We use a property from an earlier question of yours [27174924], that
[tex]\displaystyle \int_a^b f(x) \, dx + \int_{f(a)}^{f(b)} f^{-1}(x) \, dx = b\,f(b) - a\, f(a)[/tex]
Note that
[tex]f(x) = \log_2(x^3+1) \implies f^{-1}(x) = \left(2^x - 1\right)^{1/3}[/tex]
[tex]a = 1 \implies f(a) = \log_2(1^3 + 1) = \log_2(2) = 1[/tex]
[tex]b = 2 \implies f(b) = \log_2(2^3 + 1) = \log_2(9)[/tex]
so that the exact value of the integral is
[tex]\displaystyle \int_1^2 \log_2(x^3 + 1) \, dx + \int_1^{\log_2(9)} \left(2^x - 1\right)^{1/3} = 2\log_2(9) - 1[/tex]
Now, observe that
[tex]8 = 2^3 < 9 < 2^{7/2} = 8\sqrt2 \approx11.3 \\\\ \implies 3 < \log_2(9) < \dfrac72 \\\\ \implies 6 < 2\log_2(9) < 7 \\\\ \implies 5 < 2\log_2(9) - 1 < 6[/tex]
so that
[tex]\left\lfloor 2\log_2(9) - 1 \right\rfloor = \boxed{5}[/tex]
Which term best describes the figure down below
Answer:
3rd option line segment RS
Step-by-step explanation:
....
Answer:
OPTION C: LINE SEGMENT RS
Can you assist me with this question ?
Answer:C.)8+28-10-35
1. Four letters, T, H, M, A, are placed in a hat. If one is randomly pulled out of the hat at at time, what is the
probability of the order spelling MATH?
How many different ways can the 4 letters be selected when order matters?
P(MATH) = ___
(Enter your answer as a reduced fraction using / for the fraction bar)
The probability of of the order spelling MATH is 1/24.
What is probability?Probability is the chance of happening something or the occurrence of something . We can also define the probability as the chance of occurring or the chance of selecting something from the total set of value. It is always ranges from 0 to 1 where 0 is minimum value and 1 is maximum value of probability.
Formula for probability is :
[tex]prabability(event) = \frac{Favourable \ outcomes}{Total \ outcomes}[/tex]
where, the total outcomes is the sample space of our given data or we can say the total number of values in the sample space.
In the question given,
The sample space is the different ways of arranging the letter which is equals to 4 factorial.
=> Sample space = 4! = 24
and the Favorable outcome is the word "MATH".
Thus, The probability is 1/24, because out of 24 of them only one can spell math.
To know more about probability, visit:
brainly.com/question/11234923
#SPJ1
20 points
Mabrey connects 3 pieces of clay end to end that are each 3/4 inch long. how many 3/16 inch pieces of clay can Mabrey cut?
Answer:
Mabrey can cut 4 3/16-inch pieces of clay
Step-by-step explanation:
3/4 × 3 = 9/12
3/16 can fit into 9/12 4 times perfectly
Find the measures of the complementary angles that satisfy each case. The first angle is 30 degrees greater than the measure of the second angle.
The measure of both complementary angles are __ and __.
Please help me!!
The measure of both complementary angle are 30 and 60 degrees.
How to find the measures of complementary angles?When the sum of two angles is equal to 90 degrees, they are called complementary angles.
In other words complimentary angles are angles that sum up to 90 degrees.
Therefore, the first angle is 30 degrees greater than the measure of the second angle.
Hence,
let
x = measure of the second angle
first angle = x + 30
Therefore,
x + x + 30 = 90
2x + 30 = 90
subtract 30 from both sides of the equation
2x + 30 = 90
2x + 30 - 30 = 90 - 30
2x = 60
divide both sides by 2
x = 60 / 2
x = 30
Therefore, the measure of both complementary angle are 30 and 60 degrees.
learn more on complementary angles here: https://brainly.com/question/24183652
#SPJ1
The tree in Carlos's backyard is 8.7 m high. How high is it in centimeters?
