Find the derivative of tan(x).
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Derivative of tan(x) is sec²x
[tex]\qquad \sf \dashrightarrow \: \therefore \dfrac{d}{dx} ( \tan(x)) = { \sec}^{2} (x)[/tex]
You can check the first principle method of derivation in attachment
[tex]\rightarrow \sf \dfrac{d}{dx} (tan(x))[/tex]
[tex]\rightarrow \sf \dfrac{d}{dx} ( \ \dfrac{sin(x)}{cos(x)} \ )[/tex]
use the quotient rule
[tex]\rightarrow \sf \dfrac{cos(x) * \dfrac{d}{dx} (sin(x)-sin(x)*\dfrac{d}{dx}(cos(x) }{cos(x)^2}[/tex]
[tex]\rightarrow \sf \dfrac{cos(x) * cos(x)-sin(x)*(-sin(x) )}{cos(x)^2}[/tex]
[tex]\rightarrow \sf \dfrac{cos(x)^2+sin(x)^2}{cos(x)^2}[/tex]
[tex]\rightarrow \sf \dfrac{1}{cos(x)^2}[/tex]
[tex]\rightarrow \sf sec(x)^2[/tex]
used formula's :
cos²(x) + sin²(x) = 1[tex]\sf \dfrac{1}{cos^2(x) }= sec^2(x)[/tex][tex]\sf \frac{d}{dx}[/tex] cos(x) = -sin(x)[tex]\sf \frac{d}{dx}[/tex] sin(x) = cos(x)tan(x) = sin(x)/cos(x)Related Questions
Two years ago the Castillo family used $3,250 worth of electricity. Last year they switched to balanced billing averaged over 12 months. What was their monthly payment last year under balanced billing? During last year, they actually used $3,766 of electricity and their balanced billing payments were not enough to pay for their electrical usage. They had to pay the difference at the end of the year. How much did they owe the utility company?
Answers
The Castillo family made a monthly payment of $270.83 and they owed the utility company $516
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Two years ago the Castillo family used $3,250 worth of electricity. During last year, they actually used $3,766 of electricity, hence:
Monthly payment = $3250 / 12 = $270.83
Money owed = $3,766 - $3,250 = $516
The Castillo family made a monthly payment of $270.83 and they owed the utility company $516
Find out more on equation at: https://brainly.com/question/2972832
Find the number if 2 1/2 of it is 15
(please help)
Answers
[tex]2.5x = 15[/tex]
[tex]x = \frac{15}{2.5} = 6[/tex]
Answer:
or Also
[tex] \frac{5}{2} x = 15 \\ 5x = 15 \times 2 \\ 5x = 30 \\ 5x \div 5 = 30 \div 5 \\ x = 6[/tex]
what is 5x15= what help me please to hard
Answers
Answer:
75
Step-by-step explanation:
17. Kayden creates a linear function where x is the input, y, is the output, and
m and b are constants.
A. Which equation could represent Kayden's function?
y=1/x+ mb
y = mx + b
© x = my • by
.
B.
Which statement about the graph of Kayden's function is true for all
values of m and b?
~ The graph is increasing.
® The graph is decreasing.
© The graph goes through the origin.
The graph has a constant rate of change.
Answers
Answer:
see explanation
Step-by-step explanation:
A linear function has the form
y = mx + b ( m is the slope and b the y- intercept )
B
the graph has a constant rate of change , measured by the slope m of the linear function.
Tina buys 5 pounds of potatoes for $4. 35 and 3 pounds of carrots for $3. 57 how much does 1 pound of potatoes cost
Answers
Answer:
1 pound of potatoes costs $0.87
Arnold borrowed $7890 at 11.5 percent for five years.
What is the amount of Arnold's total payment?
$11,580
$10,410
$9,520
$8,560
CAN SOMEONE PLEASE HELP ME ASAP IM STUCK
Answers
Help solve this circle
Answers
You're basically using the supplement angle to find the missing number.
