Since these two lines overlap, the variable's value is 25, and the angle's value is 38 degrees.
What is intersecting lines?The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection. In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.
Here,
Both the angles are equal as they are intersecting lines and opposite angles are equal in this.
x+13=3x-37
3x-x=37+13
2x=50
x=25
x+13=25+13
angle=38
3x-37=3*25-37
angle=38
The value of variable is 25 and the value of angle in 38 degree as they are the intersecting lines.
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I thought of a number. My number tripled is 11 less than 26. Find my number?
Answer:
Not sure, maybe it's 5?
Step-by-step explanation:
[tex]26-11=15[/tex]
[tex]15[/tex] ÷ [tex]3=5[/tex]
Fathi ha
$1. 10 in hi printing account. Each heet of paper he ue reduce hi printing account balance by
$0. 25. Fathi want to print out a PDF document that i
47 page long. To ave paper, he decide to print on both ide of each heet and to print two page on each ide of the heet. After Fathi print, what will be the balance in hi printing account?
After printing the long pdf Document of 47 pages , the remained balance in Fathi's printing account is -$4.90 ..
In mathematics, a basic algebraic operation is any of the common arithmetic operations, including addition, subtraction, multiplication, division, raising integers to powers, and taking square roots.
We have given that,
Total or initial balance of fathi's printing account
= $1.10
Each sheet of paper reduce his balance by $0.25..
Total number of pages in pdf document
= 47
He wants to print this pdf document.
When he print both sides of paper then it reduce the counts of paper used for printing the pdf.
That's if he print only one side then he will print 47 pages but now, he print on both sides .
so, total pages used to print pdf Document= 47/2
= 23 both sided printed + 1 one side printed = 24 pages
Using all provided details, we get
After Fathi print, the balance in his printing account = Initial balance - 24 × balance reduce by each page print
= $1.10 - 24 × $0.25 = $1.10 - $ 6
= - $4.90
Hence, - $4.90 balance in his printing account.
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find the value of c of this triangle
Answer:
c = 20 degrees
Step-by-step explanation:
7c + c + c = 180
9c = 180
9/9 c = 180/9
c = 20
on the trip from detroit to colombus, ohio, mrs smith drove an average speed of 60 mph. returning, her average speed was 55 mph. if it took her 1/3 of an hour longer on the return trip, how far is it from detroit to columbus
Distance from Detroit to columbus is 220 miles
It is given in the question,
The average speed Mrs. smith drove = 60 mph.
Returning, her average speed was 55 mph.
Time taken = 1/3 of an hour longer on the return trip
We have to Find total distance between Detroit and Columbus
So, Let the distance between Detroit and Columbus be "x" miles
Average speed = 60
So, time taken by her to cover distance of x miles with speed of 60 mph
Time = Distance / speed
=> t = x / 60
She Took x/60 hours to reach Columbus
While returning her speed was 55 mph.
So, time taken by her to cover the same distance but at a speed of 55 mph :
=> t = x / 55
Now we are given that she took 1/3 of hour more while returning .
So, [tex]\frac{x}{55} - \frac{x}{60} = \frac{1}{3}[/tex]
⇒ x/660 = 1/3
=> x = 660/3
=> x = 220 miles
Hence , Detroit is 220 miles far from Columbus
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Kavion and Samantha like to collect stamps. Kavion 45 has stamps. This is 3 times 2 less than the number of stamps Samantha has.
Kevion and Samantha like to collect stamps and if Kevion has 45 stamps then Samantha has 45*3-2= 129 stamps.
What are Mathematical operations?The fundamental methods for mixing numbers or algebraic expressions to carry out mathematical computations are known as mathematical operations. These operations include multiplication, division, exponentiation, multiplication, and subtraction. More complex operations, such square roots, logarithms, and trigonometric functions, are available in addition to these fundamental operations. Mathematical operations are employed in a wide collection of disciplines, from elementary arithmetic to intricate computations in engineering and physics. We can use these operations to resolve issues and generate predictions based on mathematical models. We may better comprehend the world around us and make more precise predictions about what will happen in the future by applying mathematical procedures.
