If we want to evaluate the integral X+35 1- dx. x2 +16 we use the trigonometric substitution - and dx de and therefore the integral becomes, in terms of do The antiderivative in terms of 0 in (do not forget the absolute value) 1 Finally, when we substitute back to the variable x, the antiderivative becomes Use for the constant of integration Show det Submit Answer
Answers
If we want to evaluate the integral X+35 1- dx. x2 +16, we can use the trigonometric substitution x = 4tanθ, which implies dx = 4sec2θdθ. Substituting these values, we get:
∫(x+35)/(x2+16)dx = ∫(4tanθ+35)/(16tan2θ+16)×4sec2θdθ
= ∫(4tanθ+35)/(16sec2θ)×4sec2θdθ
= 4∫(tanθ+35/16) dθ
= 4∫(sinθ/cosθ+35/16) dθ
= 4∫(sinθ/cosθ)dθ + 4∫(35/16) dθ
Using the trigonometric identity tanθ = sinθ/cosθ and substituting u = cosθ, du = -sinθdθ, we get:
= 4∫(-du/u) + 4∫(35/16) dθ
= -4ln|u| + 35/4 + C
= -4ln|cosθ| + 35/4 + C
Substituting back x = 4tanθ, we get:
= -4ln|cos(arctan(x/4))| + 35/4 + C
= -4ln|cos(arctan(x/4))| + 35/4 + C
= -4ln|cos(arctan(x/4))| + 35/4 + C
Finally, the constant of integration is denoted by C.
To evaluate the integral of (X+35)/(x^2 + 16) dx, we use the trigonometric substitution x = 4tan(θ), and dx = 4sec^2(θ) dθ.
By substituting these terms, the integral becomes:
∫((4tan(θ) + 35)/(16tan^2(θ) + 16)) * 4sec^2(θ) dθ
Simplify the expression:
∫(4tan(θ) + 35) / (16(tan^2(θ) + 1)) * 4(sec^2(θ)) dθ
Since tan^2(θ) + 1 = sec^2(θ), the integral becomes:
∫(4tan(θ) + 35)/16 dθ
Integrating with respect to θ, we get the antiderivative in terms of θ:
(1/4)tan(θ) + (35/16)θ + C₁, where C₁ is the constant of integration.
Finally, substitute back the variable x using the initial substitution x = 4tan(θ):
tan(θ) = x/4
To find θ, use the arctangent function:
θ = arctan(x/4)
The antiderivative in terms of x becomes:
(1/4)(x/4) + (35/16)arctan(x/4) + C
Simplified, this is:
(1/16)x + (35/16)arctan(x/4) + C
Here, C is the constant of integration.
Visit here to learn more about integral brainly.com/question/18125359
#SPJ11
Related Questions
What is the explicit rule for this geometric sequence? PLEASE HELP
3,35,325,3125,...
an=15⋅3n−1
an=3⋅(15)n
an=3⋅(15)n−1
an=15⋅3n
Answers
Answer:
first write the formula and also send me the pick
the ratio of weight of a baby pig to it's Mother is 3 is to 7 the baby Pig has a weight of 8 kg.What is the weight of the mother pig
Answers
get the total weight of baby pig and that of her mother ..3+7=10
if the baby pig has a weight of 8kgs
compare the weight of the mother
i.e. 3/10 is equal to 8
what about 7/10
and.56/3
help me quickyly pleaseee
Answers
Answer:
It is 32:200 for the 2nd row last one
Answer:
It is 32:200 for the 2nd row last one
Describe how to evaluate the expression 5v - \(\sqrt{4x}\) for v = 2 and w = 9
Answers
idrk sorry I'm horrible at mathhh
Determine the best name for the quadrilateral with the following vertices.
A(0, 0), B(1, 3), C(5, 3), D(4, 0)
Answers
The best name for this quadrilateral is a trapezoid.
How to identify the quadrilateral?The quadrilateral can be plotted on a coordinate plane as follows:
C(5, 3) D(4, 0)
+----------------+
| |
| |
| |
| |
+----------------+
B(1, 3) A(0, 0)
The sides of the quadrilateral are AB, BC, CD, and DA.
Based on the properties of the sides and angles, this quadrilateral can be classified as a trapezoid.
A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, the pair of parallel sides are AB and CD.
So, the best name for this quadrilateral is a trapezoid.