Be sure to include the correct unit in your answer.
Answer:
8.7m to centimeters means tou move the decimal to the right twice making it 8700cm
Rewrite x4y2 − 3x3y3 using a common factor.
3xy(x3y − x2y)
3xy2(x2 − x2y)
x2y(xy − 3xy2)
x2y2(x2 − 3xy)
The equivalent expression of x^4y^2 − 3x^3y^3 when rewritten using common factors is x^3y^2(x − 3y)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to rewrite the expression using a common factor?The expression is given as
x4y2 − 3x3y3
Rewrite the above expression properly
So, we have
x^4y^2 − 3x^3y^3
Factor out x^3 from the expression
So, we have
x^4y^2 − 3x^3y^3 = x^3(xy^2 − 3y^3 )
Factor out y^2 from the expression
So, we have
x^4y^2 − 3x^3y^3 = x^3y^2(x − 3y)
Hence, the equivalent expression of x^4y^2 − 3x^3y^3 when rewritten using common factors is x^3y^2(x − 3y)
Read more about expression at
https://brainly.com/question/22019327
#SPJ1
A 1/5 increase of 400
Answer:
1/5×400=80400+80=480 1/5 increase of 400=480100 POINTS PLS HELP !!!!
Answer these three questions:
9) X value range [-2/5,0] or [2,3]
b since I can't see a or c visablely) x>1
5) -5/3 ≤ x ≤ 2
6) The time interval by which the ball spends more than 1.5m above ground is about 0.263 <x< 1.166 seconds so about 1.397 seconds
9) To find the range of x value, you have to find the interception of these two solutions, and to do that, you have to find each of their solutions
To find the solution to 2x² ≥ 4x, you would first subtract 4x on both sides, resulting in 2x² - 4x ≥ 0. Then, you would factor to common terms, which are x and -2, the new inequality is 2x (x-2) ≥ 0. Then, you divide both 2x and 0 by 2. The new inequality is x (x-2) ≥ 0; you would then make everything ≥ 0. The solution is [- inf, 0] or [2, inf] for 5x² -13x -6 ≤ 0 you are basically doing the same thing for solving x which result in -2/5 ≤ x ≤ 3. With that said you find the interception of those 2 solutions which are [-2/5,0] and [2,3]. The first image should have a picture of the steps and a graph version of the work
b) To find the answer to x - 1/ (x+2) (x+3) > 0 you multiply both sides by (x+2) (x+3) you would then get x - 1 > 0. To islolate x you add 1 on both sides the final answer is x > 1
5) To solve 2x² + 3x + 1 ≤ 11x + 4x - x² you move 11x + 4x - x² on one side and simplify you would get 3x²
-x−10≤0. Then you split the second term into two terms which are 5x and -6x -> 3x² + 5 x - 6x - 10 ≤ 0 then you factor out the common terms in the terms you would then get (3x+5) (x-2) ≤ 0. Then you solve for x you would then get - 5/3 ≤ x ≤ 2. The new graph should show the solutions in graph form.
6) The first step is to create an inequality for the problem in this case it would be 7t - 4.9t > 1.5. At this point you move 1.5 on the left side to make 7t - 4.9t - 1.5 > 0 you would then multiply all terms on both sides by -1 to make -1.5 positive you would then get in standerd form 4.9t² -7t + 1.5 < 0. You would then factor with the quadratic formula after doing so you would get in its simplest form is (x - 1.166) (x - 0.263) < 0 then you would solve for x the time intervals that satisfy the scenario is about 0.263 ≤ x ≤ 1.166 then fine the difference between the solutions and that is about 1.937 seconds. The graph version is in the last picture.
