 from both sides, then angle two and angle four must be equal. The property you would be using is the subtraction property of equality.
Answer:
Subtraction property of inequality
Step-by-step explanation:
See
<2+<3=<3+<4As <3 is same on both sides We can cancel it out
The expression yields
<2=<4Name a pair of lines that are parallel
you didn't include the picture, so I cant see what the question is, sorry.
or if you mean any lines they just have to not intersect or combined at any point like the image I attached, that is parallel lines when they never touch.
Provide one reason for when you can use the distance formula.
Answer:
Draw a right triangle such that the distance between the two points is the hypotenuse. Hence, When you use the distance formula, you are calculating the length of the Hypotenuse of a right triangle.
27
The diagram shows a right-angled triangle and a quarter circle.
D
9 m
А
6 m
B.
The right-angled triangle ABC has angle ABC = 90°
The quarter circle has centre C and radius CB.
Work out the area of the quarter circle.
Give your answer correct to 3 significant figures.
You must show all your working.
Answer:
A ≈ 35.3 units²
Step-by-step explanation:
Calculate the radius CB using Pythagoras' identity in the right triangle.
CB² + AB² = AC²
CB² + 6² = 9²
CB² + 36 = 81 ( subtract 36 from both sides )
CB² = 45 = r²
Then area of quarter circle is
A = [tex]\frac{1}{4}[/tex] × πr² = [tex]\frac{1}{4}[/tex] × π × 45 ≈ 35.3
A figure has vertices at (-3,5), (-1,8), (1,5), (1,1), (-1,-2) and (-3,1). What is the correct name
of this figure?
Answer:
regular hexagon
Step-by-step explanation:
find three rational numbees between -2/5 and -1/5
Answer:
-3/10, -25/100, -3/8
Brainliest for correct answer
express 110111 base two to base ten
Answer:
zh
Step-by-step explanation:
Mr. Chow is buying rolls of paper for the school. This is a list of the suppliers, the size of their rolls, and their cost per roll. Supplier X sells 25 meter rolls for $18.98.
Supplier Y sells 30 meter rolls for $21.89.
Supplier Z sells 40 meter rolls for $29.59.
To the nearest cent, what is the cost per meter for a roll of paper from the LEAST expensive supplier?
A. $0.72 per meter
B. $0.73 per meter
O O O
C. $0.74 per meter
OD. $0.75 per meter
E. $0.76 per meter
Answer:
B.
Step-by-step explanation:
I rounded to the nearest cent and got the cost of 73 cents per meter.
julie wants to invest $3,000 into
a mutual fund that pays 7%
interest for 10 years. suppose
the interest were compounded
monthly instead of annually.
how much would the future
value of the investment
increase?
Answer:
$400
Step-by-step explanation:
The future value of the investment increase will be $6,028.98.
What is compound Interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Given:
P = $3000
R = 7%
T = 10 years
r = R/100
r = 7/100
r = 0.07 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 3,000.00[tex](1 + 0.07/12)^{(12)(10)[/tex]
A = 3,000.00[tex](1 + 0.0058333333333333)^{(120)[/tex]
A = $6,028.98
Hence, the future value will be $6,028.98.
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How would you describe a linear learning curve. Choose the best available answer. for each unit of time the performance improves a proportional amount for each unit of time the performance decreases a proportional amount the performer displays rapid initial improvement followed by a decline in the rate of improvement the performer displays little initial improvement followed a rapid increase in the rate of improvement none of the above
Answer:
My answer would be; the performer displays rapid initial improvement followed by a decline in the rate of improvement.
Step-by-step explanation:
Usually a learning curve means that struggles are occurring after time of understanding and if we were creating a linear graph of this learning curve, it would be decreasing.
39
x
27
Solve for x round to nearest 10th
Answer:
526.50
Step-by-step explanation:
39 x 27 = 1,053
1,053 divided by 2 = 526.5
rounded to the nearest tenth would be 526.50
(im not sure if its correct)
Answer:
whats the question
Step-by-step explanation:
Question Help
Fund A sells for $15 a share and has a 3-year average annual return of $0.25 a share. The beta value is 1.07.
Fund B sells for $17 a share and has a 3-year average annual return of $0.91 a share. The beta value is 0.77.
Jonquin wants to spend no more than $3600 investing in these two funds, but he wants to obtain at least $80
in annual revenue. Jonquin also wants to minimize the risk. Determine the number of shares of each fund that
Jonquin should buy.
Set up the linear programming problem. Let a represent the number of shares in Fund A, b represent the
number of shares in Fund B, and z represent the total beta value.
Minimize
z=0
subject to
15a + 17b
0.25a +0.91b
a 20, b20.
(Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.)
Answer:
sana all may jowa jowain na kita
pls helppppp it's hard :(
Answer:
The answer is A .
Step-by-step explanation:
Good luck ;)
Find the difference 0.2−0.05
Answer:
0.15
Step-by-step explanation:
:))))))))))))))))))))
Round .67832947 to the nearest thousandths (three decimal places)
A rectangular gate is made using 6 straight pieces of steel.the weight of the steel is 2.5 kg per metre . Work out the total weight of the steel gare
Answer:
150 kg
Step-by-step explanation:
here is the complete question
A rectangular gate is made using 6 straight pieces of steel.
5 m
12 m
The weight of the steel is 2.5 kg per metre.
Work out the total weight of the steel gate.
To solve this question determine the square root of 12 and 5
√169 = 13
5 + 12+ 5 + 12+ 13 + 13 = 60 m
total weight = 60 x 2.5 = 150kg
Please help me with this it’s confusing ,
Answer:
It’s the 4th one
Step-by-step explanation:
graph
[tex]y = - 2 - {e}^{ - \frac{ - x}{2} } [/tex]
what are the transformations??
Graph attached
Y intercept is at -3Miss Patterson is getting married soon. She would like to hire a professional who will
come to her house and do hair and makeup for the bridal party on her wedding day.
She has narrowed it down to two possible choices. A woman from Burlington Salon
charges an initial fee of $30 and then an additional $20 per hour. Alternatively, a team
from Beauty by Dirk offers a free consultation and then charges a higher hourly rate of
$30. If it takes a certain amount of time to finish everyone's hair and makeup, Miss
Patterson will end up paying the same amount either way. How much would Miss
Patterson end up paying?
a) Write a system of linear equations to represent this situation.
b) Graph that system (assume the graph is increasing by 10s rather than 1s).
C) Find the solution and explain what it means.
Answer:The first team
Step-by-step explanation:The first team charges least and 30 dollers a hour is alot if the time gets 5-10 hours.
Your welcome!
Don't you times by a thousand then times the answer
I got 60,000
Answer:
i think that's right
Step-by-step explanation:
What is the sum of just the fraction parts of 1 5/8 and 1 6/8?
Answer:
Just the fraction parts: 11/8 or 1 3/8
Step-by-step explanation:
1 5/8 + 1 6/8 = 3 3/8
Hopefully this helps :3 sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~