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]
How do the fuel economies of Honda and Ford
vehicles compare in 2018? Use the drop-down menus
to complete the statements.
Shape: The distribution of fuel economy for Honda is
vand for Ford is
Outliers: There appears to be an outlier of 47 mpg for
Honda. There appears to be an outlier of 40 mpg for
Ford
Center: Fuel economy for Honda tends to be
the fuel economy for Ford.
Variability: Fuel economy for Honda varies about the
same as the fuel economy for Ford.
Answer:
1. roughly symmetric
2. skewed to the right
3. greater than
Step-by-step explanation:
correct on edge 2021 :)
1. The distribution of fuel economy for Honda is roughly symmetric vand for Ford is skewed to the right. and 3. Fuel economy for Honda tends to be greater than the fuel economy for Ford.
How to compare the fuel economies of Honda and Ford vehicles in 2018?Shape: The distribution of fuel economy for Honda is roughly symmetric vand for Ford is skewed to the right.
Outliers: There appears to be an outlier of 47 mpg for Honda. There appears to be an outlier of 40 mpg for Ford
Center: Fuel economy for Honda tends to be greater than the fuel economy for Ford.
Variability: Fuel economy for Honda varies about the same as the fuel economy for Ford.
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When d the product of 6 and 6 is divided by the sum of 6 and 6 what is the quotient? Explain.
Simplify 3 (5x-2y) +2 (4X-37)
Answer:
3x - 6y - 74
Step-by-step explanation:
Given
3(5x - 2y) + 2(4x - 37) ← distribute parenthesis
= 15x - 6y + 8x - 74 ← collect like terms
= 23x - 6y - 74
Answer:
Distribute
3
(
5
−
2
)
+
2
(
4
−
3
7
)
{\color{#c92786}{3(5x-2y)}}+2(4x-37)
3(5x−2y)+2(4x−37)
1
5
−
6
+
2
(
4
−
3
7
)
{\color{#c92786}{15x-6y}}+2(4x-37)
15x−6y+2(4x−37)
2
Distribute
1
5
−
6
+
2
(
4
−
3
7
)
15x-6y+{\color{#c92786}{2(4x-37)}}
15x−6y+2(4x−37)
1
5
−
6
+
8
−
7
4
15x-6y+{\color{#c92786}{8x-74}}
15x−6y+8x−74
3
Combine like terms
1
5
−
6
+
8
−
7
4
15x−6y+8x−74
2
3
−
6
−
7
423x}}-6y-74
23x−6y−74
Solution
2
3
−
6
−
7
4
Step-by-step explanation:
Complete the following equation using <, >, or =
7 _ 24/4
A. =
B. >
C. <
Answer:
7 > 24/4
Step-by-step explanation:
7 _ 24/4
Simplify 24/4
24/4 = 6
7 is greater than 6
7 > 24/4
7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.
Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:
1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.
2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.
3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.
The given numbers are:
7 and 24/4
To compare these numbers,
Convert the fraction 24/4 into the simplest form
Therefore,
[tex]\frac{24}{4} = 6[/tex]
Now since 7 is greater than 6 so we use ">" between them.
Hence,
The complete equation will be 7 > 24/4.
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simplify (2/3 of 21/4)
Answer: 3 1/2
Step-by-step explanation:
"Of" is the same as multiplication so,
2/3 × 21/4=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
2 × 2/13 × 4 = 42/12
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 42 and 12 using
GCF(4/2 , 1/2) = 6
4/2 ÷ 6 1/2 ÷ 6 = 7/2
The fraction
7/2
is the same as
7÷2
Convert to a mixed number using
long division for 7 ÷ 2 = 3R1, so
7/2 = 3 1/2
Therefore:
2/3 of 21/4 = 3 1/2
Hopefully, I Helped
Doug dives from a platform that is 10 meters above water. His dive takes him 3.8 meters below the
surface of the water. How far does Doug's dive take him?
***
Doug's dive takes himmeters.
Answer:
13.8
Step-by-step explanation:
His dive once he hits the water and goes below the surface water line is in the same direction as his dive off the platform. That's very important when you start to consider direction. So you add. Be sure and read this paragraph again.
Dive = platform + under the surface
Dive = 10 + 3.8
Dive = 13.8
Evaluate the expression 2−7+15
pls somone help
Answer:
answer is -20
BODMAS
So we do addition First, then subtraction so 7+15 = 22
2- 22= -20
Based on this equation 3/4 (8y +12) = 3y - 15, what is 2y - 3?