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In the figure shown, what is the value of x? Triangles A B C and D E F with side A B congruent to side D E, side A C congruent to side D F, and the included angles A and D congruent. Side B C has length 13 x minus 12 and side E F has length 7 x minus 6.
Answer:
Step-by-step explanation:
its x= 1
13-12=1
7-6=1
and i multiplied 13(1)-12 which equals one and 7(1)-6 which also equals one, the answers just have to match with each other
The value of [x] is equivalent to 9.5.
What is triangle? What is a expression? What is a mathematical equation? A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically - ∠x + ∠y + ∠z = 180°There are different types of triangles such as - equilateral triangle , scalene triangle , isosceles triangle etc.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.Given are two triangles ABC and DEF as shown.
Since AB is congruent to DE, then -
AB = DE
2x - 1 = 18
2x = 19
x = 9.5
Therefore, the value of [x] is equivalent to 9.5.
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Can someone help me out with this question? I've been practicing it this one is confusing to me
Answer:
NK = 26
Step-by-step explanation:
You have a triangle with the centroid identified and all medians drawn. You are given IK = 52 and want NK, where point N is the intersection of median JN with side IK.
CentroidThe centroid of a triangle is the point where the medians intersect. It divides each median in the ratio 2:1.
MedianA median of a triangle joins a vertex with the midpoint of the opposite side. Here, that means point N is the midpoint of side IK.
IK is given as length 52, so each half of that segment is 52/2 = 26.
IN = NK = 26
Mary has 2/5 cups of flour, 1/4 cup of sugar 1/2 cups of baking powder. How much ingredients does mary have all together
A health club charges a $50 initial fee plus $2 per visit. Brenda has spent a total of $144 at the health club this year. How many visits has she made?
Rewrite the ratio 8: 36 as an equivalent ratio of the form 1 : n.
Give any decimals in your answer to 1 d.p.
The value of n in 1:n is 4.5 in the given equivalent ratio.
What is equivalent ratio?
The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.
The given ratio is 8:36.
In fraction form = 8/36
= 1 / 4.5
=1:4.5
Hence, the value of n in 1:n is 4.5.
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You roll two dice, one red and one green. Losing combinations are doubles (both dice showing the same number) and outcomes in which the green die shows an odd number and the red die shows an even number. The other combinations are winning ones. E is the event that you roll a winning combination.
The probability of rolling a winning combination will be 7/12 as the winning combination is 21 and Total combination will be 36.
What is probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. By dividing the number of positive outcomes by the entire number of potential outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.
Here,
If the first die is red and the second one is green, then the sample space S is the following:
S=
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2,5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)
Hence n(S)=36.
Let's list the losing combinations:
E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),
(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}
n(E)=15
There are 36 total possiblities.
Out of which, winning probability is 21.
=21/36
=7/12
Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.
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What is the average rate of change in profit from hour 5 to hour 10, in dollars per hour?.
The profit increased at an average pace of $600 between Hour 5 to Hour 10.
What exactly defines rate of change?The term "rate of change" (ROC) describes the rate where something transforms over time. Thus, it is not the amount of individual themselves but rather the acceleration. (namely, the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.An indicator of the how one dimension changes in proportion to another is a rate of change.
The table for the price is given as;
Hour Profit
0 $0
2.5 $500
5 $900
7.5 $1200
10 $1500
After 5 hours, the profit is 900, and after another 5 hours, the profit is 1500.
In order to determine that average rate of change, we must take 900 away from 1500.
1500-900 = 600
Thus, an average rate of change for profit during Hour 5 to Hour is therefore $600.
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residents of three villages with three different types of water supply were asked to participate in a survey to identify the prevalence of cholera carriers. virtually everyone present at the time submitted to examination. the proportion of residents in each village who were carriers was computed and compared. what type of study was this?
The type of study was cross-sectional study.
An example of an observational study design is the cross-sectional study design. In a cross-sectional study, the researcher simultaneously assesses the participants exposures and outcomes.
