Answer:
The Marked Price is 63.75
Step-by-step explanation:
15/100 * 75 = 11.25
75 - 11.25 = 63.75
Hence the Marked Price is 63.75
[tex] \rm\int^{\infty}_{0} \frac{ \sqrt{x} \arctan(x) }{1 + {x}^{2} }\: dx\\ [/tex]
Let
[tex]I(a) = \displaystyle \int_0^\infty \frac{\sqrt x \arctan(ax)}{1+x^2} \, dx[/tex]
Differentiate with respect to a :
[tex]I'(a) = \displaystyle a \int_0^\infty \frac{x^{\frac32}}{(1+x^2)(1+a^2x^2)} \, dx[/tex]
Substitute y = √x :
[tex]I'(a) = \displaystyle 2a \int_0^\infty \frac{y^4}{(1+y)(1+a^2y)} \, dy[/tex]
Polynomial division yields
[tex]\dfrac{y^4}{(1+y)(1+a^2y)} \\\\ = \dfrac1{a^2}y^2 - \left(\dfrac1{a^2} + \dfrac1{a^4}\right)y + \dfrac1{a^2} + \dfrac1{a^4} + \dfrac1{a^6} - \dfrac{\left(1+\frac1{a^2} + \frac1{a^4} + \frac1{a^6}\right)y + \frac1{a^2} + \frac1{a^4} + \frac1{a^6}}{(1+y)(1+a^2y)}[/tex]
Computing I'(a) isn't so difficult from here. You'd find (assuming a ≥ 0)
[tex]I'(a) = \displaystyle \frac\pi{\sqrt2\left(\sqrt a + a + a^{\frac32} + a^2\right)}[/tex]
Integrate both sides with respect to a. On the right side, substituting b = √a yields
[tex]\displaystyle \int \frac{da}{\sqrt a + a + a^{\frac32} + a^2} = \int \frac{2b}{b + b^2 + b^3 + b^4} \, db \\\\ = 2 \int \frac{db}{1 + b + b^2 + b^3} \\\\ = 2 \int \frac{db}{(1+b)(1+b^2)} \\\\ = \int \left(\frac1{1+b} + \frac{1-b}{(1+b^2)}\right) \, db \\\\ = \frac14 \left(2 \arctan(b) + 2 \ln(1 + b) - \ln(1 + b^2)\right) + C \\\\ = \frac14 \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right) + C[/tex]
Noting that a = 0 makes the integral I(a) vanish, we have
[tex]0 = \dfrac14 \left(2 \arctan(\sqrt0) + 2\ln(1 + \sqrt0) - \ln(1 + 0)\right) + C \implies C = 0[/tex]
and so
[tex]\displaystyle I(a) = \frac\pi{4\sqrt2} \left(2 \arctan(\sqrt a) + 2 \ln(1 + \sqrt a) - \ln(1 + a)\right)[/tex]
We recover the integral we want with a = 1, which gives a value of
[tex]\displaystyle \int_0^\infty \frac{\sqrt x \arctan(x)}{1 + x^2} \, dx = \boxed{\frac{\pi^2 + 2\pi\ln(2)}{4\sqrt2}}[/tex]
Write an exponential equation of a function that passes through the
points (0,4) and (2,64).
Divide both systems:
16=b²4=ba(b)²=64a=64/16=4y=4(4)^x
y=4^x+1
Define the type of sequence below.
2, 0, 2, 4, 6, ....
O A. neither arithmetic nor geometric
O B. geometric
O C. both arithmetic and geometric
O D. arithmetic
========================================================
Explanation:
Going from the first term to the second, we add on -2
Then going from the second term to the third, we add on +2
This inconsistency (-2 vs +2) means we don't have a common difference, and therefore the sequence is not arithmetic.
------------
Now let's divide each term by their previous term
term2/term1 = 0/2 = 0
term3/term2 = 2/0 = undefined
We can stop here and conclude that we don't have a common ratio either, so this sequence is not geometric.
------------
Side note: The subsequence 0,2,4,6,... is arithmetic with common difference d = 2 because we add 2 to each term. It's that first 2 in the original sequence that breaks everything.
To put a fraction in simplest form, what do you do to the numerator and
denominator?
add the same
number to both
divide both by the
same number
subtract both by
same number
multiply both by
the same number
HELP FAST PLS
Answer:
It's multiply both by thesame number
Step-by-step explanation:
For example:
If we want to change this fraction to a simplest form:
5/25
We simply multiply both sides by 5,which will give us:
5/5
And if you want simplify it further, the answer will be 1
Thanks.
Help please thanks in advance
All of the following are equivalent to 8/10 except _____16/20 , 4/5, 5/6, 40/50.
Answer:
5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
All of the answers either increase or reduce to 8/10 except 5/6
Hope this helps! Please mark as brainliest answer if correct.
Stay safe, God bless, and happy studying!
angle 1 is supplementary to angle 2
angle 2is supplementary to angle 3
angle 1 and angle 3 are
9514 1404 393
Answer:
congruent
Step-by-step explanation:
Angles supplementary to the same angle are congruent.
__
Here, angles 1 and 3 are both supplementary to angle 2, so ...
angle 1 and angle 3 are congruent
Here are scores for two softball teams for seven innings. Rosie's Riveters beat The Susan Bees by how many runs?
Answer:
3
Step-by-step explanation:
Find the HCF of the given pair of numbers using the prime factorization method 48 and 60.
Answer:
12
Step-by-step explanation:
Given :-
Two numbers => 48 and 60
To Find :-
HCF of 48 and 60
Solving :-
Prime factorize the numbers.
48 = 2⁴ x 3
60 = 2² x 3 x 5
Solution :-
HCF (48, 60) = 2² x 3 = 12
true or false - Agriculture and trade influenced the growth of civilization in ancient Egypt.
True
False
Answer:
The answer is True.
Step-by-step explanation:
The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability.
Hope this helps you!
NO LINKS!! Please help me
Answer:
A
Step-by-step explanation:
Since cosine is positive and sine is negative that puts θ in Quad IV.
From right triangles we know:
Cos θ = adjacent/hypotenuse = 5/13
sin θ = opposite/hypotenuse = ?/13
To find the opposite side across from θ use the pythagorean theorem.
5² + y² = 13²
25 + y² = 169
y² = 144
y = 12
we are given that sin is < 0 so sinθ = -12/13
Answer:
A
Step-by-step explanation:
[tex]\cos(\theta)=\dfrac{\textsf{adjacent side}}{\textsf{hypotenuse}}=\dfrac{5}{13}[/tex]
[tex]\textsf{As }\cos(\theta) > 0 \textsf{ the angle is in quadrant I or IV}[/tex]
Using Pythagoras' Theorem a² + b² = c² to find the side opposite the angle:
⇒ 5² + b² = 13²
⇒ b² = 144
⇒ b = 12
⇒ opposite side = 12
[tex]\implies \sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}=\dfrac{12}{13}[/tex]
[tex]\textsf{As }\sin(\theta) < 0 \textsf{ then }\sin(\theta)=-\dfrac{12}{13} \textsf{ and the angle is in either quadrant III or quadrant IV}[/tex]
Therefore, the common quadrant is quadrant IV and
[tex]\sin(\theta)=-\dfrac{12}{13}[/tex]
Mr Green gave each of the 12 students in his math group 14 cubes.What is the total number of cubes that Mr.Green gave to his math group?use area model to show how you found the answer
Answer:
Step-by-step explanation:
look at picture need done asap!
Answer:
down
Step-by-step explanation:
c) 6 and 8
a) 7 and 1
b) 5 and 4
PLEASE HELP FAST
The Pythagorean theorem states that a² + b² = c² for a right triangle with leg lengths, a and b, and hypotenuse length, c.
The hypotenuse of a right triangle is 5 units long and has the points (3, 0) and (0, 4) as end points. One of the legs has length 3.
Use the Point and Segment tools to draw a right triangle at demonstrates the other leg length is 4.
Answer:
Uh how to use segmant tool
Step-by-step explanation:
not there
Aman borrowed $ 3000 from a bank for 3 months . A friend was cosigner of the man's personal note . The bank collected 3 1 2 \% simple interest on the date of maturity a ) How much did the man pay for the use of the money ? b Determine the amount he repaid to the bank on the due date of the note .
Answer:3500
Step-by-step explanation:
Help yalll a b d or c
Answer:
persent i think
Step-by-step explanation:
Y-2 = 7(X-4), what form of an equation is this?
Is this in correct standard form? Why or Why not
9514 1404 393
Answer:
point-slope formno -- not in standard formStep-by-step explanation:
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
Comparing this to the equation you have, you see that you have a "point-slope form" equation with m=7 and (h, k) = (4, 2).
__
The standard form of an equation for a line is ...
ax +by = c
where a, b, c are mutually prime integers and a > 0.