Answer:
-y+5
Step-by-step explanation:
3/4 (8y +12) = 3y - 15
3(2y+3)=3y-15
2y+3=y-5
-(2y-3)=y-5
2y-3=y-5/-1
2y-3=-y+5
Answer: -19
Step-by-step explanation:
Given equation
(3/4) (8y + 12) = 3y - 15
Divide (3/4) on both sides
(REMEMBER division of fraction can be converted to multiplication by using the reciprocal of the fraction)
(3/4) (8y + 12) ÷ (3/4) = (3y - 15) ÷ (3/4)
(3/4) (8y + 12) × (4/3) = (3y - 15) × (4/3)
8y + 12 = 4y - 20
Subtract 4y on both sides
8y + 12 - 4y = 4y - 20 - 4y
4y + 12 = -20
Subtract 12 on both sides
4y + 12 - 12 = -20 - 12
4y = -32
Divide 4 on both sides
4y / 4 = -32 / 4
y = -8
Evaluate the expression basing on the [y] value
2y - 3 ⇔ Given expression
=2(-8) - 3 ⇔ Substitute values into the expression
=-16 - 3 ⇔ Simplify by multiplication
=[tex]\boxed{-19}[/tex] ⇔ Simplify by subtraction
Hope this helps!! :)
Please let me know if you have any questions
I|I is an integer between 11 and 17
Yes, there is. It's 14. Hope this helps.
(5pg)3=125pg. Is wrong or correct
Answer:
125 p^3 g^3
Step-by-step explanation:
(5pg)^3
We know that (ab)^c = a^c * b^c
5^3 p^3 g^3
125 p^3 g^3
Solve. − 18 + ( − 4 ) =
Answer:
-22
Step-by-step explanation:
-18 + (-4) = -18 - 4 = -22
Danny got a raise and now makes $58,965.95 a year. Round this number to the
nearest:
a) dollar
b) thousand dollars
c) ten thousand dollars
Answer:
c) ten thousand dollars
Step-by-step explanation:
A total of 574 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 more student tickets sold than adult tickets. How many adult tickets were sold?
411 is not correct
The answer is: 250 adult tickets were sold.
To be safe, prove that your answer is correct.
If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.
Explanation:
74 more than 250, or 250+74 is 324.
250+324=574.
Now, you know the answer is correct. It satisfies all of the given conditions.
Also, note that the difference between the number of student tickets and adult tickets is 74.
So, there are 250 adult tickets and 324 student tickets.
your monthly salary increases from $2,200 to $2,376. what percent is your raise?
Answer:
8%
Step-by-step explanation:
(2376-2200):2200x100%=8%
1. If a = -1 , the value of3a + 1 is
Answer:
[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]
Therefore, -2 is the right answer.SOMER HELP ON GIS ONEEEE
Answer:
2 one
Step-by-step explanation:
well if u go the other way for it to go right it is mf
When 12x +10y is subtracted from -13x + 7y, we get
Answer:
- 25x - 3yStep-by-step explanation:
-13x + 7y - (12x +10y)
= - 13x + 7y - 12x - 10y
= - 13x - 12x + 7y - 10y
= - 25x - 3y (Ans)
John bought 3 pants for 25 dollars each and paid with a 100 dollar bill how much change did he get?
Answer:
He got $25 in change.
Step-by-step explanation:
Suppose the balance amount is x.
The cost of 3 pants is 3 × 25 = 75
John paid = $ 100
x = 100 – 75
x = 25
Answer:25
Step-by-step explanation:
25×3=75 then you subtract 100-75=25
Part A
The formula for the volume V of a cylinder is V = πr2h, where r is the radius of the base and h is the height of the cylinder. Solve the formula for h.
Choose the correct formula.
A. h=Vπr2
B. h=Vπr2
C. h=Vr2π
D. h=Vπr2
Part B
Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm.
h =
cm
Answer:
Part A. [tex]h=\frac{V}{\pi r^2}[/tex]
Part B. h= 4cm
Step-by-step explanation:
Urgent what is the numerical answer please !!
whats the full question?
Answer:
AB slope= 4/5
CD slope= - 5/4
Step-by-step explanation:
AB: (0,-1) (5,3)
Slope= (3- -1)/(5-0) = 4/5
CD: (2,3) (6,-2)
CD slope= (-2-3)/(6-2) = -5/4
please answer this question
Step-by-step explanation:
all steps are in picture
Which statement is true about the climbers’ heights?
