Please write the answer clearlyEvaluate the integral. COS X dx 9-sin? x 2
Answers
The solution to the integral is (-1/108) arctan((sin^2(x) - 9)/9) - (1/243) (1/[(sin^2(x) - 9)^2 + 1]) + C.
To evaluate the integral ∫ cos(x) dx / (9 - sin^2(x))^2, we can use the substitution u = sin(x), which gives us
du/dx = cos(x)
dx = du/cos(x)
Substituting u and dx in the integral, we get
∫ cos(x) dx / (9 - sin^2(x))^2 = ∫ du / [(9 - u^2)^2 cos(x)]
Next, we can use partial fraction decomposition to rewrite the integrand as follows
1/[(9 - u^2)^2 cos(x)] = (A/(9 - u^2)) + (B/(9 - u^2)^2)
Multiplying both sides by (9 - u^2)^2 cos(x), we get
1 = A(9 - u^2)cos(x) + Bcos(x)
Substituting u = 3 and u = -3, we can solve for A and B to get
A = -1/54
B = 1/27
Substituting these values back into the integral, we get
∫ cos(x) dx / (9 - sin^2(x))^2 = ∫ (-1/54) du / (9 - u^2) + ∫ (1/27) du / (9 - u^2)^2
Using the substitution v = u^2 - 9 for the first integral, we get
∫ (-1/54) du / (9 - u^2) = (-1/108) ∫ dv / (v^2 + 18v + 81)
We can use the substitution w = v + 9 to simplify the integrand, which gives us
∫ dv / (v^2 + 18v + 81) = ∫ dw / (w^2 + 81)
Using the substitution z = w/9, we get
∫ dw / (w^2 + 81) = (1/9) ∫ dz / (z^2 + 1)
This integral can be evaluated as arctan(z) + C, where C is the constant of integration.
Substituting the values back in reverse order, we get
∫ cos(x) dx / (9 - sin^2(x))^2 = (-1/108) arctan((u^2 - 9)/9) - (1/27)(1/9) (1/[(u^2 - 9)^2 + 81]) + C
= (-1/108) arctan((sin^2(x) - 9)/9) - (1/243) (1/[(sin^2(x) - 9)^2 + 1]) + C
Therefore, the solution to the integral is
∫ cos(x) dx / (9 - sin^2(x))^2 = (-1/108) arctan((sin^2(x) - 9)/9) - (1/243) (1/[(sin^2(x) - 9)^2 + 1]) + C.
To know more about Integral:
https://brainly.com/question/18125359
#SPJ4
Related Questions
What is the equation for -8 = p - 13
Answers
Answer: 5 is your answer hope this helped
plz make brainly
Step-by-step explanation:
Find the vertex of the quadratic equation f(x) = x2 - 4x - 10
Answers
Answer:
2
Step-by-step explanation:
Answer:
vertex = (2, - 14 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
(h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² - 4x - 10
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term )² to x² - 4x
f(x) = x² + 2(- 2)x + 4 - 4 - 10
= (x - 2)² - 14 ← in vertex form
with vertex (h, k ) = (2, - 14 )
PLEASE HELP!!! Shasha and Alan are both running on the track Shasha begins at the starting line and is running 5 feet per second Alan begins 30 feet ahead of Shasha and is running at a speed of 3 ft per second how many seconds will it take Shasha to catch up to Alan?
Answers
Answer:
All you have to do is multiply 5 and 3 by specific gaps in between new numbers then subtract 30. Keep doing that until you get evenly matched numbers.
Step-by-step explanation:
The answer is 15, it would take 15 seconds for Alan to reach Sasha.
Expand.
Your answer should be a polynomial in standard form.
(3b-4)(b+2)=
Answers
Answer:
3b^2 +2b -8
Step-by-step explanation:
Answer:
\(3b^2+2b-8\)
Step-by-step explanation:
find the value of given expression
\( \sqrt{(60 \div 10) {}^{2} } \)
Answers
Step-by-step explanation:
\( \sqrt{(60 \div 10) {}^{2} } \\ = \sqrt{(6) {}^{2} } \\ = \sqrt{36 } \\ = 6\)
6 is your answer
Answer:
\(\sqrt{\left(\frac{60}{10}\right)^2}\)
\(\sqrt{\left(\frac{60}{10}\right)^2}=\frac{60}{10}\)
\(\frac{60}{10}=6\)
----------------------
hope it helps..
have a great day!!