The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
A. 14 sec
B. 15 sec
C. 16 sec
D. 17 sec
Answers
Solving the system of equations, it is found that a viable time that the trains are side by side is given by:
B. 15 sec
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
[tex]y = 14t^2[/tex]
[tex]y = 130t + 1200[/tex]
They will be side by side when:
[tex]14t^2 = 130t + 1200[/tex]
[tex]14t^2 - 130t - 1200 = 0[/tex]
It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:
[tex]\Delta = (-130)^2 - 4(14)(-1200) = 84100[/tex]
[tex]x_1 = \frac{130 + \sqrt{84100}}{28} = 15[/tex]
[tex]x_2 = \frac{130 - \sqrt{84100}}{28} = -5.71[/tex]
Time is a non-negative measure, hence option B is correct.
More can be learned about a system of equations at https://brainly.com/question/24342899
Answer:
B: 15 sec
Step-by-step explanation:
I took the algebra exam
The perimeter of a rectangular garage
is 46 meters. The garage is 10 meters
wide. How long is it?
meters
Answers
Divide area by width:
46/10 = 4.6 meters
Answer: 4.6 meters
Answer:
The rectangular garage is 13m long.
Step-by-step explanation:
[tex]\sf\large{\star Given:-}[/tex]
Perimeter of rectangular garage = [tex]\sf\pink{46 \:m.}[/tex]Width of the rectangular garage = [tex]\sf\pink{10\:m.}[/tex][tex]\sf\large{\star To\: find:-}[/tex]
How long is the garage (length of garage).[tex]\sf\large{\star Solution:-}[/tex]
[tex]\rightarrow[/tex]As we know that,
Perimeter of rectangle = [tex]\sf\blue{2(length+width)}[/tex]
So, by putting the value of perimeter and width in this formula we get,
[tex]\rightarrow[/tex] [tex]\sf{2(l+10)\:=\: 46}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{2l+20\:=\: 46}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{2l\:=\: 46-20}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{2l\:=\: 26}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{l \:=\: \frac{26}{2}}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{l\:=\: 13m.}[/tex]
Therefore, length of the rectangular garage = [tex]\sf\purple{=\: 13m.}[/tex]
_______________________________
Hope it helps you:)
Which inequality can be used to find how many $1.25 snack packs can be purchased for $10.00?
Answers
Answer:
1.25s [tex]\leq[/tex] 10.00
Step-by-step explanation:
Let's snack = s
Note:
[tex]\leq[/tex] ⇒ Less than or equal to
[tex]\geq[/tex] ⇒ Greater than or equal to
< ⇒ Less than
> ⇒ Greater than
Since we are trying to find how many $1.25 snack packs can be purchased for $10.00.. Thus, that less than or equal to $10.00 which also means we use [tex]\leq[/tex].
Thus the equation is 1.25s [tex]\leq[/tex] 10.00
`lenvy`
Answer:
8 snacks can be purchased
Step-by-step explanation:
10.00/1.25=8
Find the value of a. Round your answer to the nearest tenth. B 10 77.5 A C 7.9
Answers
Answer:
[tex]\displaystyle 11,3[/tex]
Step-by-step explanation:
Use the Law of Cosines to find the length of the third edge:
Solving for Angles
[tex]\displaystyle \frac{a^2 + b^2 - c^2}{2ab} = cos\angle{C} \\ \frac{a^2 - b^2 + c^2}{2ac} = cos\angle{B} \\ \frac{-a^2 + b^2 + c^2}{2bc} = cos\angle{A}[/tex]
Use [tex]\displaystyle cos^{-1}[/tex]towards the end or you will throw your result off!
Solving for Edges
[tex]\displaystyle b^2 + a^2 - 2ba\:cos\angle{C} = c^2 \\ c^2 + a^2 - 2ca\:cos\angle{B} = b^2 \\ c^2 + b^2 - 2cb\:cos\angle{A} = a^2[/tex]
Take the square root of the final result or it will be thrown off!
