Therefore, the arbitrary constant is not required, our final answer is (1/2)[(1/(7+i))e^(7x + ix) + (1/(7-i))e^(7x - ix)]
To evaluate this integral using complex exponentials, we can use Euler's formula: e^(ix) = cos(x) + i sin(x). We can rewrite cos(x) as the real part of e^(ix), and then use the property that ∫ e^(ax) dx = (1/a) e^(ax) to solve the integral.
First, we rewrite the integral as ∫ (1/2) e^(7x + ix) + (1/2) e^(7x - ix) dx.
Then, using the above property, we get the answer in complex exponential form:
(1/14) e^(7x + ix) + (1/14) e^(7x - ix) + C, where C is the arbitrary constant.
To evaluate the integral ∫e^(7x)cos(x) dx using complex exponentials, we need to recall Euler's formula:
cos(x) = (e^(ix) + e^(-ix))/2
Now, substitute cos(x) with Euler's formula in the integral:
∫e^(7x)((e^(ix) + e^(-ix))/2) dx
Multiply e^(7x) into the parentheses:
(1/2)∫(e^(7x + ix) + e^(7x - ix)) dx
Now, integrate with respect to x:
(1/2)[(1/(7+i))e^(7x + ix) + (1/(7-i))e^(7x - ix)] + C
Therefore, the arbitrary constant is not required, our final answer is (1/2)[(1/(7+i))e^(7x + ix) + (1/(7-i))e^(7x - ix)]
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List the first five prime numbers
Answer:
2,3,5,7,11
Step-by-step explanation:
see above for the first five prime numbers
Answer:
2, 3, 5, 7, 11
hope this helps
have a good day :)
Step-by-step explanation:
please help me with this
Answer: A. 2[tex]\sqrt[3]{6}[/tex]
Step-by-step explanation:
what is the standard form of (-2/3)x - 4
( slope intercept )
Answer:
m=0,b for -2/3 x-4
Step-by-step explanation:
..........
Heidi is driving 200 miles. She has finished 80% of the drive. How many miles is 80% of Heidi's drive.
Answer:
160 miles
Step-by-step explanation:
200 * 0.8 is 160
Answer:
160 miles
Step-by-step explanation:
80/100*200
80*2
160
YOU CAN MARK ME AS BRAINIEST IF YOU WANT
Can you guys help me!!!
Answer:
I guess its the 3rd one not sure
10/27=a/135
what is the answer for this equation?
Answer:
So we have this equation:
10/27 = a/135
What we can do is multiply both sides by 27 and 135:
10*135 = a * 27
1350 = 27a
a = 1350/27. = 50.
In triangle KLM, the measure of angle M is 90 degrees, the measure of angle K is 75 degrees, and LM is equal to 6.3 feet. Find the length of KL to the nearest tenth of a foot.
Answer:
6.5feet
Step-by-step explanation:
Using the SOH CAH TOA identity
<K = 75 degrees
opposite = LM = 6.3 feet
Hypotenuse = KL
sin theta = opp/hyp
sin 75 = 6.3/x
x = 6.3/sin75
x = 6.3/0.9659
x = 6.5feet
Hence the length of KL to the nearest tenth of a foot is 6.5feet
help asap pleaseeee (if u do ily)))
Answer:
B) 120
Step-by-step explanation:
180 - 60 = 120
Hope that helps!
Answer:
B. 120
Step-by-step explanation:
its bigger than 90 so i did process of elimination
Please Help!! I will give Brainliest to the correct answer!!
Evaluate 12.3s +11.9t when s= 3 and t = 4
Thank you so much
Answer:
84.5
Step-by-step explanation:
12.3(3)+11.9(4)=84.5
Answer:
87.5
Step-by-step explanation:
12.3 x 3= 39.9=s
11.9 x 4= 47.6=t
47.6 + 39.9= 87.5
In Fluorescent higher secondary school there are 53 students in class 8. If number of boys is 3 morethan that of number of girls find.
a. Equation representing the number os students.
b. The number of Boys and Girls.
