Answers
Answer:
[tex]f(x) = {sec}^{ - 1} x \\ let \: y = {sec}^{ - 1} x \rightarrow \: x = sec \: y\\ \frac{dx}{dx} = \frac{d(sec \: y)}{dx} \\ 1 = \frac{d(sec \: y)}{dx} \times \frac{dy}{dy} \\ 1 = \frac{d(sec \: y)}{dy} \times \frac{dy}{dx} \\1 = tan \: y.sec \: y. \frac{dy}{dx} \\ \frac{dy}{dx} = \frac{1}{tan \: y.sec \: y} \\ \frac{dy}{dx} = \frac{1}{ \sqrt{( {sec}^{2} \: y - 1}) .sec \: y} \\ \frac{dy}{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} } \\ \therefore \frac{d( {sec}^{ - 1}x) }{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} } \\ \frac{d( {sec}^{ - 1}5x) }{dx} = \frac{1}{ |5x | \sqrt{25 {x }^{2} - 1} }\\\\y=arccos(\frac{1}{x})\Rightarrow cosy=\frac{1}{x}\\x=secy\Rightarrow y=arcsecx\\\therefore \frac{d( {sec}^{ - 1}x) }{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} }[/tex]
Related Questions
Help help pelesse please
Answers
Answer:
450
Step-by-step explanation:
9×50=450
have a good day
Use the given figure (triangular)to find the length of x. x+14 28
Answers
Step-by-step explanation:
Answer. Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2+b2=c2 a 2 + b 2 = c 2 , which is known as the Pythagorean Theorem.
si a+b = 10; ab= 3 calcula a2 + b2
Answers
94
What is the image of (4,-8) after a dilation by a scale factor of 1/4 centered at the origin?
Answers
Answer:
(1, -2)
Step-by-step explanation:
multiply each coordinate by 1/4. since the numerator is 1, you really just need to divide each number by 4.
how do i calculate slope?
Answers
Answer:
In order to calculate the slope, you'll need 2 ordered pairs (x, y).
The formula for calculating the slope is:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
where m = slope
(x1, y1) = first ordered pair
(x2, y2) = second ordered pair
Regardless of which values for the (x1, y1) and (x2, y2) you choose, you would still end up with the same slope (as long as it's done correctly).
As an example, let's say you have the following set of points:
(2, 4) (8, 1)
Let (x1, y1) = (2, 4)
(x2, y2) = (8, 1)
Plug these values into the slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{1 - 4}{8 - 2} = \frac{-3}{6} = -\frac{1}{2}[/tex]
Therefore, the slope of the line is - 1/2.
To prove that you'll end up with the same value for the slope:
This time, let (x1, y1) = (8, 1)
(x2, y2) = (2, 4)
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{4 - 1}{2 - 8} = \frac{3}{-6} = - \frac{1}{2}[/tex]
Therefore, the value of the slope is still -1/2.
Please mark my answers as the Brainliest if you find my explanations helpful :)
Which expression is equivalent to this polynomial expression?
Answers
Answer:
Where is the expression
Answer:
Its c :)
Step-by-step explanation:
plato
Please help
Dekalbs current population is 3,500 and it is increasing by 40 people pr year. Sycamores current population is 12,040 and it is decreasing by 100 people every year
Q: Write expressions for each population if x represents the number of years
And What is the current population of dekalb?
Answers
Answer:
Dekalb: 3500+40x = F
Sycamores : 12,040 - 100x = F
Step-by-step explanation:
These expressions can be used to explain each population
X = number of years for both expression
F = Final population
Dekalb: 3500+40x = F
Sycamores : 12,040 - 100x = F
The current population if 3500 if no years have gone by, plug in the year of numbers for X to find final population after the amount of years.
HELPPPPPPPPPPP. please explain how u got the answer
Answers
Step-by-step explanation:
the key is x = 0.
also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.
let's test it.
a linear function is a line :
y = ax + b
remember, x = 0 is a key element.
y = a×0 + b
-3 = a×0 + b
-3 = b
so, we know, the line function is
y = ax - 3
now, for the a. let's use the next xy pair (1, 1).
1 = a×1 - 3
4 = a
aha ! our line function is therefore
y = 4x - 3
verify with the next 2 points (2, 5) and (3, 9)
5 = 4×2 - 3 = 5 correct
9 = 4×3 - 3 = 9 correct
linear type and equation confirmed.
the second table :
yes, we see relatively big y values compared to the x values.
and the y values follow the powers of 2
so it seems to to be exponential.