HELP!!!!!!!!!! Question is posted belowwwwwwwww
Answer:
Step-by-step explanation:
bro its soo ezy A is 4 B is 6 C is 7 D IS 10 a is 30 b is 30 c is 60 d is 0
Two trains are barreling down the track! Unfortunately, they are on the same track and headed for col-
lision. The Orange Blossom Special left Sweet Town at 6 am traveling at a constant rate of 65 miles
per hour. The Early Bird left Wormville at 5 am traveling at a constant rate of 75 miles per hour. Sweet
Town and Wormville are 551 miles apart.
a) What is the exact time that the collision will occur?
B) From which town should they send the rescue vehicles? Why?
At 5 a.m., the Early Bird departed Wormville, maintaining a constant speed of 75 miles per hour collision at 9:30am and from Sweet Town they have to send the rescue vehicles.
Given that,
At 6:00 a.m., the Orange Blossom Special departed Sweet Town at a continuous 65 miles per hour.
At 5 a.m., the Early Bird departed Wormville, maintaining a constant speed of 75 miles per hour.
There are 551 miles between Wormville and Sweet Town.
We have to find the exact time that the collision will occur
Let Sweet town =ST and Wormville =W.
W⇒5am⇒75 mph
ST⇒6am⇒65 mph
W⇒6am⇒75 mph
ST⇒7am⇒65 mph
W⇒7am⇒75+75=150 mph
ST⇒8am⇒65+65=130 mph
W⇒8am⇒150+75=225 mph
ST⇒9am⇒130+65=195 mph
W⇒9am⇒225+75=300 mph
The Add both ST and W at 9am is 300+195=495 miles
We have 551 miles between Wormville and Sweet Town.
551-495=56 miles
The trains are 56 apart.
Therefore, at 9:25 am the train get collision.
From Sweet Town they have to send the rescue vehicles.
To learn more about miles visit: https://brainly.com/question/23245414
#SPJ1
The Orange Blossom Special train left Sweet Town at a constant 65 miles per hour at 6:00 a.m. The Early Bird left Wormville at five in the morning, keeping a continuous speed of 75 miles per hour. When a collision occurred at 9:30 am, they had to send the rescue vehicles from Sweet Town.
(a) The exact time that the collision will occur 9:30am
(b) The town should they send the rescue vehicles are Sweet Town.
The Orange Blossom Special left Sweet Town at a constant 65 miles per hour at 6:00 a.m.
The Early Bird left Wormville at five in the morning, travelling at a continuous pace of 75 mph.
Between Sweet Town to Wormville, there are 551 miles.
The precise moment of the collision must be determined.
Let Wormville be W and Sweet Town be ST.
W (Wormville) ⇒ 5am ⇒75 mph
ST (Sweet Town) ⇒6am ⇒65 mph
W (Wormville) ⇒6am ⇒75 mph
ST (Sweet Town) ⇒7am ⇒65 mph
W (Wormville) ⇒7am ⇒75+75 = 150 mph
ST (Sweet Town) ⇒8am ⇒65+65 = 130 mph
W (Wormville) ⇒8am ⇒150+75 = 225 mph
ST (Sweet Town) ⇒9am ⇒130+65 = 195 mph
W (Wormville) ⇒9am ⇒225+75 =300 mph
At 9:00 a.m., the addition of ST and W is 300+195 miles.
Between Wormville to Sweet Town, there are 551 miles.
551 - 495 = 56 miles
The trains are 56 apart.
Therefore, a train crash occurs at 9:25 am.
They must send the rescue vehicles from Sweet Town.
The trains at 6:00 a.m., the Orange Blossom Special departed Sweet Town at a continuous 65 miles per hour. At 5 a.m., the Early Bird departed Wormville, maintaining a constant speed of 75 miles per hour collision at 9:30am and from Sweet Town they have to send the rescue vehicles.
So,
(a) The exact time that the collision will occur 9:30am
(b) The town should they send the rescue vehicles are Sweet Town
To learn more about visit Miles :
brainly.com/question/11998442
#SPJ1
A car travel 275 miles in 5 hours . At this rate how many miles will the bus travel in 8 hours?