After choosing the study subjects, the researcher conducts the study in order to evaluate the exposure and results.
For population-based surveys and to determine the prevalence of illnesses in clinic-based samples, cross-sectional designs are employed.
These studies are typically affordable and reasonably quick to carry out.
An illustration of a cross-sectional study might be a medical investigation into the incidence of cancer in a particular community.
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Student a says the δ h value of an exothermic energy change is always positive. Student b says δ h value of an exothermic energy change is always negative. Who is correct?.
each side of a square is increasing at a rate of 7 cm/s. at what rate (in cm2/s) is the area of the square increasing when the area of the square is 64 cm2?
If each side of a square is increasing at a rate of 7 cm/s, then the rate of increasing the area of the the square when the area of the square is 64 cm square is 112 centimeter square per second
The rate of change of length with respect to the time = 7 cm per second
That is
dl / dt = 7 cm per second
The area of the square = l^2
Where l is the length of the square
The rate of change area with respect to the time is
dA / dt = 2l dl/dt
The area is given that 64 centimeter square and the side will be 8 cm
Substitute the values in the equation
dA / dt = 2 × 8 × 7
= 112 centimeter square per second
Therefore, the rate of increasing the area is 112 centimeter square per second
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if x/3 = y/9 then, 3/9 =
Answer:Y=6
Step-by-step explanation:
I will be using the substitution method:
x+y=9 y=x+3
X + (x + 3) = 9
2x + 3 = 9
*subtract 3 from both sides*
2x = 6
*divide by 2 on each side of the equal sign*
X = 3
find y:
y = 3 + 3
y = 6
check:
3 + 6 = 9
9 = 9 (correct)
The value of x is 3 and the value of y is 6
The line plot shows how far Miguel ran during each running session last week.
What is the total distance he ran during these sessions?
1/2 xxxx
1 xxx
1 1/2 xxxx
2 xxxxx
2 1/2 xxxx
The total distance is 13 units he ran during these sessions
What is Distance?The length along a line or line segment between two points on the line or line segment.
From the line plot, we have the following frequency table:
Distance Frequency
0 0
1/2 4
1 3
[tex]1\frac{1}{2}[/tex] 1
2 2
[tex]2\frac{1}{2}[/tex] 1
3 0
The total distance from the line plot is then represented as
Total distance = Sum of the product of distance and frequency
Total distance = (0×0) + (1/2 × 4) + (1 × 3) + ([tex]1\frac{1}{2}[/tex] × 1) + (2 × 2) + ([tex]2\frac{1}{2}[/tex] × 1) + (3 × 0)
Total distance = 13
Hence, the total distance is 13 units he ran during these sessions
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A scientist is determining
the mass of 30,000
molecules of oxygen.
a. How many
significant digits
should be in the
solution?
Mass of one molecule of
oxygen = 5.3 x 10-23 gram
Answer:
The mass of the 30,000 molecules is 1.59\times 10^{-18}1.59×10
−18
Given that,
There are 30,000 molecules.
And, the mass of one molecule of oxygen i.e. 5.3\times 10^{-23}5.3×10
−23
gram.
Based on the above information, the calculation is as follows:
\begin{gathered}= 30,000 \times 5.3\times 10^{-23}\\\\= 3\times10^4 \times 5.3\times 10^{-23}\\\\= 15.9\times 10^{-23+4}\\\\= 15.9\times 10^{-19}\\\\= 1.59\times 10^{-19}\times 10\\\\= 1.59\times 10^{-18}\end{gathered}
=30,000×5.3×10
−23
=3×10
4
×5.3×10
−23
=15.9×10
−23+4
=15.9×10
−19
=1.59×10
−19
×10
=1.59×10
−18
Therefore we can conclude that the mass of the 30,000 molecules is 1.59\times 10^{-18}1.59×10
−18
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help! trigonometry, ty
The logarithmic expression as a single logarithm is [tex]log_{2}[/tex](a[tex]b^{2}[/tex]/[tex]c^{3}[/tex])
What is logarithm?A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.