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.
the old trick : c-x.
again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.
64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶
=> c = 6
so, we suspect the exponential function
y = 2^(6-x)
let's verify with the other points
(1, 32)
32 = 2^(6-1) = 2^(5) = 32 correct
(2, 16)
16 = 2^(6-2) = 2^(4) = 16 correct
(3, 8)
8 = 2^(6-3) = 2^(3) = 8 correct
so, yes, it is the exponential function
y = 2^(6-x)
Thomas, a waiter at a local restaurant, is paid $ 4 an hour plus tips. His friend Marie works at a local bookstore for $12 an hour. Marie and Thomas worked the same number of hours. If Thomas made $120 in tips and both made the same amount of money, how many hours
1.please just give me the first step on how it’s written out
Answers
Answer:
15 hours
Step-by-step explanation:
Let h = numbers of hour worked, x = tips, t = Thomas' pay, and m = Marie's pay
We can set up an equation for this question:
t = 4h + x
Now plug in 120 for x
t = 4h + 120
Now we set up Marie's pay:
m = 12h
Since Thomas and Marie made the same amount of money over the same number of hours, we can say:
4h + 120 = 12h
120 = 8h
h = 15
This means they both worked for 15 hours.
The Parker company employs 68 part time workers. If this represents 4% of the total work force, how many individuals work for the company?
Answers
Answer: ite will be 3 bc i done that all ready
Step-by-step explanation:
The number of individuals that work for the company is 272 workers.
Given,
The Parker company employs 68 part-time workers.
This represents 4% of the total workforce.
We need to find out how many individuals work for the company.
What is percentage?Percentage is a fraction or a ratio in which the value of whole is always 100.
Find the total workforce.
Total workforce = 100%
We have,
4% = 68 workers
Multiply 25 on both sides.
25 x 4% = 4 x 68 workers
100% = 272 workers.
This means the number of individuals that work for the company is 272 workers.
Thus the number of individuals that work for the company is 272 workers.
Learn more about percentage decrease from a given value here:
https://brainly.com/question/14961696
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1.
Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of
the measurement pairs that could be the dimensions of Rectangle B.
A.
6 cm by 1.5 cm
B.
10 cm by 2 cm
C.
13 cm by 4 cm
D.
18 cm by 4.5 cm
E.
80 cm by 20 cm
Answers
Answer:
A,D and E
Step-by-step explanation:
You are rolling artwork to ship so it fits perfectly in a cylindrical shipping tube. The volume of the shipping tube is
169.56 cubic inches. If the radius of the shipping tube is 1.5 inches, what is the maximum height of the artwork you
can ship and what formula can you use to calculate this height?
O 6 inches; height =
volume
3.14 x (radius)?
O 18 inches; height:
volume
3.14 x radius
O 24 inches, height
volume
3.14 x (radius)2
36 inches; height
volume
3.14 x radius
O 54 inches; height
volume
3.14
Answers
The volume of a cylinder is found by using the formula V = pi x r^2 x h where r is the radius and h is the height.
Using the given volume and radius calculate the height:
169.56 = pi x 1.5^2 x h
169.56 = pi x 2.25 x h
169.56 = 7.065 x h
H = 169.56/7.065
H = 24 inches
The answer is the height is 24 inches
Answer:
b
Step-by-step explanation:
an item on sale costs 60% of the original price. If the original price. If the original price was $40, what is the sale price?
Answers
Answer: $24
Step-by-step explanation:
40 * .60 = $24
How to find t=3,500•(1.10)^100, round to the nearest whole number
Answers
Answer:
To find 3,500 by near to 3,550
Step-by-step explanation:
the nearest number of 3,500 is 3,500
also this question pls hurry with this i ready question you will be awarded 100
Answers
Answer:
1 hour equals 18 bucks
144 divided by 18 equals 8 so she works for 8 hours to get 144 bucks
Step-by-step explanation:
144 divided by 18 equals 8
45six +13six
Carry out the addition shown using base six notation
Answers
Step-by-step explanation:
45 6
13 6
_____ +
02 6
1
________
6 /..8
..... -6
_______
..... 2
0
_______
6/5
...5
_____
0
Solve the given equation: 49 = 7^(x+1) *
Answers
Answer:
x = 1
Step-by-step explanation:
49=7^x+1
Let's take the log of both sides
(x+1)*(log(7))=log(49)
x + 1 = log (49) / log (7)
x + 1 = 2
subtract 1 from both sides
x = 1
A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of 16 3/4 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of 19 4/5 liters per minute. (a) What expression represents the change in volume of solution in the tank in 1 minute? (b) Simplify and give your answer as a simplified mixed number. (c) What is the change in volume of the solution after 10 minutes? Show necessary work. Give your answer as a simplified mixed number.
