Answer:
[tex](\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C[/tex]
Step-by-step explanation:
Step(i):-
Given that the function
f(x) = [tex]e^{4x} \sqrt{1+e^{2x} }[/tex]
Now integrating on both sides, we get
[tex]\int\limits{f(x)} \, dx = \int\limits{e^{4x} \sqrt{1+e^{2x} } dx[/tex]
= [tex]\int\limits{e^{2x} e^{2x} \sqrt{1+e^{2x} } dx[/tex]
Step(ii):-
Let [tex]1 + e^{2x} = t[/tex]
[tex]e^{2x} = t -1[/tex]
[tex]2e^{2x}dx = d t[/tex]
[tex]e^{2x}dx = \frac{1}{2} d t[/tex]
= [tex]\int\limits{( \sqrt{1+e^{2x} }) e^{2x} e^{2x} dx[/tex]
= [tex]\int\limits {\sqrt{t}(t-1)\frac{1}{2} dt }[/tex]
= [tex]\frac{1}{2} \int\limits {\sqrt{t} (t) -\sqrt{t} ) dt }[/tex]
= [tex]\frac{1}{2} \int\limits {(t^{\frac{1}{2} } t^{1} +t^{\frac{1}{2} } ) } \, dx[/tex]
[tex]= \frac{1}{2} \int\limits {(t^{\frac{3}{2} } +t^{\frac{1}{2} } ) } \, dx[/tex]
= [tex]\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{3}{2}+1 } + \frac{t^{\frac{1}{2} +1} }{\frac{1}{2}+1 } )+C[/tex]
= [tex]\frac{1}{2} (\frac{t^{\frac{3}{2} +1} }{\frac{5}{2} } + \frac{t^{\frac{1}{2} +1} }{\frac{3}{2} } )+C[/tex]
= [tex]\frac{1}{2} (\frac{t^{\frac{5}{2} } }{\frac{5}{2} } + \frac{t^{\frac{3}{2} } }{\frac{3}{2} } )+C[/tex]
= [tex](\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C[/tex]
Final answer:-
= [tex](\frac{(1+e^{2x}) ^{\frac{5}{2} } }{{5}} + \frac{(1+e^{2x} )^{\frac{3}{2} } }{{3}} )+C[/tex]
describe and correct the error in writing an equation of the line with a slope of 2 and a y intercept of 7
Answer:
An equation of the line with a slope of 2 and a is inercept of 7
Step-by-step explanation:
I think this is what you are saying?
3. A data set that consists of 50 numbers has a minimum value of 16 and a maximum value of 74. Determine the class boundaries using the 2k >n rule if the data are a. Discrete b. Continuous3. A data set that consists of 50 numbers has a minimum value of 16 and a maximum value of 74. Determine the class boundaries using the 2k >n rule if the data are a. Discrete b. Continuous
Answer:
discrete, the class boundaries are;
16 - 25
26 - 35
36 - 45
46 - 55
56 - 65
66 = 75
continuous, the class boundaries are;
16 to less than 26
26 to less than 36
36 to less than 46
46 to less than 56
56 to less than 66
66 to less than 76
Step-by-step explanation:
Given that;
Range of the dataset = maximum value - minimum value = 74 - 16 = 58
total number of data set n = 50
Rule : [tex]2^{k}[/tex] ≥ n
substitute value of n
[tex]2^{k}[/tex] ≥ 50
k × log(2) = log( 50 )
k × 0.3010 = 1.69897
k = 1.69897 / 0.3010
k = 5.64
Hence, we have a total of 6 number of classes needed to be constructed.
so,
class width = 74 - 16 / 6 = 58 / 6 = 9.67
If the Data is discrete, the class boundaries are;
16 - 25
26 - 35
36 - 45
46 - 55
56 - 65
66 = 75
If the Data is continuous, the class boundaries are;
16 to less than 26
26 to less than 36
36 to less than 46
46 to less than 56
56 to less than 66
66 to less than 76
Please solve -6+7x=50
Answer:
x = 8
Step-by-step explanation:
Let's solve your equation step-by-step.
−6+7x=50
Step 1: Simplify both sides of the equation.
7x−6=50
Step 2: Add 6 to both sides.
7x−6+6=50+6
7x=56
Step 3: Divide both sides by 7.
7x/7 = 56/7
x=8
have a wonderful day
[tex] \sqrt{361} [/tex]
Answer:
19
Step-by-step explanation:
Answer:
19
Step by step explanation:
I need help please rndnddmdndnxxnxx
9514 1404 393
Answer:
a) f(-2.5) = 62.6875; f(-1.5) = -13.0625; (-2.5, -1.5) contains a real root
b) there are 1 each of positive and negative real roots; 2 complex roots
c) -2 and 1/3 are the rational real roots
d) x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}
Step-by-step explanation:
a) f(-2.5) = 62.6875; f(-1.5) = -13.0625. The function changes sign between -1.5 and -2.5, so there is a real root in that interval.