==================================================
Explanation:
Let's find the speed or rate of the car
distance = rate*time
rate = distance/time
rate = (275 miles)/(5 hours)
rate = 55 mph
If the bus traveled this same speed, and did so for 8 hours, then...
distance = rate*time
distance = (55 mph)*(8 hours)
distance = 440 miles
Write an expression that would have a value less than 3/4
Answer: 1/2
Step-by-step explanation:
1/2 is 2/4 which is smaller than 3/4
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the most accurate rate of speed Morris is traveling?
answer:48 miles per hour
A calculator displays 8.717E8. How do you write 8.717E8 in scientific notation?
Answer: 8.717 x 10^8
Step-by-step explanation:
Answer: 8.717 × 10^{8}
Step-by-step explanation:
hope this helps <3
What is the midpoint of the line segment?
Drag the coordinates to the boxes to correctly match the endpoints and midpoint
Using the midpoint formula, the midpoints of the following are:
(4, √2) and (-2, 5√2) --> M(1, 3√2)
(-⅔, ⅘) and (⅓, ½) --> (-1/6, 13/20)
What is the Midpoint Formula?The formula that is used to determine the coordinates of the midpoint of a line segment is called the midpoint formula, and it is expressed as:
M(x, y) = [(x1 + x2)/2, (y1 + y2)/2]
Find the midpoint between (4, √2) and (-2, 5√2):
Let,
(4, √2) = (x1, y1)
(-2, 5√2) = (x2, y2)
Plug in the values
M(x, y) = [(-2 + 4)/2, (5√2 + √2)/2]
M(x, y) = [2/2, (6√2)/2]
M(x, y) = (1, 3√2)
M(1, 3√2)
Find the midpoint between (-⅔, ⅘) and (⅓, ½):
Let:
(-⅔, ⅘) = (x1, y1)
(⅓, ½) = (x2, y2)
Plug in the values
M(x, y) = [(-⅔ + ⅓)/2, (⅘ + ½)/2]
M(x, y) = [(-⅓)/2, (13/10)/2]
M(x, y) = [(-⅓ × ½), (13/10 × ½)]
M(x, y) = (-1/6, 13/20)
In summary, using the midpoint formula, the midpoints of the following are:
(4, √2) and (-2, 5√2) --> M(1, 3√2)
(-⅔, ⅘) and (⅓, ½) --> (-1/6, 13/20)
Learn more about the midpoint formula on:
https://brainly.com/question/13115533
#SPJ1
Please help i need help
Answer:
7040 yards is that
Step-by-step explanation:
I don't know
Answer:
Step-by-step explanation:
5 miles=8800 yards
1 mile=8800÷5=1760 yards
4 miles=1760×4=7040 yards
An elephant can drink up to 6,400 fluid
ounces of water a day. How many gallons of
water can an elephant drink per day?
Answer: They require 18 to 26 gal of water. But they may also consume 40 gal
Step-by-step explanation:
1. Julianne found a job listed in the classified ads that pays a yearly salary of $41K. What is the
weekly salary based on this annual salary?
Julianne's weekly salary based on this annual salary is $788.46
The yearly salary that the job pays Julianne = $41K
No. of weeks in a year = 52 weeks
When referring to a Participant, the term Weekly Salary refers to the weekly rate of pay for services that the Employer had been providing to the Participant at the time of his or her termination from the Employer. According to the Employer's payroll records, the Weekly Salary of a Participant whose rate of pay for services is based on an annual rate shall be equivalent to 1/52 of the yearly such rate at the time of his or her Termination of Employment from the Employer.
Therefore, finding out the weekly salary of Julianne we get:
=Annual salary of Julianne/No. of weeks in a year
= 41000/52 = $788.46
Hence, Julianne's weekly salary based on this annual salary is $788.46
Learn more about arithmetic:
https://brainly.com/question/22260035
#SPJ9
Which is not a pair of congruent angles in the diagram below?