Answers
The change in volume per minute and the total change in the volume of the solution after 10 minutes will be [tex] - 3 \frac {1}{20} \: litres [/tex] and [tex]- 30 \frac {1}{2} \: litres [/tex] respectively.
Entry rate = [tex] 16 \frac{3}{4} [/tex] per minute Discharge rate = [tex] 19 \frac{4}{5} [/tex] per minuteChange in the volume of solution in the tank per minute can be calculated thus :
Change in volume = (Entry rate - Discharge rate) × time [tex] 16 \frac{3}{4} - 19 \frac{4}{5} = \frac{67}{4} - \frac{99}{5} = \frac{(335 - 396)}{20} = \frac{-61}{20} = - 3\frac{1}{20} \: litres \: per \: minute [/tex]The total change in the volume of solution in the tank after 10 minutes can be calculated thus :
Change in volume per minute × time [tex] - \frac{61}{20} \times 10 = - \frac{610}{20} = - 30 \frac {1}{2} \: litres [/tex]Therefore, the solution in the tank decreases by [tex] 30 \frac {1}{2} \: litres [/tex] after 10 minutes
Learn more :https://brainly.com/question/18796573
From a random sample of 92 male students at Hope College, 8 were left-handed. Using the Theory Based Inference applet, determine a 99% confidence interval for the proportion of all male students at Hope College that are left -handed.
Answers
Answer:
mkkkmnsine kgsk jtb jgjdb Geeta kl John ku
4. Tom rides his bike a total of 6 14 miles to work over the course of 5 days.
How far does he ride each day?
How far will Tom ride his bike to and from work in 3 weeks?
Answers
6 14 miles in 5 days.
In 1 day Tom rides 6 14/5 = 1 228 miles
1 week has 7 days
5 weeks have 35 days
1 day Tom rides 1 228 miles
35 days Tom rides for 1 228 * 35 = 42 98miles.
fill in the blank (no word bank)
Answers
Answer:
Angle, Lengths
Step-by-step explanation:
Angle measurements and segment lengths are preserved as the transformations neither change the scale factor nor change the angle measurements
Which number has the greatest absolute value?
A. −7.5
B. −12
C. 5
D. 3/4
Answers
Answer:
B
Step-by-step explanation:
The value of 1x10 when x = -2, can be
written in simplest form as a36, where
a=
and b=
DONE
Answers
Answer 8
Step-by-step explanation:
PLEASE i need help, someone can help me ?!
Answers
answer please. bots will obvious be deleted
Answers
Answer:
A right triangle needs to have all the sides of the same length. Since this obviously does not, it is not a right triangle. Infact, this is a scalene triangle because all of its sides are unequal.
HELP MEEEEE PLZZZZZ!!!
Answers
Answer:
75.02 ft and 64.62 ft.
In ΔFGH, g = 39 cm, h = 54 cm and ∠F=34°. Find the area of ΔFGH, to the nearest square centimeter.
Answers
Answer:
≈ 589 cm²
Step-by-step explanation:
area = 1/2 * 39 * 54 * sin34°
= 1/2 * 39 * 54 * 0.559194
= 588.83
≈ 589
What is the domain of the function in this table?
A. {3, 4, 5, 6)
B. {2,4,5)
C. (3,4)
D. (3, 4), (4,4), (5,2), (6,5)
Answers
Answer:
3, 4 , 5 , 6 is your answer.
I HOPE IT WILL HELP YOU.
Thank you.
TEDDYLOVER....
Find the area of the triangle.
6
8
Answers
Answer:
24
Step-by-step explanation:
the area formula for a triangle is
base x high
----------------
2
so 6x8=48 and divided by 2 is 24
Answer:
24
Step-by-step explanation:
8×6 then Divide by 2........
Select the correct answer. Which equation represents a line that is parallel to the x-axis, is perpendicular to the y-axis, and has a slope of 0? A. y=4/5x + 4/5 B. y=5/4x
C. y=4/5 D. x=5/4
Answers
Answer: D
Step-by-step explanation: i did this
Answer:
C. y = 4/5Step-by-step explanation:
The line parallel to the x-axis has same coordinate for any value of x. The slope is zero.
This line has the form:
y = b, where b is the y-intercept.The only option with similar form is C