Let us get to wourk:
[tex]\displaystyle 10^2 + 7,9^2 - 2[10][7,9]\:cos\:77,5 = a^2 \hookrightarrow 100 + 62,41 - 158\:cos\:77,5 = a^2 \hookrightarrow \sqrt{128,212541} = \sqrt{a^2}; 11,323097677... \\ \\ \boxed{11,3 \approx a}[/tex]
I am joyous to assist you at any time.
Find the area of the trapezoid. {?} Square centimeters
Answers
Answer:
68
Step-by-step explanation:
Use the formula provided...
6 and 11 are b1 and b2, and 8 is h.
So, 6+11 = 17
17/2 = 8.5
8.5*8 = 68
Claudius took out an unsubsidized stafford loan at the beginning of his six-year college career. the loan had a principal of $4,850, an interest rate of 6.5% compounded monthly, and a duration of ten years. if claudius started paying off the loan when he graduated, what is his monthly payment? round all dollar values to the nearest cent. a. $71.37 b. $81.25 c. $55.07 d. $76.55
Answers
Answer:
b.
$81.25
Step-by-step explanation:
taking it rn
Answer:
b 81.25
seen it on quizlet
Step-by-step explanation:
write down the next two terms of the number pattern 2,5,8,11,14
Answers
Answer:
17 and 20
Step-by-step explanation:
Write down the next two terms of the number pattern 2, 5, 8, 11, 14
Looking at the numbers, we can tell that they are increasing by 3:
2 + 3 = 5
5 + 3 = 8
8 + 3 = 11
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
Hope this helps!
What are the circumstances under which a person will feel disadvantage, if the parking ticket is lost
Answers
The circumstances where an individual will feel disadvantaged if they misplace or lost a parking ticket is that:
The parking attendant will find it difficult and tasking to locate your car in an absence of a parking ticket.You'll also be charged an extra expensive fee for a lost ticket.What is a parking ticket?A parking ticket is a piece of paper informing someone that they have parked a car unlawfully or for an excessively lengthy period of time and must pay a fine.
It is also know to be a notice informing a driver of a fee levied for improperly parking, usually written by a traffic officer and placed to a vehicle windscreen.
However, an individual will feel disadvantaged if they misplace or lost the ticket because:
The parking attendant will find it difficult and tasking to locate your car in an absence of a parking ticket.You'll also be charged an extra expensive fee for a lost ticket.Learn more about a parking ticket here:
https://brainly.com/question/26968718
Find the distance between A(5, -2) B(3, -6)
Answers
Answer:
Over 2 up 4
Step-by-step explanation: I just learned this so I am not a pro but, 5 would be X for A, So to the right, down 2, 3 right for B, down 6
Given triangle ABC is congruent to DEC find m
Answers
Answer:
angle d = 106
BRAINLIEST HURRY HURRY By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one month, you spent 280 minutes on the phone, and paid $23.80. In another month, you spent 340 minutes on the phone, and paid $25.90.
Let x be the number of minutes you talk over the phone in a month, and let y be your cell phone bill, in dollars, for that month. Use a linear equation to model your monthly bill based on the number of minutes you talk over the phone.
This linear model’s slope-intercept equation is_______ .
If you spent 160 minutes over the phone in a month, you would pay _____.
If in a month, you paid $30.80 of cell phone bill, you must have spent _____ minutes on the phone in that month.
Answers
Answer:Y = Co + C*x.22.45 = Co + C*200,Co = 22.45 - 200C.29.65 = Co + C*350.Co = 29.65 - 350C. = 22.45 - 200C150C = 7.20, C = 0.048/min.Co = 22.45 - 200*0.048 = $12.85/mo. = Initial cost.Y = 0.048x + 12.85.2. Y = 0.048*110 + 12.85 = $18.13.3. 34.10 = 0.048x + 12.85, X = ?.