Are Figures A and B congruent? Explain your reasoning.
Answers
Answer:
no bc the two figures need to be exactly the same size
Step-by-step explanation:
which of the following represents the graph of this equation?
Answers
Use the information given to enter an equation in standard form.
Slope is 7, and (1, 8) is on the line.
Answers
The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant b.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
Now,
At x = 0 ⇒ y = b so it will be a y-intercept.
Put m = 7 , x = 1 and y = 8
8 = 7(1) + b
b = 1
Thus, y = 7x + 1
Hence "The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1".
For more about the linear function,
brainly.com/question/21107621
#SPJ1
2x-3=5
(x+2)(3x-15)=0
Answers
Answer:
the first one gat to be x=4
Answer: 17
Step-by-step explanation: :)
Martin thinks of two numbers. He says, "The Highest Common Factor (HCF) of my two numbers is 6 The Lowest Common Multiple (LCM) of my two numbers is a multiple of 15" Write down two possible numbers that Martin is thinking of.
Answers
Answer:
30 and 42
Hope this helps
Which of the following fractions converts to a repeating decimal? A 3/8 B 2/9 C 3/10 D 5/16
Answers
Just divide the numerator by the denominator.
A. 3/8= 0.375
B. 2/9= 0.222222222222222
C. 3/10=0.3
D. 5/16= 0.3125
Answer:
B. 2/9
Step-by-step explanation:
3/8 = 0..375
2/9 = 0.2222222222
3/10 = 0.3
5/16 = 0.3125
the repeating decimal among these is 2/9 = 0.22222222222222222, because it has a repeated decimal numbers
I’ll give Brainly
Which side lengths form a right triangle?
Choose all answers that apply:
А
3, √27, 6
B
8, 15, 17
5,5, 50
Rer
Answers
Answer:
C 5,5, sqrt(50)
Step-by-step explanation:
so basically a^2+b^2=c^2
and 5^2+5^2 = 50 so c is sqrt of 50
Answer:
the answer is all three of them because I just got it right on khan academy
what is the value of 4! + (18 - 13)!?
plzz help me...
Answers
Answer:
9
Step-by-step explanation:
4+(18-13)
4+(5)
9
mark me brainliest
Answer:
\(4i + 5i = 4i \times (1 + 5) = 4 \times 3 \times 2 \times 1 \times 6 = 144\)
Can you please help me?
Answers
Answer:
59 + 163 + x = 360
(cus a circle is 360 degrees ya feel me boi?)
x = 360 - 59 - 163
x= 138
Don't do drugs kids. Stay in school. Chase morality.
Step-by-step explanation:
Answer:
1. +17°
2.x=138°
Step-by-step explanation:
1. (Counted on my fingers lol -8 to 9)
2. 163+53=222
360-222=138
Marcie cooked dinner for herself. The original recipe has a serving size of 3 and requires three and three sevenths pounds of chicken. How many pounds of chicken will be needed for a single serving?
one and one seventh pounds
nine and three sevenths pounds
two over 49 pounds
three sevenths pounds
Answers
Using proportions, the number of pounds that will be needed for a single serving is: one and three seventh pounds.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The number of pounds for 3 people is given by:
\(3 \frac{3}{7} = 3 + \frac{3}{7} = \frac{24}{7}\)
Hence, for one person, the number of pounds can be divided by three(multiplied by 1/3), hence:
\(\frac{24}{7} \times \frac{1}{3} = \frac{24}{21}\)
24 divided by 21 has a quotient of 1 and remainder of 3, hence as a mixed number, the amount is:
one and three seventh pounds.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Answer:
Step-by-step explanation:
the awnser is cerrot.
John saves $32.40 within 3 months, how much money can John save in 2 years
ℙℤ ℕ ℍℙ ℍ ℍ ☹︎
I will give points | (• ◡•)|
Answers
Answer: $259.20
Step-by-step explanation: Divide $32.40 by 3 to get $10.80. Then multiply $10.80 by 24 (2 years).
Answer:
$259.20
Step-by-step explanation:
32.4·4=129.6
129.6·2=259.2
Additional info
Twelves months in one year so 12÷3=4
Two years so 129.6·2
Just in case you were wondering how I got 4 and 2
If P = (-2, 7), Find: Rx= 1 (P)
Please help!
Answers
according to question the answer is Rx= 1 (P) = (4, 7).
To find Rx= 1 (P), we need to reflect point P about the line x = 1.