[tex]log_{2}a + 2log_{2}b - 3log_{2}c[/tex]
[tex]2log_{2}b[/tex] may be simplified as [tex]log_{2}b^{2}[/tex]
[tex]3log_{2}c[/tex] may be simplified as [tex]log_{2}c^{3}[/tex]
Which reduces the expression as
[tex]log_{2}a[/tex] + [tex]log_{2}b^{2}[/tex] - [tex]log_{2}c^{3}[/tex]
factor out log2 since it is common
and replace addition sign with multiplication and subtraction sign with division
[tex]log_{2}(\frac{a * b^{2} }{c^{3} })[/tex] which finally becomes [tex]log_{2}(ab^{2} /c^{3})[/tex]
In conclusion, the simplified form of the logarithmic expression is [tex]log_{2}(ab^{2} /c^{3})[/tex]
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6you can mow 800 sq ft of lawn in 15 minutes. at this rate, how many minutes will you take to mow a lawn that measures 6000 sq ft
It will take 112.5 minutes to mow a lawn that measures 6000 sq ft .
In the question ,
it is given that ,
the time taken to mow 800 sq ft of the given lawn is = 15 minutes ,
So , the time taken to mow 1 sq ft of lawn is = 15/800 minutes .
to find the time taken to mow 6000 sq ft , we multiply by 6000 ,
We get ,
time taken to mow 6000 sq ft of the lawn is = 6000*(15/800)
on solving , we have
= 90000/8000
Simplifying further ,
we get ,
= 112.5 minutes
Therefore , 6000 sq ft lawn will be mowed in 112.5 minutes .
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The strength of the linear relationship between two numerical variables may be measured by the
a) scatter diagram. b) slope. c) coefficient of correlation. d) Y-intercept.
The strength of the linear relationship between two numerical variables may be measured by the coefficient of correlation
What is meant by coefficient of correlation?The correlation coefficient is a statistical indicator of how strongly two variables are linearly related. Its values may be between -1 and 1. A correlation coefficient of -1 indicates a complete negative, inverse, or inverse-correlation, where values in one series increase as those in the other fall and vice versa. A coefficient of 1 denotes a perfect positive correlation or a straight line. A correlation value of 0 indicates that there is no linear relationship.
In both science and finance, correlation coefficients are used to measure the degree of relationship between two variables, components, or data sets. For example, because high oil prices benefit crude producers, one might assume that the correlation between oil prices and forward returns on oil stocks is strongly positive.
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determine the area under the standard normal curve that lies to the right of the z-score −0.97 and to the left of the z-score −0.59.
0.1116 is the area under the standard normal curve using the given z-score.
What is Z-score?The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed.
Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
The 90th percentile's z-score is 1.2816, as calculated by the Percentile to Z-Score Calculator.
Therefore, a student's z-score would be deemed "excellent" if it was greater than or equal to 1.2816.
So, the area under the standard normal curve will be:
Find the z-scores by looking at the table's intersection of the 0.9 down and 0.07 across columns, which is 0.1660.
Similarly, find -0.5 down and 0.09 across to get 0.2776.
Add them together now: 0.2776 - 0.1660 = 0.1116
Therefore, 0.1116 is the area under the standard normal curve using the given z-score.
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Please help now asap !!!!!!!!!?!
Answer: 2.12 miles.
Step-by-step explanation: To find the width of Hardee County, we need to determine the length of one of its sides. We can use the fact that the area of a rectangle is equal to its length times its width to find the length of one of its sides.
The area of Hardee County is 637 square miles, and we know that its width is 30 miles. We can use this information to write the following equation: 637 square miles = 30 miles * length
We can solve this equation for the length by dividing both sides by 30: 637 square miles / 30 miles = length
This simplifies to: 21.2 square miles = length
Since the length of a rectangle is one of its sides, the width of Hardee County is 21.2 miles.
help me omg omg i need help
Answer: Note that log(a) + log(b) is the same thing as log(a × b) This gives us: log7(x(x +5)) = log7(14)
the purpose of a short-term measurement is to substitute for a long-term measurement. for this purpose, which do you think is more relevant, the confidence interval or the prediction interval? explain.