__
b) The given coefficients have one sign change, so there is one positive real root. Changing the signs of odd-degree terms makes the signs + - + - -, so there are three sign changes. There are 1 or 3 negative real roots, and possibly 2 complex roots. The constant term is non-zero, so zero is not a root. Here's your table:
positive real roots: 1
negative real roots: 1 or 3
complex roots: 2 or 0
zero roots: none
The graph is attached. It shows 2 real roots, one positive and one negative, so there are 2 complex roots. (There are 4 roots in total, so if only 2 are real, the other 2 are complex.)
__
c) Possible rational roots are of the form ...
±{1, 2}/{1, 3, 9}
Listed, they are ...
±{1/9, 2/9, 1/3, 2/3, 1, 2}
The actual real roots are -2 and 1/3.
__
d) The graph shows the real roots to be -2 and 1/3. The original leading coefficient of 3 is the product of the leading coefficients of the factors. Writing the factor (x -1/3) as (3x -1) lets us reduce the leading coefficient of the quadratic term from 9 to 3. The result of dividing factors (x+2) and (3x-1) from the original function is shown in the attachment. It is a parabola with vertex (-1/3, 2/3), so the factorization is ...
f(x) = (x +2)(3x -1)(3(x +1/3)² +2/3)
The roots of the quadratic term are ...
3(x +1/3)² = -2/3
x +1/3 = ±√(-2/9)
x = (-1 ±i√2)/3
So, the entire list of roots is ...
x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}
_____
Additional comment
The roots of a quadratic are easily found by knowing its leading coefficient and its vertex. If factoring known real roots from a higher-degree polynomial results in a quadratic, then the remaining complex roots are easily found. A graphing calculator is a wonderful tool for this process.
Keith buys 6 pencils for 90p how much would 11 pencils cost
Answer:
keith buy 11 pencils at the cost of 165 paise
Step-by-step explanation:
6 pencils cost = 90 paise
so 1 pencil cost = 15 paise
Can you help me please with this
-39/100 is the answer according to me ..
Plz mark me as brainliest if u found it helpful
help help meeee!!!!!
Answer:
The correct answer will be $725
Answer:I believe it is $725
Step-by-step explanation: 12.50(1+0.16)
= 14.5 then 14.5 times 50 = 725
Many newspapers carry a certain puzzle in which the reader must unscramble to form words. how many ways can the letters LEZBA be arranged?
Ricardo works as a real estate agent. he earns 6% commission for every how he sells. last month, Ricardo sold two homes. One sold for $135,000 and the other sold for $160,000. how much did Ricardo earn by selling these two homes?
Add the two houses together:
135000 + 160000 = 295,000
Multiply the total by the percentage:
295,000 x 0.06 = $17,700
He earned $17,700
What is 5/9 of 18? I need it for my homework.
Answer: 10
Step-by-step explanation:
(5 x 18) / 9 = 90/9 = 10
Answer:
Step-by-step explanation:
how much is 1/2÷8×57÷13+15
Answer:
Use the BODMAS method and at the end work the fraction left by adding it to 15
My answer was 15.274
The bottom part of this block is a rectangular prism. The top part
is a square pyramid. How much paper is needed to completely
cover the block? Explain.
Answer:
Check question number 9 in that file you may be able to understand the problem
Step-by-step explanation:
Is graphite all of the following?
Pure substance
Element
Compound
And Molecule
Pls help asap
Answer: Yes!
Step-by-step explanation:
Yes, graphite is composed of 100%carbon. With this, can we say that graphite is an element or compound of carbon? Compound is composed of two or more elements combined in a substance in definite proportions, in the form of molecules held together by chemical bonds.
PLEASE HELP 22 POINTS
Answer:
y = 15 m<a = 78 m<b = 68
Step-by-step explanation:
(5y+3) + (4y+8) --> 9y + 11
9y + 11 = 146
y = 15
plug in 15 into the equations for the angles and you get
m<a = 78
m<b = 68
An environmental study was conducted. It reported that houses with more inhabitants do not necessarily produce more or less trash. What can be determined?
A. There is no correlation between number of inhabitants and amount of trash produced.
B. There is a correlation between number of inhabitants and amount of trash produced. However, there is no causation. This is because there is probably an increase in the amount of trash produced with an increase in the number of inhabitants.
C. There is a correlation between number of inhabitants and amount of trash produced. There may or may not be causation. Further studies would have to be done to determine this.
Answer:
C.
Step-by-step explanation:
There's no problem for now but it still needs to be monitored in case something might happen.
7. Mangoes are sold at 5 for $4.00 and oranges are sold at 3 for $10.50. Mother bought 8
mangoen and 7 oranges. How much did she pay in all for the Items?
working
Answer:
hi hahahah
Step-by-step explanation:
What is the area of the composite figure?
Hello! :)
[tex]\large\boxed{A = 32.5cm^{2}}[/tex]
We can use the following area to solve for the area of the trapezoid pictured:
[tex]A = \frac{1}{2}(b_{1} + b_{2})h[/tex]
Where:
h = height
b1 = bottom base
b2 = top base
Plug in the given values:
[tex]A = \frac{1}{2}(9 + 4)(5)[/tex]
Simplify:
[tex]A = \frac{1}{2}(65)\\\\A = 32.5 cm^{2}[/tex]
Write the percent as a fraction in simplest form.
