I need some help with the homework problem. I have a list of formulas, but can't seem to get it done.
[tex]\int\frac{9}{\sqrt{1+e^{2x}}} \, dx[/tex]
I started by taking the constant out and setting u = [tex]\sqrt{1+e^{2x\\}}[/tex]
After this I can't seem to progress.
After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives
[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]
Then taking differentials, you get
[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]
Replacing everything in the original integral then gives
[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]
Split up the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]
so that
[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]
Based on your answer to the last question, which of the following prices of trade (that is, price of cheese in terms of beer) would allow both Sweden and Greece to gain from trade? Check all that apply.
Please Help!!
Find the equation (in terms of x) of the line through the points (-5,-4) and (4,1)
Step-by-step explanation:
we first find the gradient
when y1=-4, x1=-5 and y2=1, x2=4
gradient={(y2-y1)÷(x2-x1)}
gradient={1-(-4)}÷{4-(-5)}
gradient=(1+4)÷(4+5)
gradient=5÷9 OR 0.5555
To find the equation interm of x
we substitute for the gradient in the formula
y-y1=gradient (x-x1)
y-(-4)=(5÷9)(x-×-5)
y+4=(5÷9)(x+5)
y+4=(5x+25)÷9 Cross multiply ✖️
9(y+4)=(5x+25)(1)
9y+36=5x+25 collect like terms
9y=5x+25-36
9y=5x-11 divide both sides by 9
y=(5x-11)÷9.......ans
Whatis (-5 + 3i) -(4+7i)?
Answer:
-5-4i is your answer.
I hope it will help youplease help meeee out
Answer:
between 15.5 and 16
Step-by-step explanation:
which std
Given the sequence -14, -6, -2, 0, 1, ..., find the recursive formula.
Answer:
C is the answer to your question
. Evaluate the expression below for x = 4. 6(x+8) (please
Answer:
D
Step-by-step explanation:
6(x + 8) = Plug in x with 4
6(4 + 8) =
6(12) =
72
Match the terms to their definition.
1. union
2. intersection
3. compound inequality
Hurry plz
Step-by-step explanation:
compound inequality: a statement formed by two.......
intersection: elements that are in both set A and B
union: elements that are in either set A or B
HELP ME OUT PLZZZZZZ
Answer:
x=5
JK = 40 units
Step-by-step explanation:
JM=MK since the have the little red line which shows they are equal
7x+5 = 8x
Subtract 7x from each side
7x+5 -7x= 8x-7x
5 = x
JK = 7x+5 = 7(5)+5 = 35+5 = 40
How many area codes (ABC) would be possible if all three digits could be any value 3-9
Answer:
Step-by-step explanation:
A multiple choice test contains 25 questions with 5 answer choices. What is the probability of correctly answering 8 questions if you guess randomly on each question?
Answer: 0.0623
Step-by-step explanation:
The probability of correctly answering 8 questions if you guess randomly on each question is 0.062348.
It is given that multiple choice test contains 25 questions with 5 answer choices.
To find probability of correctly answering.
What is probability?The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
Given that:
The probability of each correct answer is [tex]p_{s}[/tex][tex]=\frac{1}{5}[/tex]
The probability of 8 successful answers in 25 independent trials for a binomial probability distribution is:
p(k|n)=[tex]\frac{n!}{(n-k)!*n!}[/tex][tex]p_{s}^{k} (1-p_{s})^{n-k} \\[/tex]
p(8|25)=[tex]\frac{25!}{(25-8)!*8!}[/tex][tex]{\frac{1}{5} }^{k} (1-1/5)^{25-8} \\[/tex]
p(8|25)=0.062348
So, the probability of correctly answering 8 questions if you guess randomly on each question is 0.062348.
Learn more about probability here:
https://brainly.com/question/24385262
#SPJ2
What is the value of the expression 4x^3 – 3x when x = 6?
A 16-ft steel beam is to be cut into two pieces so
that one piece is 1 foot longer than twice the other.
Find the length of each piece.
Answer:
8.5 feet and 7.5 feet.
Step-by-step explanation:
Hope this helps :)
pls help with this problem
====================================================
Explanation:
Refer to the diagram below. The rectangle MATH has the diagonal MT that cuts the rectangle into two identical right triangles.
We then use the pythagorean theorem to find the length of the hypotenuse MT.
a^2 + b^2 = c^2
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
c^2 = 676
c = sqrt(676)
c = 26
Segment MT is 26 cm long.
This applies to the other diagonal AH as well.
If m ABC=122 and m ABD=71 then m DBC =
Answer:
Angle DBC = 51
Step-by-step explanation:
Angle ABC = angle ABD + angle DBC
We are given that angle ABC = 122 and angle ABD = 71
So 122 = 71 + angle DBC
* Solve for angle DBC *
Subtract 71 from both sides
122 - 71 = 71 - 71 + angle DBC
51 = angle DBC
Lines m and n are parallel lines. If line m has a slope of -1, find the slope of linen. Type a numerical answer in the space
provided. If necessary, use the key as a fraction bar. Do not type spaces in your answer.
Solve for h. s=6πsh+6πs²
I got h=1/6π-s but it says the answer is correct but the format is not, ideas?
Answer:
Try h=(1-6πs)/6π
Step-by-step explanation:
That's the same answer in another format
Two major league players got a total of 226 hits. Washington had 18 more hits than Sanchez. Find the number of hits for each player.
Answer:
Washington had 115 hits and Sanchez had 111 hits.
Step-by-step explanation:
2s + 4 = 226
2s = 222
s = 111
s + 4 = 115
i need help answering the question in the picture provided
answer:
(a).
Equation of circle is x² + y² - 25 = 0
(b).
(-5, 0) » yes
(√7, 1) » no
(-3, √21) » no
(0, 7) » no
Step-by-step explanation:
(a).
If centred at origin, centre is (0, 0)
General equation of circle:
[tex]{ \boxed{ \bf{ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0}}}[/tex]
but g and f are 0:
[tex] {x}^{2} + {y}^{2} + c = 0 \\ but : \\ c = {g}^{2} + {f}^{2} - {r}^{2} \\ c = { - 25} [/tex]
How do i express x^2-3x into the form of (x-m)^2+n.
I will give brainliest to first correct answer
Well this could be incredibly easy, by just saying [tex]m=0[/tex] and [tex]n=-3x[/tex].
This is a completely valid case but nevertheless seems too easy. The requirements are probably that n and m are integers or natural numbers but since that was not specified such probable requirement ought not to be followed.
Hope this helps :)
Find the supremum and infimum of each of the following sets of real numbers
S = {3x 2 − 10x + 3 < 0}
Answer:
[tex]\sup(S) = 3[/tex].
[tex]\displaystyle \inf(S) = \frac{1}{3}[/tex].
Step-by-step explanation:
When factored, [tex]3\,x^{2} - 10\, x + 3[/tex] is equivalent to [tex](3\, x - 1)\, (x - 3)[/tex].
[tex]3\, x^{2} - 10\, x + 3 < 0[/tex] whenever [tex]\displaystyle x \in \left(\frac{1}{3},\, 3\right)[/tex].
Typically, the supremum and infimum of open intervals are the two endpoints. In this question, [tex]\sup(S) = 3[/tex] whereas [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex].
Below is a proof of the claim that [tex]\sup(S) = 3[/tex]. The proof for [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex] is similar.
In simple words, the supremum of a set is the smallest upper bound of that set. (An upper bound of a set is greater than any element of the set.)
It is easy to see that [tex]3[/tex] is an upper bound of [tex]S[/tex]:
For any [tex]x > 3[/tex], [tex]3\,x^{2} - 10\, x + 3 > 0[/tex]. Hence, any number that's greater than [tex]3\![/tex] could not be a member [tex]S[/tex]. Conversely, [tex]3[/tex] would be greater than all elements of [tex]S\![/tex] and would thus be an upper bound of this set.To see that [tex]3[/tex] is the smallest upper bound of [tex]S[/tex], assume by contradiction that there exists some [tex]\epsilon > 0[/tex] for which [tex](3 - \epsilon)[/tex] (which is smaller than [tex]3\![/tex]) is also an upper bound of [tex]S\![/tex].
The next step is to show that [tex](3 - \epsilon)[/tex] could not be a lower bound of [tex]S[/tex].
There are two situations to consider:
The value of [tex]\epsilon[/tex] might be very large, such that [tex](3 - \epsilon)[/tex] is smaller than all elements of [tex]S[/tex].Otherwise, the value of [tex]\epsilon[/tex] ensures that [tex](3 - \epsilon) \in S[/tex].Either way, it would be necessary to find (or construct) an element [tex]z[/tex] of [tex]S[/tex] such that [tex]z > 3 - \epsilon[/tex].
For the first situation, it would be necessary that [tex]\displaystyle 3 - \epsilon \le \frac{1}{3}[/tex], such that [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex]. Let [tex]z := 1[/tex] (or any other number between [tex](1/3)[/tex] and [tex]3[/tex].)
Apparently [tex]\displaystyle 1 > \frac{1}{3} \ge (3 - \epsilon)[/tex]. At the same time, [tex]1 \in S[/tex]. Hence, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex] when [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex].With the first situation [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex] accounted for, the second situation may assume that [tex]\displaystyle 0 < \epsilon < \frac{8}{3}[/tex].
Claim that [tex]\displaystyle z:= \left(3 - \frac{\epsilon}{2}\right)[/tex] (which is strictly greater than [tex](3 - \epsilon)[/tex]) is also an element of [tex]S[/tex].
To verify that [tex]z \in S[/tex], set [tex]x := z[/tex] and evaluate the expression: [tex]\begin{aligned} & 3\, z^{2} - 10\, z + 3 \\ =\; & 3\, \left(3 - \frac{\epsilon}{2}\right)^{2} - 10\, \left(3 - \frac{\epsilon}{2}\right) + 3 \\ = \; &3\, \left(9 - 3\, \epsilon - \frac{\epsilon^{2}}{4}\right) - 30 + 5\, \epsilon + 3 \\ =\; & 27 - 9\, \epsilon - \frac{3\, \epsilon^{2}}{4} - 30 + 5\, \epsilon + 3 \\ =\; & \frac{3}{4}\, \left(\epsilon\left(\frac{16}{3} - \epsilon\right)\right)\end{aligned}[/tex].This expression is smaller than [tex]0[/tex] whenever [tex]\displaystyle 0 < \epsilon < \frac{16}{3}[/tex]. The assumption for this situation [tex]\displaystyle 0 < \epsilon < \frac{8}{3}[/tex] ensures that [tex]\displaystyle 0 < \epsilon < \frac{16}{3}\![/tex] is indeed satisfied. Hence, [tex]\displaystyle 3\, z^{2} - 10\, z + 3 < 0[/tex], such that [tex]z \in S[/tex].At the same time, [tex]z > (3 - \epsilon)[/tex]. Hence, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex].Either way, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex]. Contradiction.
Hence, [tex]3[/tex] is indeed the smallest upper bound of [tex]S[/tex]. By definition, [tex]\sup(S) = 3[/tex].
The proof for [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex] is similar and is omitted because of the character limit.
Multiply (2 − 7i)(9 + 5i). (6 points)
53 − 53i
−17 − 53i
18 − 35i2
18 − 53i − 35i2
the answer would be
A. 53-53i !! :)
it was also the correct answer on the test ,, goodluck !!
Answer = B. -17 -53i
can someone help me please
Step-by-step explanation:
11.
[tex] \frac{x - 4}{ \frac{x}{4} - \frac{4}{x} } [/tex]
[tex] \frac{x - 4}{ \frac{ {x}^{2} }{4x} - \frac{16}{4x} } [/tex]
[tex] \frac{x - 4}{ \frac{ {x}^{2} - 16 }{4x} } [/tex]
[tex] \frac{x - 4}{ \frac{(x + 4)(x - 4)}{4x} } [/tex]
[tex] \frac{4x}{x + 4} [/tex]
12.
[tex] \frac{ \frac{ {x}^{2} - 1 }{x} }{ \frac{(x - 1) {}^{2} }{x} } [/tex]
[tex] \frac{ {x}^{3} - x}{ {x}^{3} - 2 {x}^{2} + x } [/tex]
[tex] \frac{x( {x} - 1)(x + 1) }{x( {x} - 1) {}(x - 1) } [/tex]
[tex] \frac{x + 1}{x - 1} [/tex]
13.
[tex] \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1} } - \sqrt{ {t}^{2} + 1} }{ {t}^{2} } [/tex]
[tex] \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1 } } - \frac{ {t}^{2} + 1}{ \sqrt{ {t}^{2} + 1 } } }{ {t}^{2} } [/tex]
[tex] \frac{ \frac{1}{ \sqrt{ {t}^{2} + 1 } } }{ {t}^{2} } [/tex]
[tex] \frac{ - \frac{ \sqrt{ {t}^{2} + 1 } }{ {t}^{2} + 1 } }{ {t}^{2} } [/tex]
[tex] - \frac{ \sqrt{ {t}^{2} + 1} }{ {t}^{2}( {t}^{2} + 1) } [/tex]
14.
[tex] \frac{3x { }^{ \frac{1}{3} } - x {}^{ \frac{ - 2}{3} } }{3x {}^{ - \frac{2}{3} } } [/tex]
[tex] \frac{3x - 1}{3} [/tex]
Consider f(x)=4x and g(x) = square root of x^2-1 and h(x)= square root of 16x-1
f(x) = 4x
g(x) =
[tex] \sqrt{x^{2} \: - \: 1 } [/tex]
h(x) =
[tex] \sqrt{16x \: - \: 1} [/tex]
We want to check if h(x) = g(f(x))
So g(f(x)) =
[tex] \sqrt{(4x) {}^{2} - \: 1} [/tex]
Simplified;
g(f(x)) =
[tex] \sqrt{16x {}^{2} \: - \: 1 } [/tex]
But h(x) =
[tex] \sqrt{16x \: - \: 1} [/tex]
Hence g(f(x)) is not equal to h(x)
In the coordinate plane, plot AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ given by the points A(−4, 5), B(−4, 8), C(2, −3), D(2, 0)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The x-coordinate is the same in each pair of points, so the line segment will be a vertical line segment 3 units long.
Write an equation that expresses the following relationship.
p varies directly with d and inversely with the square of u
In your equation, use k as the constant of proportionality.
Answer:
p = k(d)/u^2
Step-by-step explanation:
BRAINLIEST, PLEASE!
Graph the line with slope 2 passing through the point (-5, 2)
Answer:
Equation is y=2x+12
The image is a picture of the graph(it's not the best but it's something.
Simplify 24 ÷ (3 + 2 square)
Answer:
3.42
Step-by-step explanation:
24/7=3.42
Can a triangle be formed with side lengths of 2inches, 3 inches, and 6 inches?
If a ribbon that is 30.1 inches long is cut into equal pieces that are 1.75 inches long, how many pieces of ribbon can be created?
1.72
12.7
17.2
172.0
Answer:
17.2
Step-by-step explanation:
30.1÷1.75=17.2
plssss mark brainliesttr