The pair of angles that is not a pair of congruent angles as shown in the diagram above is: ∠AEB ≅ ∠CDB.
What are Congruent Angles?Congruent angles are angles that have equal angle measure or angle measure that are the same. They are often indicated with the same number of marks in triangles.
In the triangles shown in the image, the following are pairs of congruent angles:
Angle ABE is congruent to angle DBC
Angle EAB is congruent to angle CDB
Angle AEB is congruent to angle DCB
Thus, angle AEB is not congruent to angle CDB.
Therefore, from the options given, the pair of angles that is not a pair of congruent angles as shown in the diagram above is: ∠AEB ≅ ∠CDB.
Learn more about congruent angles on:
https://brainly.com/question/2938476
#SPJ1
What kind of sequence is this?
-514, -514, -514, -514, ...
arithmetic. geometric. both. neither.
[tex]\: u_{1} - u_{0}= u_{2} - u_{1} \\ - 514 + 514 = - 514 + 514 \\ 0 = 0 \\ true \: so \: u_{n} \: arithmetic \: \: (d = 0)[/tex]
[tex] \frac{u_{1}}{u_{0}} = \frac{u_{2}}{u_{1}} \\ \frac{ - 514}{ - 514} = \frac{ - 514}{ - 514} \\ 1 = 1 \\ true \: so \: u_{n} \: geometric \: (r =1 )[/tex]
[tex]conclusion = \\ u_{n} \: is \: both \: arithmetic \: and \: geometric[/tex]
What does it mean to determine the two positive integers that each value is between??? I'm confused
Answer:
11. {7, 8}
12. {8, 9}
13. {8, 9}
14. {4, 5}
Step-by-step explanation:
You want consecutive integers that bracket each of the given irrational roots.
Square rootsA square root of an integer will be rational only if the integer is a perfect square. The first few perfect squares are ...
1² = 12² = 43² = 94² = 165² = 256² = 367² = 498² = 649² = 81You know these because you know your multiplication tables.
The square root of a number between these perfect squares will lie between the roots of the squares.
11. √5050 lies between the squares 49 = 7² and 64 = 8². That means √50 lies between 7 and 8.
Your calculator tells you that √50 ≈ 7.0710678, which is a number that lies between the integers 7 and 8.
12. √7272 lies between the squares 64 = 8² and 81 = 9². That means √72 lies between 8 and 9.
13. √6565 lies between the squares 64 = 8² and 91 = 9². That means √65 lies between 8 and 9.
14. √2323 lies between the squares 16 = 4² and 25 = 5². That means √23 lies between 4 and 5.
__
Additional comment
The purpose of questions like this appears to be to have you make use of your knowledge of integer perfect squares to guess an approximation of a square root.
A calculator can answer these questions immediately. Of course the two consecutive integers are the integer part of the root, and the next higher integer.
The question is not well-posed. The answer to "integers each value is between" could be 1 < √50 < 50. For integers greater than 1, the square root is always smaller than the integer being rooted. We've seen questions like this enough times that we can guess the intention is for you to identify consecutive integers.
Extra credit
Knowing the integer part of the root and the difference between the number and its next lower perfect square, you can approximate the root as follows:
For integer n = a² +b, the root √n lies between a +b/(2a+1) and a +b/(2a).
For example, 65 = 8²+1, so √65 lies between 8 1/17 and 8 1/16.
Determine which integer will make the inequality 3(n + 1) > 5(n − 3) true.
A: S:{9}
B: S:{0}
C: S:{15}
D: S:{18}
n < 9 makes the inequality 3(n + 1) > 5(n − 3) true.
Hence, option A) S:{ 9 } is the correct answer.
What integer will make the given inequality true?Given the inequality in the question
3(n + 1) > 5(n − 3)
To determine the integer will make the inequality true, we simply solve for n.
3(n + 1) > 5(n − 3)
Remove the parenthesis using distributive property
3×n + 3×1 > 5×n + 5×−3
3n + 3 > 5n - 15
Collect like terms
3n + 3 > 5n - 15
3n - 5n > - 15 - 3
-2n > - 18
Divide both sides by -2.
Note that; when dividing or multiplying both sides of an inequality by a negative value, the inequality sign flips to the opposite direction.
-2n/-2 < -18/-2
n < 9
n < 9 makes the inequality 3(n + 1) > 5(n − 3) true.
Hence, option A) S:{ 9 } is the correct answer.
Learn more about inequality here: https://brainly.com/question/17675534
#SPJ1
Answer:
a) S:{9}
Step-by-step explanation:
Given equation,
→ 3(n + 1) > 5(n - 3)
Now the value of n will be,
→ 3(n + 1) > 5(n - 3)
→ 3n + 3 > 5n - 15
→ 3n - 5n > -15 - 3
→ -2n > -18
→ n < (-18)/(-2)
→ n < 18/2
→ [ n < 9 ]
Hence, the value of n is 9.
A scale drawing of a tennis court is 10 inches wide
by 12 inches long. The actual length of the tennis
court is 60 feet wide. What is the actual area of
the tennis cour
10in wide x 12in long
10/12ft x 1
?ft wide x 60ft long
10/12*60=50
1*60=60
50ft by 60ft real size
3000 square feet
Determine the value of expression one 5(x+2)-7 When X equals 4 justify how you found your answer
5(x+2)-7
5(4+2)-7
20+10-7
30-7
23
what is the effect on the graph of f(x)=1/x when it is trandformed to g(x)=1/x - 7
When f(x) = 1/x is converted to g(x) = 1/x - 7, the impact that this has on the graph of f(x) is that the graph of f(x) is moved down by seven units.
What is a Graph?The connection that exists between lines and points in a network may be described using a graph, which is a mathematical description of a network.
g(x)=1/x - 7
f(x)= 1/x
There is a negative seven when the change occurs.
As a result, the graph of f(x) is moved 7 units below.
Learn more about graphs here:
brainly.com/question/14375099
#SPJ1
Solve the inequalityr divided by negative 2.5 is less than or equal to 8.7 for r.
r ≥ −3.48
r ≤ 3.48
r ≥ −21.75
r ≤ −21.75
The solved inequality for r is r ≥ −21.75. Therefore, option C is the correct answer.
Given that, r/(-2.5) ≤ 8.7.
We need to solve the inequality for r.
What is inequality?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Now, the given inequality can be solved as follows:
Here, multiply -2.5 on both sides of the inequality.
That is, r/(-2.5) × -2.5 ≤ 8.7 (-2.5)
⇒ r ≥ −21.75 (Inequality gets reversed when multiplied by negative integers)
The solved inequality for r is r ≥ −21.75. Therefore, option C is the correct answer.
To learn more about inequality visit:
https://brainly.com/question/17557685.
#SPJ1
What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour?
Select one:
A.
30 cents
B.
45 cents
C.
60 cents
D.
67 cents
The cost of lighting a 500-watt outdoor light for 8 hours according to the task content is; 30 cents.
What is the cost of lighting a 500-watt outdoor for 8 hours?According to the task content, the energy consumption for lighting the 500-watt outdoor light for 8 hours is; 500 × 8 = 4000 watt-hour = 4 kilowatt-hour.
On this note, since electricity costs 7.5¢ per kilowatt-hour, the cost of 4 kilowatt-hour is; 7.5¢ × 4 = 30 cents.
Read more on proportion;
https://brainly.com/question/12024093
#SPJ1
round the number 2,499 to the nearest thousand
Answer:
2000 is the nearest thousand
X/4-3/4=16
What property is applied
Answer:
x/4-3/4=16
x-3/4=16
x-3=64
x=64+3
x=67