Answer:
a. 3g + g = 53
b. 40 boys and 13 girls
Step-by-step Explanation:
(3g = number of boys)
(g = number of girls)
3g + g =53
4g = 53
g = 13.2
53 - 13.2 = 39.8 (boys)
we round to the nearest tenth on both
girls 13.2---13
boys 39.8---40
I need help with my home work pls
Si un terreno tiene 15 m de ancho y 40 m de largo y ademas al lado existen 5 terrenos identicos ¿cual es el area de todos los terrenos?
no se boy a septimodkxkdkdkdkdkdoi
Please help me to solve the 7th part !
Answer:
i don't know
Step-by-step explanation:
sorry sorry sorry berry much
Un reloj marca las 4:55 horas . Que valor tiene el ángulo que forman las manecillas? Escribe tu resultado considerando el ángulo positivo y el ángulo negativo.
Answer: what does this say please help
Step-by-step explanation:
HELP AND WILL GIVE BRAINLIEST!!! Solve for x
Answer:
let the opposite angle of 43=y
57°+43°+y=180°[by sum of all angle is 180°]
100+y=180°
y=180°-100
y=80°
opposite angle of x is equal to the 80°
so the equation will be like this
x+x+80°=180°
2x+80°=180°
2x=180°-80°
2x=100
x=100/2
x=50°
so the value of x is 50°
solve for b
ցb – m = 9
Answer:
I couldn't write it since I don't have the format, but it is attached.
4. (Claim 1 Example)
Bob uses a 20 foot ladder to paint a section of his house that is 16 feet high.
H
16 ft
Ladder
20 ft
0°
Х
Ground
Select all equations that can be used to solve for e.
12
12
sino =
cos 0 =
A.
20
B.
20
tan
C.
12
20
16
sin =
20
16
cos O =
20
tan
16
20
D.
E.
F.
Answer:
D
Step-by-step explanation:
using Sohcahtoa we know that we can only use Soh (since we have the opposite,16 and the hypotenuse, 20)
D is the only one that uses the correct equation of S = o/h
(this explanation isn't the best so please search up Sohcahtoa if it doesn't make sense)
Help me out
Length = m
[tex]perimeter = a + b + c[/tex]
[tex]perimeter = 4 + 3 + c[/tex]
//
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {4}^{2} + {3}^{2} = {25}^{2} [/tex]
[tex] \sqrt{25} = 5[/tex]
[tex]c = 5 \: meters[/tex]
//
[tex]perimeter = 4 + 3 + 5[/tex]
[tex]perimeter = 12 \: meters[/tex]
//
[tex]the \: length \: of \: the \: fencing \: is\: 12 \: meters[/tex]
H
(3n - 15)°
(2n + 5)º
E
F
G
What is the value of n ?
plzz write with formula and explanation plzzzzzzzz
Given:
[tex]-\dfrac{33}{16}[/tex] should be divided by a number to get [tex]-\dfrac{11}{4}[/tex].
To find:
The unknown number.
Solution:
Let [tex]-\dfrac{33}{16}[/tex] should be divided by x to get [tex]-\dfrac{11}{4}[/tex].
[tex]\dfrac{-\dfrac{33}{16}}{x}=-\dfrac{11}{4}[/tex]
[tex]-\dfrac{33}{16}=-\dfrac{11}{4}x[/tex]
Multiply both sides by 16.
[tex]-33=-44x[/tex]
Divide both sides by -44.
[tex]\dfrac{-33}{-44}=x[/tex]
[tex]\dfrac{3}{4}=x[/tex]
Therefore, the unknown number is [tex]\dfrac{3}{4}[/tex].
Can someone plz help me with this?
Answer:
D
Step-by-step explanation:
because the odds have to be even if the possobility number is even
This graph shows how the total distance Jack has walked depends on the number of trips he has made to school.
ASAP BEFORE 11:59
Answer:
whats the question
Step-by-step explanation:
thats the answer
Which inequality has a closed circle when it is graphed on a number line?
x greater-than 0.4
x greater-than negative 3
x less-than 4
x greater-than-or-equal-to 3
Answer:
Less than 4 I guess??