Read more about trapezoid here:
https://brainly.com/question/1463152
#SPJ1
SOMEONE HELP PLSSS
3. Which ratio would NOT be involved in the altitude or leg rule?
Answers
Answer:
AB/AD = AD/AC
Step-by-step explanation:
From the triangle given, we can get the required expression to calculate CD using the altitude theorem as shown:
AB/CB = CB/DB (Hypotenuse/Adjacent side using the similar triangle ABC and CDB)
AB/AC = AC/AD (Hypotenuse/Opposite side using the similar triangle ABC and ACD)
BD/CD = CD/AD (Adjacent/Opposite side using the similar triangle BCD and ACD)
Hence the odd one out will be option C AB/AD = AD/AC (since there is no altitude CD in the expression)
Answer:
AB/AD = AD/AC
Step-by-step explanation:
Had it on my quiz
Consider the following rational function. f(x) = - 3x + 2/x - 2 Step 3 of 3: Identify four ordered pairs on the graph of the function. Answer
Answers
The ordered pairs of the given rational function are:
(-2, -5¹/₂), (-1, -5²/₃),(0, -1), (1, -5),(-1,
How to find the Ordered Pairs?In mathematics, an ordered pair (a, b) is a pair of objects. The order in which objects appear in pairs is important.
The ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (By contrast, the unordered pair {a, b} corresponds to the unordered pair {b, a}.)
We are given a rational function as:
f(x) = -3x + (2/(x - 2))
Now, to get the ordered pair, we can use different values of x and find the corresponding value of y.
Thus:
At x = 0, we have:
f(x) = -3(0) + (2/(0 - 2))
f(x) = -1
At x = 1, we have:
f(x) = -3(1) + (2/(1 - 2))
f(x) = -5
At x = -1, we have:
f(x) = -3(-1) + (2/(-1 - 2))
f(x) = -5 - 2/3
= -5²/₃
At x = -2, we have:
f(x) = -3(-2) + (2/(-2 - 2))
f(x) = -5 - 1/2 = -5¹/₂
Read more about Ordered Pairs at: https://brainly.com/question/1528681
#SPJ4
How to convert 400 kg to lbs?
Answers
400 kilograms is equal to 881.848 pounds.
When it comes to measuring weight, kilograms (kg) and pounds (lbs) are both commonly used units of measurement. In order to understand the conversion of kilograms to pounds, it is important to know that there are 2.20462 pounds in one kilogram.
So, to convert 400 kilograms to pounds, you would multiply 400 by 2.20462. When you do this calculation, you get 881.848 pounds. So,
In summary, to convert kilograms to pounds, you simply need to multiply the number of kilograms by 2.20462. 400 kg is equal to 881.848 pounds, 200 kg is equal to 440.924 pounds and 300 kg is equal to 661.386 pounds.
to know more about kgs to lbs refer here
https://brainly.com/question/24545553#
#SPJ11
The first To Answer Gets Brainliest!!!
Answers
These lines never intersect, there are no solutions to the equation.
Describe Graph?In mathematics, a graph is a visual representation of a set of objects and the relationships between them. Graphs are widely used in many areas, including mathematics, computer science, engineering, social sciences, and more.
A graph consists of two main components: vertices (also known as nodes) and edges. The vertices represent the objects, and the edges represent the connections or relationships between them. The edges can be directed or undirected, meaning they can be one-way or two-way relationships.
There are many types of graphs, including:
Undirected graphs: Graphs in which edges have no direction.
Directed graphs: Graphs in which edges have a direction, often represented by arrows.
Weighted graphs: Graphs in which edges have weights or values, representing some kind of numerical data.
Bipartite graphs: Graphs in which the vertices can be divided into two distinct sets, with edges only connecting vertices in different sets.
Complete graphs: Graphs in which every vertex is connected to every other vertex by an edge.
Graphs are used to model and analyze various kinds of data, such as social networks, transportation systems, financial transactions, and more. They are also used in algorithms and data structures, such as shortest path algorithms and tree data structures. In addition, graphs are often visualized using software tools to help people better understand complex relationships and patterns in data.
The given equation is 3x + 1 = 3x + 2.
Subtracting 3x from both sides, we get:
1 = 2
This is a contradiction and there are no values of x that can satisfy this equation.
On a graph, this can be seen as follows:
Plotting the graphs of y = 3x + 1 and y = 3x + 2, we get two parallel lines.
Since these lines never intersect, there are no solutions to the equation.
