To integrate 1 / sqrt(25 - 16x^2) dx, we use trigonometric substitution with x = (5/4)sinθ. After substitution, integration, and back-substitution, the result is arcsin(4x/5) + C, where C is the constant of integration.
Explanation:The integral to solve is ∑ (1 / sqrt(25 - 16x^2)) dx, which resembles the inverse trigonometric function, specifically the arcsine function. To solve this integral, we can use a trigonometric substitution. Since the integral involves a square root of a difference of squares, we can substitute x with (5/4)sinθ, which simplifies the integral considerably.
After substitution, we can then use the derivative of sinθ, which is cosθ, in order to find the full differential dx to replace in our integral. The resulting integral in terms of θ can be integrated using standard techniques, yielding an arcsine function as the antiderivative. After integrating, we must then convert back from θ to x to express the solution to the original integral in the original variable.
The answer to the integral ∑ (1 / sqrt(25 - 16x^2)) dx is arcsin(4x/5) + C, where C is the constant of integration. The substitution step is crucial in solving this type of problem and is a commonly used method in calculus.
At president bush's inauguration in 2005,the newspaper headline stated there were about 400,000 people in attendance of the newspaper rounded to the nearest 10,000 what is the largest number of smaller number of people who could been there
6-4x verbal expression
1. Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.
2. A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?
a)1, –5, 25, –125, ...
b)2, 10, 50, 250, ...
c)3, –2, –7, –12, ...
d)4, 9, 14, 19, ...
The length of a rectangle is five centimeters more than its width w if the perimeter of the rectangle is 26 centimeters what is the area of the rectangle i'm square centimeters
What is used to repair big, brass instruments
Repairing big, brass instruments requires the use of specialized tool kits made of steel alloys and brass instrument repair kits. These tools are designed to be gentle on the brass surface, ensuring the instrument's quality and longevity.
Explanation:Repairing big, brass instruments, such as trombones and trumpets, often requires the use of certain materials and techniques. Since brass is an alloy of copper and zinc, it is prone to tarnish and damage over time. Hence, it is important to use cleaning and repair tools made of similar or non-abrasive materials to avoid causing further damage to the instrument.
The most common methods of repairing dents and scratches in brass instruments involve specialist tool kits composed of various steel alloys, which are strong and durable, but also gentle on the brass surface. Additionally, using specialized brass instrument repair kits, which include various mutes, cleaning agents, and brushes, can help maintain the instrument's quality and longevity.
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becky works 16 days each month.how many days will she work in 6 months
Becky will work 96 days in 6 months.
Explanation:To find out the number of days Becky will work in 6 months, we need to multiply the number of days she works each month by the number of months. Given that Becky works 16 days each month, we can calculate the number of days she will work in 6 months as follows:
Number of days Becky works each month = 16Number of months = 6Number of days Becky will work in 6 months = 16 days/month * 6 months = 96 daysLearn more about number of days worked here:
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What is 43/50 as a percent?
Four points A, B, C, and D are coplanar, but only two at a time are collinear. Suppose a line is drawn through each pair of points. How many lines can you draw? ...?
When point E (-9, 3) is rotated 180� about the origin, its coordinate becomes (3, 9).
True
False
...?
Which CANNOT be used in a proof?
A. Theorems
B.Postulates
C.Properties
D.Undefined Terms
The triangle PQR shown on the coordinate grid below is reflected once to map onto triangle P´Q´R´.
If vertex P’ is at (7, -6), what are the coordinates of vertex R’?
A)(5, -3)
B)(3, -5)
C) (3, -2)
D)(5, -2)
The answer is (5,-2)
To find the coordinates of vertex R' in the reflected triangle, we can use the midpoint formula. Using the given point P' at (7, -6) and the original point P at (x, y), the x-coordinate of vertex R' is 5. Similarly, using the given point P' at (7, -6) and the original point R at (x, y), the y-coordinate of vertex R' is -2.
Explanation:To find the coordinates of vertex R', we need to map the reflection of triangle PQR onto triangle P'Q'R'. Since vertex P' is at (7, -6), we can use the midpoint formula to find the coordinates of the reflected point R'.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Using the given point P' at (7, -6) and the original point P at (x, y), we can write the equation:
(x + 7) / 2 = 7
Solving for x, we get x = 5.
Similarly, using the given point P' at (7, -6) and the original point R at (x, y), we can write the equation:
(y - 6) / 2 = -2
Solving for y, we get y = -2.
Therefore, the coordinates of vertex R' are (5, -2).
What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3?
A.9xy2 – 6x2y + 5x3
B. 9xy2 – 6x2y – 5x3
C. 9xy2 + 6x2y + 5x3
D. 9xy2 – 6x2y + 5x3
Answer:
The answer is B.
Step-by-step explanation:
The additive inverse of the given polynomial is:
-9xy^2 - 6x^2y + 5x^3
How to find the additive inverse of a polynomial?The additive inverse of a polynomial would be another polynomial, such that when we add the two, the outcome is zero.
For a given polynomial the additive inverse is given by multiplying the given polynomial by -1.
Here we have:
p(x) = 9xy^2 + 6x^2y – 5x^3
Then the additive inverse is:
q(x) = -p(x) = -9xy^2 - 6x^2y + 5x^3
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Lets say I had an 80% in a class, yet I got a 100% percent on the midterm, which is 10% of my grade. What would my new grade be?
Solve the system of equations.
5x + y = 9
3x + 2y = 4
the formula a= d/g gives the average gas milege a of a vehicle that uses g gallsons of gas to travel d miles. use the formula to find how many gallons of gas a vehicle with average gas mileage of 20.2 miles per gallon will use to travel 75 miles. round your answer to the nearest tenth.
Answer: 3.7 gallons
Step-by-step explanation:
Given : The formula [tex]a=\dfrac{d}{g}[/tex] gives the average gas mileage a of a vehicle that uses 'g' gallons of gas to travel 'd' miles.
The average gas mileage : a =20.2 miles per gallon
Distance : d=75 miles.
To find : g
Substitute all the values in the above formula , we get
[tex]20.2=\dfrac{75}{g}\\\\\Rightarrow\ g=\dfrac{75}{20.2}=3.71287128713approx3.7\ \ \ \text{ Rounded o the nearest tenth}[/tex]
Hence, the required amount of gas = 3.7 gallons
The diagonals of a rhombus divide it into four triangles of equal area.
True
False
Answer:
True
Step-by-step explanation:
For this figure, find the value of x.
x = _____?
Im not sure if i take 77 + 58 + x=180 or 77+28+x=180 or something else.
What is the value of the expression when a = 5 and b = 2? a 2b−3
You travel 2,557 km in 190 days how far did you travel per hour
At a pet show, the ratio of dogs to cats is 4:3. if the number of cats is 45, find the number of dogs at the show.answer:
The number of dogs would be 60 when the ratio of dogs to cats is 4:3.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
Given that the ratio of dogs to cats is 4:3. if the number of cats is 45
We have to determine the number of dogs.
Let the number of dogs would be x
As per the given condition, we can write a proportion as
4 dogs : 3 cats = x : 45 cats
⇒ 4 / 3 = x / 45
Apply the cross-multiplication operation,
⇒ 45 × 4 = x × 3
⇒ x = (45 × 4)/3
⇒ x = 15 × 4
⇒ x = 60
Therefore, the number of dogs would be 60.
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5+3i/4-2i written as a complex number?
The expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.
How to write 5+3i/4-2i written as a complex numberTo write the expression (5 + 3i)/(4 - 2i) as a complex number, we can multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator.
The conjugate of 4 - 2i is 4 + 2i.
Multiplying both the numerator and denominator by the conjugate:
((5 + 3i) * (4 + 2i))/((4 - 2i) * (4 + 2i))
Expanding the numerator and denominator:
(20 + 10i + 12i + 6i^2) / (16 - 8i + 8i - 4i^2)
Simplifying and combining like terms:
(20 + 22i - 6) / (16 + 4)
(-14 + 22i) / 20
Now, we can simplify the expression further by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(-7 + 11i) / 10
Therefore, the expression (5 + 3i)/(4 - 2i) can be simplified as (-7 + 11i)/10, which is a complex number.
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Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.
What percentage of blue pigment is in the mixture of the two inks?
45%
49%
60%
75%
Answer:
45%
Step-by-step explanation:
I took the test!
what capital letters are reflect symmetry
What is the percentage of 13/18?
The slope of a line is 0, and the y-intercept is 6. What is the equation of the line written in slope-intercept form? y = 6 y = 6x y = x + 6
Answer:
The answer is
y = 6
Which absolute value function, when graphed, will be narrower than the graph of the parent function, f(x) = |x|? f(x) = |x| – 3 f(x) = |x + 2| f(x) = 0.5|x| f(x) = 4|x|
f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.
What is an absolute function ?An Absolute function is a function that returns a positive value at any given point.
It is given that
The parent function is
f(x) = |x|
To find the function which will be narrower , it will be plotted to check
It is the known fact that when a function is multiplied by a number greater than 1 , the resulting function gets narrower , This can be easily identified from the graph.
f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.
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Create a trinomial that can be factored and write it in standard form.
To create a trinomial, use a basic factored form like (x+a)(x+b), and expand this via the distributive property. This yields as an example x²+8x+15, a trinomial in standard form.
Explanation:To create a trinomial that can be factored and to write it in standard form, we need to consider a basic factored form first. Let's use (x+a)(x+b) as our basic factored form. In this form, 'a' and 'b' are the roots of the trinomial.
To create the trinomial, we then expand this expression by using the distributive property: (x+a)(x+b) = x² + bx + ax + ab, which simplifies to x² + (a+b)x + ab. This is now our trinomial in standard form.
Let's take a concrete example. If we let 'a' be 3 and 'b' be 5, our factored form is (x+3)(x+5). Expanding this, we get x² + 5x + 3x + 15, which simplifies to x² + 8x + 15. Thus, x² + 8x + 15 is a trinomial that can be factored and is written in standard form.
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Rock music accounted for 30.5% of the total sales of recorded music in 1999 , and 20.4% of the total sales of recorded music in 2009 . Find the average rate of change of the percentage of sales of rock music from 1999 to 2009 .
Round to the nearest hundredth of a percent. Note that the percentage sign is already given in the answer, so you do not need to enter it.
The average rate of change is
What is 9 x ( 3 x 5 ) = ( 9 x n ) x 5?
Answer:
n=3
Step-by-step explanation:
The Sky High Ski Club dues are $450 per season. This fee includes transportation to and from the slopes and lift tickets. Skis cost $159.90, boots $78.25, and poles $19. What is the total cost?
Answer:
The total cost is $707.15.
Step-by-step explanation:
The Sky High Club dues are = $450 per person
and the Skis costs = $159.90
Cost for boots = $78.25
Cost of poles = $19.00
To find the total cost we will add all the amounts.
Total cost = 450 + 159.90 + 78.25 + 19.00
= $707.15
The total cost is $707.15.