Prediction interval is more relevant than confidence interval.
What is Prediction Interval?
A prediction interval is an estimate of the range within which a future observation will fall, with a particular probability, given what has already been observed, in statistical inference, more especially predictive inference.
Short term measures:
Undoubtedly, short-term decisions and actions serve as important starting points for both real accomplishments and symbolic commitments. Taking into account the challenges, assets, and weaknesses that have been identified, a number of immediate activities seem to have the highest chance of fostering intelligent growth in the long run.
Long term measures:
The phrase "Long-Term Performance Measures" refers to the performance metrics developed and employed by the Committee to evaluate the Company's performance and ascertain the quantity of Common Stock to be paid to the Participant at the end of a Restriction Period.
Here,
Prediction intervals must take into consideration both the random variation of the individual values and the uncertainty in predicting the population mean. Consequently, a prediction interval is always larger than a confidence interval. Additionally, as the sample size grows, the prediction interval won't condense to a single value.
Hence, Prediction interval is more relevant than confidence interval.
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mgse8.ee.8c solve real-world and mathematical problems leading to two linear equations in two variables.
Two linear equations in two variables can be solved using the substitution techniques, graphical method or by the elimination method.
Let us consider any two real world linear equations in two variables.
x - y = 0
x + y = 4
Now let us first solve them by substitution method:
equation 1 can be written as : x = y ,
Now we substitute this value of x in the second equation:
x + y = 4
or, y + y = 4
or, 2y = 4
or, y = 2
At x = 2 , y = 2. Hence the solution is (2,2)
Now let us solve by elimination method:
adding equation 1 and 2 we get:
x - y = 0
x + y = 4
2x = 4
or, x =2
at x=2 , y = 4-2 =2 Hence the solution is (2,2)
Now we will solve the equations graphical method.
In the graph attached below we can clearly see that the straight line representation of the two equations intersect at the point (2,2)
Hence the solution is (2,2) .
Therefore any linear equation in 2 variables can be solved by substitution , elimination and graphically.
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Please help me with this escape room due at 12 tonight
Answer:
Step-by-step explanation:
ben
The simultaneous equations mx + ny = 8 and m²x-n²y = - 10 has a solution x = 2 and y = 3. Find the possible values of the constants m and n.
The possible values of (m,n) are (1,2) and (-17,14).
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, the solution of the simultaneous equations is x = 2 and y = 3.
The given equations are:
mx + ny = 8
m²x - n²y = -10
Substitute x = 2 and y = 3 into the above equations:
2m + 3n= 8 (1)
2m² - 3n² = -10 (2)
Rewrite equation (1):
2m + 3n= 8
2m = 8 - 3n
m = (8 - 3n)/2 (3)
Substitute it into equation (2):
[tex]2\frac{(8-3n)^2}{4}-3n^2 = -10\\\\2(64 +9n^2-48n)-12n^2+40 =0\\\\128 +18n^2-96n-12n^2+40=0\\\\6n^2-96n+168=0\\\\n^2-16n+28=0\\\\n^2-14n-2n+28=0\\\\n(n-14)-2(n-14)=0\\\\(n-2)(n-14)=0[/tex]
n = 2 or n =14
Now, substitute n = 2 into equation (3):
m = (8-3×2)/2
m = 1
Further, substitute n = 14 into equation (3):
m = (8-3×14)/2
m = -17
Hence, the possible values of (m,n) are (1,2) and (-17,14).
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select all the equations that have the same solution as 2x-5=15
The equations that have the same solution as 2x-5=15 include :
2x = 20
2x - 20 = 0
4x - 10 = 30
The options are B, D, E.
How to calculate the equation?We have,
2x - 5 = 15
Here,
The solution is 10.