First, we find the distance between the x-coordinate of point P and the line x = 1:
|1 - (-2)| = 3
This means the distance between point P and the line x = 1 is 3 units.
To reflect point P about the line x = 1, we need to move the same distance (3 units) in the opposite direction. Since the point P is to the left of the line x = 1, we need to move to the right.
So, the x-coordinate of the reflected point is:
1 + 3 = 4
The y-coordinate remains the same since the line of reflection does not affect the y-coordinate.
To learn more about line visit:
brainly.com/question/17188072
#SPJ11
In the following exercises, vectors u, v, and w are given.
a. Find the triple scalar product u · (v × w).
b. Find the volume of the parallelepiped with the
adjacent edges u, v, and w.
Answers
a. Triple scalar product is defined as the product of three vectors, u, v and w which results in a scalar value and is denoted as [u, v, w].
Triple scalar product [u, v, w] can be calculated as follows:[u, v, w] = u · (v × w) where v × w is the cross product of vectors v and w and u · (v × w) is the dot product of vectors u and (v × w).
\(u · (v × w) = 6(-3) - 3(-4) + 2(-3)
u · (v × w) = -18 + 12 - 6
u · (v × w) = -12\)
b. Volume of the parallelepiped with adjacent edges u, v and w can be calculated as the absolute value of the triple scalar product of vectors u, v and w. It is denoted by |[u, v, w]|.
The volume of the parallele piped with adjacent edges u, v and w can be calculated as:
\(|[u, v, w]| = |6(-3) - 3(-4) + 2(-3)| = |-18 + 12 - 6| = 0\)
The volume of the parallelepiped with adjacent edges u, v and w is 0.
To know more about Triple scalar product visit:
https://brainly.com/question/13419505
#SPJ11
Please help! What is the range of the function shown in the graph below?
Answers
Step-by-step explanation:
the range of a function is the interval or set of all valid y (function result) values.
so, what values is this function creating ?
we see that y never gets larger than -4.
but it will clearly go and go and go ... further down without any limit.
so, the range is
-infinity < y <= -4
Jamie has 2 pounds of butter. She used 3/8 pound of butter to make batter for pancakes. How much butter is left?
Answers
Answer:
Step-by-step explanation:
Basically 3/8 "times" 2
The equations
8/2 = 4
So it will be 3/4
What is the formula for the area of a circle?
O A. A = 727
O B. A = 20
O C. A = terd
O D. A = 2
Answers
WILL MARK BRAINLIEST!!!
1. Describe three different ways to solve a quadratic equation. Describe the strengths and limitations of each method, and explain how you would decide which one to use to solve a particular problem.
2. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
Divide all terms in the equation by a.
Subtract the constant (the term without an x) from both sides.
Add a constant (in terms of a and b) that will complete the square.
Take the square root of both sides of the equation.
Solve for x.
3. Write a linear equation that intersects y = x2 at two points. Then write a second linear equation that intersects y = x2 at just one point, and a third linear equation that does not intersect y = x2. Explain how you found the linear equations.
Thank You!!
Answers
The ways that can be used to solve a quadratic equation include:
Factorization
Using the quadratic formula.
Completing the squares.
What is a quadratic equation?It should be noted that a quadratic equation simply means an algebraic equation of the second degree in x.
Here, the factorization, using the quadratic formula, and completing the squares method can be used.
Learn more about quadratic equation on:
brainly.com/question/121433
#SPJ1
Calculate the size of angle
x and y
Answers
Answer:
x = 116
y = 64
Step-by-step explanation:
x and the angle given are supplemental. That means that together the angles equal 180
180 - 64 = 116
angle y is congruent to angle 64 (they have the same measurements)
Write the equation of the tangent line to the graph of y = (6x² − 6x + 3)(1 + 2x) at x = 1. Check the reasonableness of your answer by graphing both the function and the tangent line.
Answers
To find the equation of the tangent line to the graph of y = (6x^2 − 6x + 3)(1 + 2x) at x = 1, we need to find the slope of the tangent line at that point and use the point-slope form of a line equation. Here's a summary of the solution:
Calculate the derivative of the function y = (6x^2 − 6x + 3)(1 + 2x) using the product rule and simplify the expression.
Evaluate the derivative at x = 1 to find the slope of the tangent line.
Substitute the coordinates of the point (1, f(1)) into the point-slope form of the line equation, where f(1) is the value of the function at x = 1.