Step-by-step explanation:
If the scale factor here is 3 (k=3), and if the distance from A to B is 8 units, then what would be the distance from A’ to B’?
8
8/3
24
3
Answers
Distance between A'B':-
8k8(3)24Option C
Sarah and Lily mow lawns during the summer to earn money. Sarah
determined that she can earn between $6. 00 and $6. 25 per hour. Lily estimates
that she earns between $7. 50 and $8. 00 per hour. About how much more money will
Lily earn than Sarah if they each work 22 hours?
Answers
Answer:
21.75
Step-by-step explanation:
Because 6.00+6.25=12.25+7.00=19.75+8.00=27.75
You and your friend buy a bag of assorted fruit that contains 3 apples, 5 oranges, and 2 bananas. You each randomly choose a piece of fruit and eat it. What is the probability you both will get a banana?
Answers
Jackson recorded the following data: 2,5, X, 2, 4, 3. If the mean
of the data is 3, what is the value of x? Explain how you found your answer
Answers
Answer:
x = 2
Step-by-step explanation:
mean = sum of data / number of data
3 = 2 + 5 + x + 2 + 4 + 3 / 6
3 = 16 + x / 6
18 = 16 + x
2 = x
The missing value of data is 2.
What is arithmetic Mean?The simplest and most popular way to measure a mean or average is the arithmetic mean. It simply entails adding up a collection of numbers, then dividing that total by the total number of numbers in the series.
We have,
Data: 2,5, X, 2, 4, 3
Mean= 3
So, Mean
3 = Sum of data/ Total number of data
3 = (2 + 5 +x + 2 + 4 +3)/ 6
18 = 16 + x
x = 18 - 16
x= 2
So, the missing value of data is 2.
Learn more about Arithmetic Mean here:
https://brainly.com/question/13000783
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Jacob had a cube. When Jacob made a cross section parallel to the base, what shape did the cross section form? trapezoid square parallel triangle
Answers
Answer: Square
Step-by-step explanation:
A cross section cut parallel to a base will be the same shape as the base itself, and the base of a cube is a square. :)
Answer:
A square because it is not diagonal.
Step-by-step explanation:
A group of students is riding in a bike tour. They have biked 15 miles, which is 25% of the tour. How long is the tour?
Answers
Answer:
60 miles
Step-by-step explanation:
25% of 60 = 15
Hoped this helped<33
please help me please
Answers
Answer: 8 x 2 = 4
1 x 4 = 4
9 x 3 = 27
2 x 4 = 8
Step-by-step explanation:
In a survey of 250 voters, 3 out of 5 voters said they planned to vote for a proposed
new county library.
a) how many of these voters plan to vote for the library?
N
b) how many are not planning to vote for the library?
Answers
The experimental probability of a quarter landing on HEADS is 3/5 if the quarter landed on TAILS 36 times how many times tossed.
Answers
Answer:
90 times
Step-by-step explanation:
I don't rly know how to explain it but it's 90 and I hope this helps you at least know the answer if not then sorry for wasting your time and may God bless you:)
What is the difference?
74 – 26 =
47
48
52
58
Answers
48 is the correct answer
help pls asap i be grateful
Answers
Area of a cube is length times width times height
4 x 2 x 2 = 16
Answer: number a
Step-by-step explanation:4 times 2 is 8 8 times 2 is 16
6.
Rahman sets off by car to his office at 08 55. He takes 20 minutes to arrive at his office, What time does he
arrive at his office?
huh its was so hardd can someone explain and solve it for me? :(
Answers
Answer:
he will arrive at work by 9:25 to push the time but its rea£y 9:20
Steps:
Time to travel is 00:20
Start time is 08:55
Time of arrival is ?
20 minutes from 8:55.
An hour has 60 minutes.
There is 5 more minutes until 09:00.
20 - 5 = 15
15 minutes from 09:00 is 9:15.