To know more about contradiction visit:
https://brainly.com/question/30373679
#SPJ1
a researcher wishes to conduct a study of the color preferences of new car buyers. suppose that 30% of this population prefers the color green . if 16 buyers are randomly selected, what is the probability that at least 4 buyers would prefer green ?
Answers
The probability that at least 4 buyers would prefer green is 0.9963.
The researcher wishes to conduct a study of the color preferences of new car buyers.
Suppose that 30% of this population prefers the color green.
If 16 buyers are randomly selected, the probability that at least 4 buyers would prefer green is 0.9963.
Let X be the number of new car buyers who prefer the color green.
X follows a binomial distribution with n = 16 and p = 0.30.
The probability of at least 4 buyers preferring green is:
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = 16)
Using the binomial probability formula, P(X = k) = (n C k) pk qn-k
where q = 1 - p = 1 - 0.30 = 0.70
Then: P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = 16)
P(X ≥ 4) = [16 C 4](0.30)4(0.70)12 + [16 C 5](0.30)5(0.70)11 + [16 C 6](0.30)6(0.70)10 + ... + [16 C 16](0.30)16(0.70)0= 0.9963
Therefore, the probability that at least 4 buyers would prefer green is 0.9963.
Learn more about car buyers:
https://brainly.com/question/31097305
#SPJ11
I’ll give the Brainliest to who answers these questions with reasonable explanations.
1. A bag has 16 marbles in it: 6 red, 4 blue, 3 yellow, and 3 green. A marble is drawn and put back, and then another marble is drawn. What is the probability that a blue marble was drawn followed by a yellow marble?
2. A bag has 16 marbles in it: 6 red, 4 blue, 3 yellow, and 3 green. A marble is drawn and not put back, and then another marble is drawn. What is the probability that a blue marble was drawn followed by a yellow marble?
Thank you.
Answers
Answer:
1. 0.0469 (4.d.p)
2. 0.05
Step-by-step explanation:
1. First we'll find the probability of drawing a blue marble.
P = (No. favourable events)/(Total events)
In this case it's:
P = (No. blue marbles)/(Total Marbles)
Therefore P(Blue) = 4/16 = 0.25
Now we find the probability of drawing a yellow marble:
The total number will be the same because the blue marble will have been put back.
P(Yellow) = 3/16 = 0.1875
Now, since we are calculating the probability of both happening we multiply together the two individual probabilities to get the combined probability of both:
0.25 x 0.1875 = 0.0469 (4.d.p)
2. The probability of drawing a blue marble is still the same so we can keep that: P(Blue) = 0.25
But this time, the marble is not replaced. This means that the total number of marbles has changed when drawing the yellow marble:
P(Yellow) = 3/15 = 0.2
Now we multiply them together again to find the combined probability of both happening:
0.25 x 0.2 = 0.05
Hope this helped!
Ndjshsuhsjshahhaha helpppppooo
Answers
Answer:
15.7 ft cause 5 x 3.14 = 15.7
Step-by-step explanation:
Find the lowest common denominator (multiple). Type the equivalent fractions. Then, add or subtract. Simplify your answer. 1
2
1
3
Answers
Answer:what
Step-by-step explanation:what does this mean
Every year, Martha and her sister attend 'The Nutcracker' at the Greenpoint Ballet. Last year, orchestra seating cost $60 per ticket. This year, each ticket was 15% cheaper. What was the cost of each ticket this year?
Answers
Answer:
$51
Step-by-step explanation:
You convery the percentage into a decimal, by dividing it by a hundred.
15÷100= 0.15
then you multiply the decimal and the price.
60×0.15= 9.
The question said it got cheaper so we have to subtract 9 from the original price.
60-9=51.
HELP PLEASEEEEE!!!!!!
Answers
If that answer doesn't work, then try 29 without the percent sign.
============================================================
Explanation:
We know with absolute certainty that the person ordered a hot drink, due to the "given".
This means we only focus on the values in the first row.
There are 5+48+22 = 75 hot drinks ordered. Of that total, 22 hot drinks are large.
The probability of getting a large drink, given it was a hot beverage, is 22/75 = 0.2933 approximately.
This converts to 29.33% and that rounds to 29%
How many 5/8 does it take to make 15/4?
Answers
Answer:How many 5/8s go into 15/4, answer : 6.