2x = 15 + 5
2x = 20
x = 20/2
x = 10
We have,
A. 2x = 10
x = 10/2
x = 5
B. 2x = 20
x = 20/2
x = 10
C. 2(x - 5) = 15
2(x - 5) = 15
x - 5 = 15/2
x = 15/2 + 5
x = 12.5
D. 2x - 20 = 0
2x = 20
x = 20/2
x = 10
E. 4x - 10 = 30
4x = 30 + 10
4x = 40
x = 40/4
x = 10
F. 15 = 5 - 2x
15 - 5 = -2x
10 = -2x
x = -10/2
x = -5
The correct options are B, D and E.
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Complete question
What equations have the same solution as 2x - 5 = 15?
A. 2x = 10
B. 2x = 20
C. 2(x - 5) = 15
D. 2x - 20 = 0
E. 4x - 10 = 30
F. 15 = 5 - 2x
state the derivatives for the six inverse trigonometric functions. what study suggestions would you recommend for fellow students to learn these?
Derivative of six inverse trigonometric functions are as follow:
d/dx(sin⁻¹x) = 1 / √1 - x²
d/dx(cos⁻¹x) = -1 / √1 - x²
d/dx(tan⁻¹x) = 1 / √1 + x²
d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1
d/dx(sec⁻¹x) = 1 / |x|√ x² -1
d/dx(cot⁻¹x) = -1 / √1 + x²
As given in the question,
Explanation of the derivative of six inverse trigonometric functions are as follow:
1. y = sin⁻¹x
⇒ x = siny
⇒d/dx(x) = d/dx(siny)
⇒ 1 = cosy dy/dx
⇒dy/dx = 1/cosy
⇒dy/dx = 1/√1-sin²y
⇒dy/dx = 1/√1-x²
⇒d/dx( sin⁻¹x) = 1/√1-x²
2. y = cos⁻¹x
⇒ x = cosy
⇒d/dx(x) = d/dx(cosy)
⇒ 1 =-siny dy/dx
⇒dy/dx = -1/siny
⇒dy/dx = -1/√1-cos²y
⇒dy/dx = -1/√1-x²
⇒d/dx( cos⁻¹x) = -1/√1-x²
3. y = tan⁻¹x
⇒ x = tany
⇒d/dx(x) = d/dx(tany)
⇒ 1 =sec²y dy/dx
⇒dy/dx = 1/sec²y
⇒dy/dx = 1/√1+ tan²y
⇒dy/dx = 1/√1 + x²
⇒d/dx( tan⁻¹x) = 1/√1+x²
4. y = cosec⁻¹x
⇒ x = cosecy
⇒d/dx(x) = d/dx(cosecy)
⇒ 1 =-cosecy coty dy/dx
⇒dy/dx = -1/cosecy coty
⇒dy/dx = -1/cosecy√cosec²y-1
⇒dy/dx = -1/|x|√x²-1
⇒d/dx( cosec⁻¹x) = -1/|x|√x²-1
5. y = sec⁻¹x
⇒ x = secy
⇒d/dx(x) = d/dx(secy)
⇒ 1 =secy tany dy/dx
⇒dy/dx = 1/secy tany
⇒dy/dx = 1/secy√sec²y-1
⇒dy/dx = 1/|x|√x²-1
⇒d/dx( sec⁻¹x) = 1/|x|√x²-1
6. y = cot⁻¹x
⇒ x =coty
⇒d/dx(x) = d/dx(coty)
⇒ 1 =-cosec²y dy/dx
⇒dy/dx = -1/cosec²y
⇒dy/dx = -1/√1+ cot²y
⇒dy/dx = -1/√1 + x²
⇒d/dx( cot⁻¹x) = -1/√1+x²
Therefore, the derivative of the six inverse trigonometric functions are given below:
d/dx(sin⁻¹x) = 1 / √1 - x²
d/dx(cos⁻¹x) = -1 / √1 - x²
d/dx(tan⁻¹x) = 1 / √1 + x²
d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1
d/dx(sec⁻¹x) = 1 / |x|√ x² -1
d/dx(cot⁻¹x) = -1 / √1 + x²
Learn more about inverse trigonometric functions here
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