36% =
Answer:
36%= 9/25 in fraction form (:
Answer:
36/100 sorry if wrong
Step-by-step explanation:
What is the constant proportionally of the graph
Help me
Answer:
The constant proportionally of the graph is:
k = 8Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
here 'k' is called the constant of proportionality.
From the graph, it is clear that:
at x = 0.5, the value of y = 4
so substituting x = 0.5 and y = 4 in the equation
k = y/x
k = 4/0.5
k = 8
at x = 1, the value of y = 8
so substituting x = 1 and y = 8 in the equation
k = y/x
k = 8/1
k = 8
Therefore, the constant proportionally of the graph is:
k = 8how do i write 0.87 in words
zero pint eight seven ......
. In a study, a radiologist correctly identifies 80 cases that contain a lesion (abnormality) and falsely diagnoses 10 cases as normal when they are not. In addition, he incorrectly diagnoses 15 cases as abnormal. However, he correctly identifies 165 normal cases. Calculate the diagnostic sensitivity and specificity.
Answer:
The sensitivity rate of the test is 88%. For its part, the specificity rate of the test is 91%.
Step-by-step explanation:
The sensitivity of a medical test is its ability to detect positive cases of the disease, while the specificity of the test is its ability to detect negative cases.
In total, there are 270 cases:
-80 positives
-10 false negatives
-15 false positives
-165 negatives
Thus, to calculate both concepts, the following calculations must be performed:
Sensitivity = positives / (positives + false negatives)
X = 80 / (80 + 10)
X = 80/90
X = 0.88
Thus, the sensitivity rate of the test is 88%.
Specificity = negatives / (negatives + false positives)
X = 165 / (165 + 15)
X = 165/180
X = 0.91
For its part, the specificity rate of the test is 91%.
Which expression is the same as (2 x 7) x 3 ?
Answer:
[tex]42x^{2}[/tex]
HELP QUICK ILL GIVE TOU BRAINLIEST
find the surface area...
Drag and drop the correct terms to classify the triangles based on sides or angles.
The triangles are classified below.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
An equilateral triangle is a triangle where all three sides are equal.
The right triangle is a triangle where one angle is 90 degrees.
An isosceles triangle is a triangle where two sides are equal.
An obtuse triangle is a triangle where the angle is greater than 90 degrees
An acute triangle is a triangle where the angles are less than 90 degrees.
A scalene triangle is a triangle where all three sides are different.
Now,
Side 5 cm, 5 cm, 5 cm, and 5 cm is an equilateral triangles.
Since all the sides are the same.
Sides of 3 cm, 5 cm, and 5 cm is an isosceles triangle.
Since the two sides are the same.
Sides of 3 cm, 5 cm, and 7 cm is a scalene triangle.
Since all three sides are different.
Angles of 40°, 50°, and 90° is a right triangle.
Angles of 40°, 60°, and 80° is an acute triangle.
Angles of 40°, 40°, and 100° is an abtuse triangle.
Thus,
The triangles are classified above.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ5
HELP HELP HELP HELP HELP PLEASE PLEASE!!!!!!
9514 1404 393
Answer:
84 = j × 7
Step-by-step explanation:
A product results from multiplying two numbers. Here, the two numbers are said to be "Julie's score" and 7. "Julie's score" is represented by j, so the product is ...
j × 7
Then the translation can be ...
84 is the product of j and 7
84 = j × 7
__
In algebra, we can indicate a product without the multiplication symbol, simply by writing the factors next to each other. Generally, we write the numeric factor first:
84 = 7j . . . . another way to write the answer
Note that this latter method does not seem to appear in the forms available for your answer box.
Find the area of these shapes
Answer:
Step-by-step explanation:
Left figure:
area of rectangle = 4×6 = 24 cm²
area of triangle = ½×(base of triangle)×(height of triangle) = ½×6×4 = 12 cm²
area of shape = 24+12 = 36 cm²
Right figure:
area of rectangle = 6×8 = 48 m²
area of triangle = ½×(base of triangle)×(height of triangle) = ½×8×(8-6) = 8 m²
area of shape = 48+8 = 56 m²
Isabella is making a display board for the school trip. The display board is 2.50m by 2m rectangle. She needs to cover the entire display board with card. How much card would she needs?
Answer:
5m^2
Step-by-step explanation:
Given data
Length of board= 2.50m
Width of board= 2m
The cover need should have the same area as the board
Area= Length*Width
Area= 2.5*2
Area=5m^2
Hence the area of the cover is 5m^2
How heavy is a 225 meter cable if a 3 meter section weighs 1.3 kg?
(GIVING BRAINLYIST) 4 ÷ 1/2 YOU HAVE TO show your work on paper using fraction models!
Answer:
8
Step-by-step explanation:
so my school uses the method called kcf (keep change flip)
keep the 4
change the division sign to a multiplication sign
flip 1/2 to 2/1
4x2=8
Answer:
8 i first said two but used a caculater and found out it was 8
Step-by-step explanation:
