The antiderivative of f(x) = tan⁻¹(x) is x tan⁻¹(x) − ln(x²+1)/2 + C
The term antiderivative in math is referred as a function that reverses what the derivative does
Here we have given the expression f(x) = tan⁻¹(x).
Now, the antiderivative of the expression is calculated by doing the integral
=> ∫tan⁻¹(x)dx
By using the integration by parts ∫udv = uv−∫vdu
Here let us consider that u=tan⁻¹(x) and dv=dx
And the value of du is calculated as,
=> du = ∫tan⁻¹(x)dx = dx/(x² + 1)
And the value of v = x.
Then the expression is written as,
=> ∫tan⁻¹(x)dx = x tan⁻¹(x) - ∫x/(x² + 1)dx
As per the concept of the constant of integration, it can be simplified as,
=> x tan⁻¹(x) − ln(x²+1)/2 + C
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A shop charges `\$4. 95` for a large `9`-ounce frozen yogurt. What is the cost per ounce of the frozen yogurt?.
Answer:
$0.55/ounce
Step-by-step explanation:
The problem gives us the ratio of cost to ounce. We need to create a proportion (when you set two ratios equal to each other) to solve for one variable of the second ratio.
⭐ The first ratio is [tex]$4.95/9 ounces[/tex], which means that it costs $4.95 for 9 ounces.
⭐ The second ratio is [tex]x/1 ounce[/tex], where x is the cost for 1 ounce of frozen yogurt.
. . . . . . . "per ounce" means "for every 1 ounce"
⭐ We need to set these two ratios equal to each other and solve for x.
. . . . . . . In proportions, keep the units of the numerators and denominators the same. In this case, we'll keep the cost as the numerators and the ounces as the denominators.
. . . . . . . [tex]\frac{4.95}{9} = \frac{x}{1}[/tex]
. . . . . . . [tex]\frac{4.95}{9}(1) = x[/tex]
. . . . . . . ∴ x = $0.55/ounce
Find the inverse of the following functions. Show all work
f(x) = 2√x+7
Answer:
the inverse of f(x)=2x−7 f ( x ) = 2 x - 7 .
Step-by-step explanation:
check if f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) )
Answer:
f(x) = 1/4 x² - 7
Step-by-step explanation:
x + 7 ≥ 0
x ≥ -7
y/2 = 2 /2 √(x+7)
y/2 = √(x+7)
y ≥ 0
(y/2)² = √(x+7)²
y²/4 = x +7
x = y²/4 - 7
f(x) = x²/4 - 7
A stock lost 8 3/8 points on Monday and then another 1 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the
net gain or loss of the stock for these three days?
a. a gain of 6 1/2 points
b. a loss of 1 points
c. a gain of 17 1/2 points
d. a gain of 23 points
Answer:
A gain of 3 points
Step-by-step explanation:
I'm not sure the options are correct. But normally, you add up the lost points on the both days. Then you compare it to the gained point on Wednesday.
Which among the options is one of the factors of x2 x6 − 16?
The sum of two or more numbers that results in a third number is called a factor.
The factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] exists 2x + 1.
What is meant by factors?The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them.
What can split a number exactly are factors. So there is no residual after division. Factors are the sums of two or more numbers that produce a third number. Consequently, a factor is a number that divides another.
The use of more variable factors—those whose values do fluctuate with output—occurs as production rises and falls. Workforce, energy, and directly used raw materials are examples of typical variable components.
Let the given equation be [tex]$& x^2+\frac{x}{6}-\frac{1}{6} \\[/tex]
[tex]$& =\frac{6 x^2+x-1}{6} \\[/tex]
simplifying the above equation, we get
[tex]$& =\frac{1}{6}\left(6 x^2+x-1\right)[/tex]
We will factorize the polynomial by splitting its middle term.
[tex]$& \frac{1}{6}\left(6 x^2+x-1\right) \\[/tex]
[tex]$& =\frac{1}{6}\left(6 x^2+3 x-2 x-1\right) \\[/tex]
simplifying the above equation, we get
[tex]$& =\frac{1}{6}(3 x(2 x+1)-1(2 x+1)) \\[/tex]
[tex]$& =\frac{1}{6}(3 x-1)(2 x+1)[/tex]
[tex]$\frac{1}{6^{}}(3 x-1)$[/tex] and (2x + 1) are factors of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex]
Therefore, the correct answer is option B. 2x + 1
The complete question is:
Which among the following is a factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] ?
A. 3x + 1
B. 2x + 1
C. [tex]$x-\frac{1}{5}$[/tex]
D. [tex]$x-\frac{1}{2}$[/tex]
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What does changing the base of a log function do to the graph?
The larger the base of a log function, the closer the graph approaches the asymptote of x = 0.
We know that for a exponential function b^x = y, b is the base, y is the exponent to which the base b is raised and x is the result obtained.
We can write this in logarithmic form as:
log_b(x) = y
A logarithm base is the subscript of the logarithm that carries or raises the exponent.
For example in case of log_(3) 9 = 2, the base here is 3.
The change of base formula is:
log_b(x) = log_c(x) / log_c(b)
Also as we know the bigger the logarithm base, the smaller the curve on the graph. This means, the larger the base of a log function, the closer the graph approaches the asymptote of x = 0.
The log function may increase at a slower rate if the base increases.
Therefore, if the base of a log function is large, the graph approaches the asymptote of x = 0.
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1>-1=-3>-5 this property is called?
Answer:
linear inequation with 1 variable
Now answer the following question: compute the area of an ellipse using green's theorem if the vertex is 2 and co-vertex is 3
Answer:
2+3=5
Step-by-step explanation:
2+
3=
5
answer 2+3=5
B, D, E and F are points on a circle, centre O. ABC is a tangent to the circle. ODC is a straight line. BOE is a diameter of the circle. Angle BCD = 48° Find the size of angle DFE.
Answer:
m∠DFE = 69°
Step-by-step explanation:
The tangent of a circle is always perpendicular to the radius.
Therefore, as ABC is the tangent to the circle, and OB is the radius of the circle:
⇒ m∠CBO = 90°
Interior angles of a triangle sum to 180°. Therefore:
⇒ m∠COB + m∠CBO + m∠BCO = 180°
⇒ m∠COB = 180° - m∠CBO - m∠BCO
⇒ m∠COB = 180° - 90° - 48°
⇒ m∠COB = 42°
Angles on a straight line sum to 180°. Therefore:
⇒ m∠DOE + m∠COB = 180°
⇒ m∠DOE = 180° - m∠COB
⇒ m∠DOE = 180° - 42°
⇒ m∠DOE = 138°
The angle at the center is twice the angle at the circumference.
Therefore:
⇒ m∠DOE = 2 × m∠DFE
⇒ m∠DFE = m∠DOE ÷ 2
⇒ m∠DFE = 138° ÷ 2
⇒ m∠DFE = 69°
If f(x)=root 4x+9+2 which inequality can be used to find the domain of f(x )
Answer:
x>=-11/4
Step-by-step explanation:
f(x)=[tex]\sqrt{4x+9+2}[/tex]
The number which has a square root has to be greater than or equal to 0.
Hence, 4x+9+2>=0
Solve the inequality:
4x+9+2>=0
4x+11>=0
4x>=-11 ==> subtract 11 on both sides to isolate x
x>=-11/4 ==> divide both sides by 4
Which is a factor of the polynomial f x 6x 4 21x 3 4x 2 24x 35?
One of the factor of the given polynomial 6x^4 - 21x^3 - 4x^2 + 24x - 35 is (2x-7).
According to Rational Root Theorem,
Leading coefficient = 6
Trailing constant = 35
Factors of leading coefficient = 1, 2, 3, 6
Factors of trailing constant = 1, 5, 7, 35
Check for the rational roots
Let P = 7, Q = 2, then
P/Q = 3.5
F(P/Q) = 0
Apply Factor theorem which means the given polynomial must be divisible by P/Q, that is (2x-7)
Divide the polynomial into two groups
Group 1 6x^4 - 21x^3
Take 3x^3 common, we get
3x^3(2x - 7)
Group 2 - 4x^2 + 24x - 35
When we divide it by (2x - 7) we get (-2x + 5)
⇒ - 4x^2 + 24x - 35 = (-2x + 5)(2x - 7)
⇒ 6x^4 - 21x^3 - 4x^2 + 24x - 35 = (2x - 7)(3x^3 - 2x + 5)
Hence the correct option is A.
-- The given question is incomplete, the complete question is
"Which is a factor of the polynomial f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35? A) 2x - 7 B) 2x + 7 C) 3x - 7 D) 3x + 7" --
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How should I solve this problem? I need steps..
Refer to the photos taken.
What is the slope of the line perpendicular to y 1 4x 10?
The slope of the line perpendicular to the given line is equal to -4/1.
The equation is in the form y=mx+b
so, y=(1/4)x -10
First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4
To find the slope perpendicular to the line you must find the negative reciprocal of 1/4. (Which just means change the sign then flip the fraction)
Multiplying 1/4 by -1 which is -1/4
Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1
Thus, the slope of the line perpendicular to the given line is equal to -4/1.
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The equation is in the form y=mx+b
so, y=(1/4)x -10
First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4
Multiplying 1/4 by -1 which is -1/4
Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1
An archer performs 100 joules of work pulling back the string of a bow. What will be the distance traveled by a 0. 5 kg arrow when it is fired from the bow to the nearest tenth of a meter?.
The distance traveled by the arrow cannot be determined from the given information. The distance traveled by the arrow depends on the speed at which it is fired, which is determined by the amount of energy released when the bowstring is released.
write 125 feet in 5 seconds as a unit rate
Distance of 125 feet covered in 5 seconds, so the speed is 25 feet/second.
What is speed?Any object's distance traveled in a unit of time is referred to as speed.
In mathematical term, Speed is express as S = D/T,
where S=speed, D=distance, T= time.
Given that,
The distance = 125 feet.
The time taken to cover the distance = 5 seconds.
To find the unit rate.
Apply formula,
speed = distance / time
= 125 / 5
= 25 feet / second
The required speed is 25 feet / second.
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Help me please on this IXL
Answer:
61
Step-by-step explanation:
Using the exterior angle theorem,
[tex]c-15+c-18=c+28 \\ \\ 2c-33=c+28 \\ \\ c-33=28 \\ \\ c=61[/tex]
please help me solve this:40= -3x+10
Answer:
x = -10
Step-by-step explanation:
Solve means to get the x all by itself on one side of the equation.
40 = -3x + 10
Subtract 10 from both sides.
30 = -3x
Divide both sides by -3.
30/-3 = x
-10 = x
x = -10
You can check your answer by putting it back into the equation and seeing if you get a true statement.
40 = -3x + 10
x = -10
Substitute.
40 = -3(-10) + 10
Multiply.
40 = 30 + 10
Add.
40 = 40
True! This means
x = -10 is correct.
Someone pls help me answer this question and give a thorough explanation!!!!!
Answer:
The boats cross paths at the points (1,8) and (4,11)
Step-by-step explanation:
First, we want to find the points of intersection between the two paths. We are given two equations, both in the form y=(equation). Since we want to find the intersection points, we set the two equations equal to each other (since both equal y we can plug one of the equations in for y into the other equation) to get
-x^2+6x+3=x+7
From here, we solve this like a normal quadratic equation, move all variables to one side first
-x^2+5x-4=0
This factors to -(x-1)(x-4)=0, giving us x=1 and x=4
Now we plug these back into one of the original equations (in this case the linear equation is much more simple) to give us the points (1,8) and (4,11)
How do you write the equation of the line in point slope slope intercept form and standard form?
The equation of line passing through the points (3,-2) and (-2,3) in
(a) point slope form is y + 2 = -(x - 3) ;
(b) slope intercept form is y = -x + 1 ;
(c) standard form is x + y = 1 .
The Standard Form of equation of line is written as ⇒ " Ax + By = C " .
it is given that the line is passing through the points (3,-2) and (-2,3) ;
So , the slope(m) is = (3+2)/(-2-3) = 5/(-5) = -1 .
(a) the point slope form is (y - y₁) = m(x - x₁) ;
substituting x₁ = 3 and y₁ = -2 ;
we get ;
(y + 2) = (-1)(x - 3)
y + 2 = -(x - 3) .
(b) the slope intercept form is ⇒ y = mx + c ,
-2 = (-1)3 + c ;
-2 = -3 + c ,
c = -2 + 3 ;
c = 1 ; the equation is ⇒ y = -x + 1 .
(c) the standard form is :
arranging the equation y = -x + 1 ,
we get ;
x + y = 1 .
Therefore , the required equations of line are mentioned above .
The given question is incomplete , the complete question is
How do you write the equation of the line in point slope form , slope intercept form and standard form given that it passes through (3, -2) , (-2, 3) ?
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-9(z-8)
write an equivalent expression
Answer:
-9z + 72
Step-by-step explanation:
The diagrams show the position of a tap when off and fully on. When fully on, water flows out of the tap at 15 litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned 123° 123 The water flows into a tank with a capacity of 90.2 litres. How long, in minutes, will it take to fill the tank?
Answer:
8.8 mins
Step-by-step explanation:
to find how long in mins it would take to fill the tank
at 180 degrees the speed of water is 15 liters/min at 123 degrees
so [tex]\frac{15}{180} *123[/tex] = 10.25 liters/min
the capacity of the tank is 90.2 liters
[tex]\frac{90.2}{10.25} \\[/tex] = 8.8 mins
The table shows the location below sea level of hikers on a trail. What is the difference between tommy location and Theresa location? Write your answer in simplest form.
By taking the modulus value of both of their balances we obtain that the difference Maria and Charles allowable balance is $10.
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
Given, The table shows the allowable balance of several children.
From the given table we can conclude that Maria's allowable balance is
- 15.25 and Charles's allowable balance is - 5.25.
So, The difference of their allowable balance is |- 15.25| - |- 5.25|.
= 15.25 - 5.25.
= 10.
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how does the digit 5 in the number 357 compare with the digit 5 in the number 465?
Answer:
The digit 5 in the number 357 is in the tens so it represents 50 whereas the digit in the number 465 is in the ones/units so it represents 5.
What is the relationship between the area and the volume of two similar solids?
If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
Volume of A /Volume of B = ( a / b )^3
a is the radius of solid A and b is the radius of solid B.
solid figures
In Geometry, the shape or the figure that has three dimensions (length, breadth and height), are known as solids or three-dimensional shapes. Example:-Cube, Cuboid and Sphere. The major types of solid shapes are: cubes, cuboids, prisms, pyramids, platonic solids, torus, cone, cylinder, and sphere.
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For what value of x makes 5/x-2 undefined?
Answer:
x = 2
Step-by-step explanation:
5 / 2-2
5 / 0 = 0
0 is undefined
What is the area of a 10x10 square?
Answer: The answer is 100 :)
Step-by-step explanation:
you multiply L x W and that would be 10 x 10 and if you do the math right you should get an answer of 100
please help me and explain it
Answer:
Divide both sides by -3.
Step-by-step explanation:
This question is asking you how to get from step 1: [tex]-3(p-7) = -15[/tex] to step 2: [tex]p - 7 = 5[/tex].
We can see that the expression inside of the parentheses (p - 7) didn't go away from step 1 to step 2, and the term that was being multiplied by (p-7) had gone away. The only way you can "get rid" of a multiplied term is by doing the inverse of multiplication, which is division. Thus, you have to divide both sides by -3 to get to step 2.
What are the 5 types of expression?
The 5 types of expression include:
monomial, polynomial, binomial, trinomial, multinomialWhat is an expression?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it. They include monomial, polynomial, binomial, trinomial, multinomial.
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A dodecahedral die has 12 sides numbered from 1 to 12. The die is rolled once. Find the probability that the upward face shows a number that is a multiple of 3.
The probability that the upward face shows a number that is a multiple of 3 is p = 1/3 .
Given :
When a dodecahedral die is rolled the possible outcomes are:
s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
The total numbers of possible outcomes is 12.
The numbers of outcomes whose upward face is multiple of 3 .
= { 3 , 6 , 9 , 12 }
so Number of favorable outcomes = 4
What is probability ?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Probability = number of favorable outcomes / number of possible outcomes
= 4 / 12
= 1 / 3
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What are the names of radicals?
The name of radicals are cation and anion
What are radicals?A radical is an atom, molecule, or ion that has an unpaired valence electron. A notable example of a radical is the calcium ion
A radical can be electrically stable, positively charged and negatively charged.
Positively charged radicals are called cations and the negatively charged radicals are called anions.
If a balanced atom loses one or more electrons, it will become a positively charged cation.And if a balanced atom gains one or more electrons, it will become negatively charged anions.
Therefore the names of radicals are cations and anions i.e positively charged radicals and negatively charged radicals respectively.
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Where are the asymptotes in a function?
The asymptotes in a given function is a line that the graph of a function approaches as either x or y go to positive or negative infinity.
What is an asymptote in a function?An asymptote in a function is defined as the a line that the graph of a function approaches as either x or y go to positive or negative infinity.
There are various types of asymptote which include the following:
vertical,horizontal and obliqueTo determine the asymptote of a function in a graph is a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve.
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