Simplify the equation to obtain the equation of the tangent line.
To check the reasonableness of the answer, graph both the function and the tangent line using a graphing tool or software. Plot the function and the tangent line on the same graph to visually verify that the line is indeed tangent to the function at x = 1.
By taking the derivative of the function, evaluating it at x = 1, and applying the point-slope form, you can determine the equation of the tangent line. Graphing both the function and the tangent line together allows you to visually confirm the tangent relationship at x = 1.
To learn more about tangent click here:
brainly.com/question/10053881
#SPJ11
Which expression is equivalent to -14-(-2)?
14-2
O 14+2
0 -14+2
14-2
Answers
Answer:
-14 +2
Step-by-step explanation:
because you would do kcc aka keep change change
you would keep -14 change the minus to a addition sign and change the -2 to a positive 2
Can someone help with this please!!
Answers
Answer:
D) L+S=9 ; 6L+3S=9
Step-by-step explanation:
Given this information, we know that the total number of large and small Ubers must be 9, so we can eliminate choices A and C as the first part of the system of equations is L+S=9
Also, since the large Ubers can fit only 6 people per vehicle and the small Ubers can only fit 3 people per vehicle, then we can eliminate choice B as the second part of the system of equations is 6L+3S=39
Therefore, the only correct choice is D
If AD = 6, DC = 14, and BE = 4.75, calculate EC. Image not set to scale.
Answers
Answer:
\(\Large \boxed{11.08}\)
Step-by-step explanation:
The triangles are congruent, we can use ratios to solve.
AD/DC = BE/EC
Let the length of EC be x.
6/14 = 4.75/x
Solve for x.
Cross multiply.
6 × x = 14 × 4.75
6x = 66.5
Divide both sides by 6.
(6x)/6 = (66.5)/6
x = 11.083333...
Greetings from Brasil...
Here we can use similarities of triangles
AC/DC = BC/EC
20/14 = (4.75 + X)/X
X ≅ 11.1
see attachment
Find m<1 and m<2 Tell which theorem can be used.
Answers
By applying the alternate interior angles theorem, m∠1 is equal to 140°. By applying the supplementary angle theorem, m∠2 is equal to 40°.
What is the alternate interior angles theorem?The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
By applying the alternate interior angles theorem, the value of x would be calculated as follows:
m∠1 = 140°.
What is a supplementary angle?A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees (180°).
Mathematically, a supplementary angle can be calculated by using this formula:
Q + R = 180°
Where:
Q and R are measure of the angles subtended.
By applying the supplementary angle theorem, we have:
m∠2 + 140° = 180°.
m∠2 = 180° - 140°
m∠2 = 40°.
Read more on alternate interior angle here: brainly.com/question/2497532
#SPJ1
hello, may someone help me, I have more and it’s due at 11:59
Answers
answer 14: x=5
answer 15: x=-5
a franchise restaurant chain is considering a new store in an unserved part of town. its finance group estimates an npv of $20 million if the population growth is 10% (40% probability), an npv of $8 million if the population does not grow (30% probability), and an npv of 2$8 million if the population shrinks 5% (30% probability). what is the expected value of npv (to the nearest dollar) of opening the store?
Answers
Considering the probabilities and corresponding NPVs associated with different population growth scenarios, The expected value of the Net Present Value (NPV) of opening the store is $15.6 million.
To calculate the expected value of NPV, we multiply each possible NPV outcome by its corresponding probability and sum them up.
Let's denote the NPVs as follows:
NPV1 = $20 million (population growth: 10% probability)
NPV2 = $8 million (no population growth: 30% probability)
NPV3 = $8 million (population shrinkage: 5% probability)
Now we can calculate the expected value (E) using the formula:
E = (NPV1 * P1) + (NPV2 * P2) + (NPV3 * P3)
Substituting the given probabilities:
E = ($20 million * 0.4) + ($8 million * 0.3) + ($8 million * 0.3)
E = $8 million + $2.4 million + $2.4 million
E = $12.8 million + $2.4 million
E = $15.2 million
Rounding the expected value to the nearest dollar:
E ≈ $15.6 million
The expected value of the Net Present Value (NPV) of opening the store is approximately $15.6 million. This means that, on average, the franchise restaurant chain can expect to earn $15.6 million from the new store, considering the probabilities and corresponding NPVs associated with different population growth scenarios.
To know more about probabilities , visit
https://brainly.com/question/25839839
#SPJ11