Putting your equation into standard form would make it look like ...
7x - y = 26
Your equation is not in correct standard form.
_____
see https://brainly.com/question/18537811 for more information
3x≤ -6. Graph the solution.
Answer:
x less than or equal to -2
Jude is arranging for a party to be held in the students' union. The use
of the hall will be free but security costs of £300 will have to be met.
The cost of the main band will be £2,500 and the supporting band will
cost £500. Tickets will be priced at £16 each. On arrival, every ticket
holder will be given a bottle of water, worth £1 per bottle. If Jude sells
400 tickets as he anticipates, what profit will he make?
19:08
The profit that Jude made during the party was £3700.
What is profit?Profit is the difference between revenue and cost. It is given by:
Profit = Revenue - Cost
From the question:
The total cost = 300 + 2500 + 500 + (1 * 400 people) = £3700
Revenue = 400 ticket * £16 = £6400
Profit = Revenue - Cost = £6400 - £3700
The profit that Jude made during the party was £3700.
Find out more on profit at: https://brainly.com/question/23103804
Lines M and N are parallel. Name the relationship between ∠a and ∠b.
Answer:
alternate angled
Step-by-step explanation:
add up to 180
the table shows a relation between x and y.
is the relation a function, and why?
A function is a relation in which there is only one y-value for every x-value.
If we given an input of 3 for x, for example, we would only get one output for y, like 1, for example.
AnswerIf we look at the table, we can see that the x-value of 3 gives us two outputs: 7 and 9.
Therefore, this relation is not a function.
Solve for m:
m/4.2 =7
please show me the steps
[tex]\frac{m}{4.2} =7\\m = 4.2 * 7 = 29.4[/tex]
Hope that helps!
Answer:
m = 29.4
Step-by-step explanation:
[tex]\frac{m}{4.2}=7[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}4.2[/tex]
[tex]\frac{4.2m}{4.2}=7\cdot \:4.2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]m=29.4[/tex]
Check Answer;
[tex]\frac{29.4}{4.2}[/tex]
[tex]\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:10[/tex]
[tex]\frac{294}{42}[/tex]
[tex]\mathrm{Write\:the\:problem\:in\:long\:division\:format}[/tex]
[tex]42\overline{|\smallspace294}[/tex]
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\\ 42\overline{|\smallspace294}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace2\emptyspace9\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
Hence, m = 29.4
~learn with Lenvy~
It looks like rsu might be a right angle is it?
Please help with A and B
Answer:
(b) NO
Step-by-step explanation:
It must have the square to to be a right angle
Answer:
A: It is obtuse
B: It is a right angle
Step-by-step explanation:
A: Angle RST equals 110*, if it is greater than 90*, it is obtuse
B: Right Angles are 90*, so this is simple, you subtract RST by UST, so 110-20=90
The circumference of the yellow circle is about for 2.5
Answer:
what are you trying to solve?
A bag contains ten tiles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.
What is the probability of picking a letter that is not a vowel?
Answer:
4/5
Step-by-step explanation:
There are 10 tiles total, and E and I are vowels. This makes 2/10 of the tiles tiles. The other 8/10 are not vowels.
8/10 can be simplified down to 4/5.
There is a 4/5 probability of picking a letter that is not a vowel.
solve the following
a)n^2-n=0
b) 9q^2 -1 =0
c)(n-1)^2=16
kindly help me with this
How to find imaginary and real zeros the function has
18x² +15x-12 factor
The variables y and x have a proportiurial relationship, and y = 28 when x = 21.
What is the value of x when y = 42?
x= 14
x = 18 2/3
x= 31 1/2
x=56
Answer:
x = 31 1/2
Step-by-step explanation:
If y = 42, that means the original y = 28 was multiplied by 1.5, so we have to multiply x = 21 by 1.5 to find the answer.
21 * 1.5 = 31.5 A.K.A 31 1/2
Simone wrote that 2+5.8=6.
Use the drop-down menus to explain why 6 is incorrect.
2+5.8 cannot be 6 because 2+5.8 is
Six is a correct sum to the expression +5.8, not 2+5.8.
Answer: The correct equation should be 0.2+5.8=6
Step-by-step explanation: First of all let's look at the equation without the decimal ".8". So, it would be 2+5 which equals 7. Since the sum is greater, adding a decimal will make the sum larger than 6. 2+5.8=7.8, therefore the correct equation being 0.2+5.8=6. Hopes this makes sense and helps!