Step-by-step explanation:
Steps for dividing fractions
Find the reciprocal of the divisor
Reciprocal of
5
8
:
8
5
Now, multiply it with the dividend
So,
15
4
÷
5
8
=
15
4
×
8
5
=
15 × 8
4 × 5
=
120
20
no angle given how do i solve
Answers
Answer:
the square means those to lines make a 90 degree angle aka. right angle
Step-by-step explanation:
Answer:
Sine of x = \(\frac{\sqrt{288} }{18}\)
Cos of x = 6 / 18
Step-by-step explanation:
To solve this:
We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle:
\(a^{2} + b^{2} = c^{2}\)
In any right angled triangle, for any angle:
The sine of the angle = the length of the opposite side / the length of the hypotenuse
The cosine of the angle = the length of the adjacent side / the length of the hypotenuse
In this right triangle, we know the opposite side is \(\sqrt{288}\), the adjacent side is 6, and the hypotenuse is 18
So to find the sine of x, we would do \(\frac{\sqrt{288} }{18}\)
And to find the cos of x, we would do 6 / 18
Hope this helps!! Pls mark as brainliest, ty.
7. A carpenter has a plank of wood that is 121.92 centimeters
long. The carpenter cuts the plank into 4 equal pieces. About
how long is each piece?
about
centimeters
Answers
The length of each wooden plank will be 30.48 cm
What is the length of each wooden plank?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.There are three kinds of fractions. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator.Here given,
The total length of the wooden plank is 121.92 centimeters.
Also given that ,
A carpenter cuts the plank into 4 equal parts
=> 121.92 / 4
=> 30.48
Therefore the length of each piece will be 30.48 cm
To learn more about fraction refer to :
https://brainly.com/question/17220365
#SPJ1
Holly bought 23 tickets to the baseball game. She got a group rate that gave her $4 off of the regular ticket price for each ticket. The total cost was $184.
What was the regular price for each ticket?
Enter your answer in the box.
$: (answer)
Answers
Answer:
$4.13
Step-by-step explanation:
let x = the regular price of tickets
23x-4=184
subtract 4 from each side
23x=180
divide 23 by each side to get x by itself
x= $.13 per ticket add 4 because she got $4 off
the original price is $4.13
The fire department needs to rescue a man from a house. There is a large, unstable puddle below the house. The ladder needs to be placed 60 feet from the house and reach up to a 40 foot window. How long must the ladder be?
Answers
Answer: 100 feet
Step-by-step explanation:
60+40=100
Answer:
at least 73 feet
Step-by-step explanation:
40^2+60^2=5200
square root 5200=72
Graph the inequality on a coordinate plane.
2x - 5y< -10
Answers
Answer:
espero te sirva siuuuuuuuuuuu
Factor X squared minus 2X -80
Answers
Answer:
(x - 10)(x + 8)
Step-by-step explanation:
x² - 2x - 80
Consider the factors of the constant term (- 80) which sum to give the coefficient of the x- term (- 2)
The factors are - 10 and + 8 , since
- 10 × 8 = - 80 and - 10 + 8 = - 2 , then
x² - 2x - 80 = (x - 10)(x + 8)
(67)
1. A book was lengthened by 8 pages for the second edition. If the book
was originally 200 pages long, what was the percent increase?
Answers
Answer:
4% I believe
Step-by-step explanation:
how many times larger is 8*10^4 than 8*10^1
Answers
Do the activity please it's trigonometry
Answers
Answer:
SinA=k/g
cotA=k/j
secA=g/j
cosecB=g/k
tanB=l/k
cosB=k/g
sammy is classifying quadrilateral efgh. how can she use coordinate geometry to determine whether efgh is a rectangle? e(7, 10), f(4, 7), g(6, 5), h(9, 8)
Answers
Based on the slopes calculated, Sammy can conclude that quadrilateral EFHG is a rectangle.
To determine whether quadrilateral EFHG is a rectangle using coordinate geometry, Sammy can follow these steps:
1. Calculate the slopes of the opposite sides:
- Slope of EF: mEF = (yF - yE) / (xF - xE)
- Slope of HG: mHG = (yG - yH) / (xG - xH)
2. Calculate the slopes of the adjacent sides:
- Slope of FG: mFG = (yG - yF) / (xG - xF)
- Slope of EH: mEH = (yH - yE) / (xH - xE)
3. Check if the opposite sides have equal slopes:
- If mEF = mHG and mFG = mEH, then EFHG is a parallelogram.