This part I have scribbled so I can answer
no x Ehud ihehiexbhhenxkjwbhxnwbxhuebxbuebxh
Answer:
D
Step-by-step explanation:
There are 4 red balls in a bag and an unknown number of white balls. If we randomly
choose a ball from the bag, the probability of getting a white ball is larger than the
probability of getting a red ball. What might be the number of white balls in the bag?
Step-by-step explanation:
well if there were 5 white the probability is 5/9 vs 4/9 for red. so the number of white balls is anything greater than or equal to 5
1. In the expression x2, 2 is what we call
A. Base
B. Exponent
C. Multiple
Answer:
hello! if you're talking about x², then 2 is what we call: B. Exponent.
what is bigger 6/5 or 4/5?
Answer:
6/5 is bigger
Step-by-step explanation:
6/5 simplifies to 1 and 1/5 which is greater than just 4/5
Answer:
6/5, the numerator is the number that determins the amount that is an improper fraction actually, the proper way of writing it is 1 and 1/5 but both are acceptable. most teachers prefer it this was though.
Step-by-step explanation:
hope this helps
If a model of a dinosaur is 3.75 feet and the scale factor for the actual dinosaur is 1:24. What is the size, in feet, of the actual dinosaur?
Answer: 120
Step-by-step explanation:
Next, write ratios to represent the unknown actual length and width of the display to the scale length and width of the display.
LengthWidth=scaleactual=4l=scaleactual=8w
Then, write two proportions by setting the two length ratios equal to one another and the two width ratios equal to one another. The given unit is feet.
LengthWidth=4l=1160=8w=1160
Next, cross multiply each equation.
LLWW=4×160=640 feet=8×160=120 feet
Then, to find the area of the display, multiply length times width.
The actual size of the dinosaur is 90 feet.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
A model of a dinosaur is 3.75 feet,
and the scale-factor for the actual dinosaur is 1:24.
So,
the size of the actual dinosaur = model size x the scale-factor
The size of the actual dinosaur = 24 x 3.75
The size of the actual dinosaur = 90 feet.
Therefore, the actual size is 90 feet.
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Help please
3 |X-4| +1 = 19
A parking lot has the shape of a parallelogram. The length of two adjacent sides are 70 meters and 100 meters. The angle between them is 70°. What is the area of the parking lot?
The area of the parking lot is 4606 square meter.
What is parallelogram?
It is a special type of quadrilateral that has both the pairs of opposite sides parallel and equal.
What is the area of parallelogram?
The area of a parallelogram is the product of its base and height.
We have,
length of two adjacent sides are 70meters and 100meters.
And base of parallelogram is 70m. (length of parallelogram is its base)
Angle between the adjacent sides is 70 degrees.
Let, side AB and BC be the two adjacent sides whose lengths are 70m and 100m.And h be the height of the parallelogram.
For the height of the parallelogram
In ΔADE, we have
[tex]sin70=\frac{DE}{AD}[/tex] [tex](sinx=\frac{perpendicular}{hypotenuse})[/tex]
⇒ [tex]0.9397=\frac{h}{70}[/tex]
⇒ [tex]0.9397[/tex]×70[tex]=h[/tex]
⇒ h=65.8m
Formula to find the area of parallelogram:
Area= base× height
so, the area of parking lot=base × height
substitute the value of base and height of the parallelogram in the above formula.
Therefore,
[tex]Area=65.8[/tex]×[tex]70[/tex]
[tex]Area=4606m^{2}[/tex]
Hence, the area of the parking lot is 4606 square meter.
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what is the y value when x=-1?
what is the y value when x=0?
what is the y value when x=-1?
Answer:
2
0
-2
Step-by-step explanation:
sub x into formula
-2(-1)=2
-2(0)=0
-2(1)=-2
Answer:
60
Step-by-step explanation:
A line graph titled Car Mileage for a Hybrid Car has number of gallons on the x-axis, and number of miles on the y-axis. 1 Gallon is 60 miles, 2 gallons is 120 miles, 3 gallons is 180 miles, and 4 gallons is 240 miles.
What is the value of y when the value of x is 1?