What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
15
18
21
27
Write the equation of the line that
passes through (5,-7) and (0, -1)
4,3,2,1,0,-1, -2, -3, -4,
Equation of a line can be given by :
y = mx + b
Let's find the slope of the line (m) :
[tex] \mathcal{ \hookrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex]
[tex] \mathcal{ \hookrightarrow \: \dfrac{ - 1 - ( - 7)}{0 - 5} }[/tex]
[tex] \hookrightarrow \: \dfrac{6}{ - 5} [/tex]
[tex] \hookrightarrow \: m = \dfrac{ - 6}{5} [/tex]
now let's solve for b :
[tex] \hookrightarrow \: y = mx + b[/tex]
Let's plug the values of x and y from the coordinates of a point .
[tex] \hookrightarrow \: - 7 = (\dfrac{ - 6}{5} \times 5) + b[/tex]
[tex] \hookrightarrow \: - 7 = - 6 + b[/tex]
[tex] \hookrightarrow \: b = - 1[/tex]
now, let's put the value of m (slope) and b (y-intercept) in the equation.
[tex] \hookrightarrow \: y = mx + b[/tex]
[tex] \boxed{ \boxed{\: y = \dfrac{ - 6}{5}x - 1 }}[/tex]
That's All, I hope it helped ya
Two cylinders are similar the volume of one is 27cm^3 the volume of the other cylinder is 1331cm^3 what is the scale factor between them
Answer:
scale factor = 3 : 11
Step-by-step explanation:
Given 2 similar figures with scale factor a : b , then
ratio of volumes = a³ : b³
Here
ratio of volumes = 27 : 1331 . so
scale factor = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11
Answer:
3:11
Step-by-step explanation:
HELP Please with this question please NO LINKs OR I WILL REPORT YOU PLEASE GIVE EXPLANATION
Answer:
87/54 = m
Step-by-step explanation:
-11/6 + m = -2/9
Here is one way to solve this:
First, we can remove the fractions. We can do this by multiplying both sides by both denominators.
multiply both sides by 6
-11 + 6m = -12/9
multiply both sides by 9
-99 + 54m = -12
add 99 to both sides to isolate the m and its coefficient
-12+99= 54m
87 = 54m
divide both sides by 54 to isolate m
87/54 = m
Translate to an inequality
nine increased by the product of a number and 8 is less than -20
Use the variable c for the unknown number.
Answer: - 29/8
Step-by-step explanation:
9 + 8c < - 20
8c < - 20 - 9
8c < - 29
c < - 29/8
Answer:
give this other guy or girl branliest
Step-by-step explanation:
3/10 = 15/50 what is the multiplier
Answer:
the answer is 150
Step-by-step explanation:
you will do cross multiplication where 3 will multiply 50 and 15 will multiply 10. u will get 150=150
A room has to be painted and worker A does 1/3 of the work then leaves. Next worker B does 1/4 of the remaining work and then leaves and finally worker C does 1/5 of the remaining work and then leaves.
What fraction of the room still needs to be painted?
a)3/5
b)2/5
c)13/60
d)7/15
Here, we are given that a room is painted by A, B and C so here three of them have done the work. So, we'll add all these fractions and assume the total work as 1 after that we will substract all the added ones from 1
Let us assume the room completely painted be 1
Now,
A has done 1/3, B has done 1/4 and C has done 1/5 work of the remaining
So, let us add them
A + B + C ⅓ + ¼ + ⅕Getting the L.C.M. The L.C.M of 3,4,5 is 60
20/60 + 15/60 + 12/6047/60Hence, 47/60 room has been painted
Remaining to paint
Total is assumed as 1
Work done = 47/60
Fraction of room needs to painted = 1 - 47/60
(60 - 47)/6013/6013/60 of the room needs to be painted, OPTION C IS CORRECT
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
g(f(4)) =
]
9514 1404 393
Answer:
g(f(4)) = 9
Step-by-step explanation:
Put the argument value where the variable is and do the arithmetic.
g(f(4)) = g(4 -7) = g(-3) = (-3)^2
g(f(4)) = 9
If f(x, y, z) = z sin (xy), find the rate of change of f at the point P(0, 0, 2) in the direction from P to Q(3, 0, 0)
Answer:
0
Step-by-step explanation:
We are looking for the directional derivative of f at P in the direction of PQ.
First we compute
[tex]\nabla f=\langle yz\cos(xy),zx\cos(xy),\sin(xy)\rangle\\\nabla f(0,0,2) =\langle 0,0,0\rangle[/tex]
But if we dot any vector to the zero vector we always get 0. So the rate of change is zero.