4. Check if the adjacent sides have perpendicular slopes:
- If mEF * mFG = -1 and mHG * mEH = -1, then EFHG is a rectangle.
Let's calculate the slopes using the given coordinates:
mEF = (7 - 10) / (4 - 7) = 3 / -3 = -1
mHG = (5 - 8) / (6 - 9) = -3 / -3 = 1
mFG = (5 - 7) / (6 - 4) = -2 / 2 = -1
mEH = (8 - 10) / (9 - 7) = -2 / 2 = -1
Since mEF = mHG = -1 and mFG = mEH = -1, we have equal slopes for opposite sides and perpendicular slopes for adjacent sides.
Therefore, Sammy is able to determine that the quadrilateral EFHG is a rectangle based on the calculated slopes.
Learn more about coordinate geometry on:
https://brainly.com/question/18269861
#SPJ11
A bouncy ball is dropped such that the height of its first bounce is 4.5 feet and each successive bounce is 73% of the previous bounce's height. What would be the height of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
The height of the 10th bounce of the ball will be 0.6 feet.
What is geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
What is the formula for finding the nth term of geometric sequence?The nth term of the geometric sequence is given by
\(\sf T_n=ar^{n-1}\)
Where,
\(\sf T_n\) is the nth term.r is the common ratioa is the first termAccording to the given question.
During the first bounce, height of the ball from the ground, a = 4.5 feet
And, the each successive bounce is 73% of the previous bounce's height.
So,
During the second bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 10\)
\(=\dfrac{73}{100}(10)\)
\(\sf = 0.73 \times 10\)
\(\sf = 7.3 \ feet\)
During the third bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 7.3\)
\(=\dfrac{73}{100}(7.3)\)
\(\sf = 5.33 \ feet\)
Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...
And the common ratio of the geometric sequence is 0.73
Therefore,
The sixth term of the geometric sequence is given by
\(\sf T_{10}=10(0.73)^{10-1\)
\(\sf T_{10}=10(0.73)^{9\)
\(\sf T_{10}=10(0.059)\)
\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)
Hence, the height of the 10th bounce of the ball will be 0.6 feet.
Find out more information about geometric sequence here:
brainly.com/question/11266123
Find the value of x. Round your answer to the nearest tenth.
Answers
it’s a special triangle and that side would be 8√3 which is 13.9
Answer:
c. 13.9
Step-by-step explanation:
we can work out the third angle
all angles add up to 180
90 + 30 = 120, 180 - 120 = 60
using law of sines
\( \frac{x}{ \sin(a) } = \frac{b}{ \sin(b) } \)
where sin(a) = 60, b = 30 and sin(b) = 30
\( \frac{x}{sin(60)} = \frac{8}{ \sin(30) } \)
\(x = \frac{8}{sin(30)} \times \sin(60) \)
x = 13.9
Evaluate:
Σ12(n - 4) = [ ? ]
Answers
The final answer depends on the specific range of values for n, denoted by a and b.
To evaluate the expression Σ12(n - 4), we need to find the sum of the terms for a given range of values of n.
The expression Σ12(n - 4) represents the sum of the terms obtained by substituting different values of n into the expression 12(n - 4). The sum is taken over a specific range of values for n.
Let's assume that the range of n is from n = a to n = b. To evaluate the expression, we need to find the sum of the terms for all values of n within this range.
Expanding the expression 12(n - 4), we get 12n - 48. Now, we can rewrite the expression as Σ(12n - 48).
To find the sum, we can use the formula for the sum of an arithmetic series:
Σ(12n - 48) = [(b - a + 1) / 2] * [first term + last term]
The first term is 12a - 48, and the last term is 12b - 48.
Using this formula, we can evaluate the sum of the expression Σ12(n - 4) for the given range of values a and b.
In conclusion, the final answer depends on the specific values of a and b.
For more questions on range
https://brainly.com/question/30339388
#SPJ8
Complete Question:
What is the value of the sum Σ12(n - 4)?
what is the average velocity between 3.00 and 6.00 seconds.
Answers
The average velocity between 3 and 6 seconds will be found with the following equation:
\(\begin{gathered} v=\frac{v2-v1}{t2-t1} \\ v=\frac{36-9\text{ m}}{6-3\text{ }}\text{ (Replacing the values)} \\ v=\frac{27}{3}m/s\text{ (Subtracting)} \\ v=9\text{ }m/s\text{ (Dividing)} \\ \text{The answer is 9 m/s} \end{gathered}\)