Answer:
y = x - 2π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopePre-Calculus
Unit CircleCalculus
The definition of a derivative is the slope of the tangent line.
Derivatives of Trig Functions
sin(x) = cos(x)cos(x) = -sin(x)tan(x) = sec²(x)sec(x) = sec(x)tan(x)csc(x) = -csc(x)cot(x)cot(x) = -csc²(x)Step-by-step explanation:
Step 1: Define
y = sinx
x = 2π
Step 2: Find Derivative
Take derivative: y' = cosxThis is the function of the tangent line for y.
Step 3: Find slope
Substitute in x into y': y'(2π) = cos2πEvaluate: y'(2π) = 1This tells us that the slope of the tangent line is 1 at x = 2π.
Step 4: Write equation
Find a point.
Substitute x into y: y(2π) = sin2πEvaluate: y(2π) = 0Write coordinate: (2π, 0)Write tangent function.
Substitute: y - 0 = 1(x - 2π)Simplify: y = x - 2πThis is the equation of the tangent line at x = 2π.
What is the amount earned by a car salesman if he sold a truck for $37.500 at a 2% commission? 15
The equation C = 5 9 F − 160 9 gives the relation between temperature readings in Celsius and Fahrenheit.
(a) Is C a function of F? Yes, C is a function of F. No, C is a not a function of F.
(b) What is the mathematical domain of this function? (Enter your answer using interval notation. If C is not a function of F, enter DNE.)
(c) If we consider this equation as relating temperatures of water in its liquid state, what are the domain and range? (Enter your answers using interval notation. If C is not a function of F, enter DNE.) domain range
(d) What is C when F = 71°? (Round your answer to two decimal places. If C is not a function of F, enter DNE.) C(71) = °C
Step-by-step explanation:
The question is wrong. The correct equation is :
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]
We know that the equation gives the relation between temperature readings in Celsius and Fahrenheit.
Therefore, giving that we know the value in Fahrenheit ''F'' we can find the reading in Celsius ''C''. This define a function C(F) that depends of the variable ''F''.
So for the incise (a) we answer Yes, C is a function of F.
For (b) we need to find the mathematical domain of this function. Giving that we haven't got any mathematical restriction, the mathematical domain of the function are all real numbers.
Dom (C) = ( - ∞ , + ∞)
For (c) we know that the water in liquid state and at normal atmospheric pressure exists between 0 and 100 Celsius.
Therefore the range will be
Rang (C) = (0,100)
Now, we need to find the domain for this range. We do this by equaliting and finding the value for the variable ''F'' :
For C = 0 :
[tex]0=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒ [tex]F=32[/tex]
And for C = 100 :
[tex]100=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒ [tex]F=212[/tex]
Therefore, the domain as relating temperatures of water in its liquid state is
Dom (C) = (32,212)
For (d) we only need to replace in the equation by [tex]F=71[/tex] and find the value of C ⇒
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒
[tex]C=(\frac{5}{9})(71)-\frac{160}{9}[/tex]
[tex]C=\frac{65}{3}[/tex] ≅ 21.67
C(71) = 21.67 °C
a. Yes, C is a function of F.
b. Domain of the function is: ( - ∞ , + ∞)
c. Range of function C is: (0, 100)
the domain of function C is: (32, 212).
d. [tex]\mathbf{C(71) = 21.67^{\circ}C}[/tex]
Range and Domain of A FunctionThe domain of a function is the input value, while the range is the corresponding output value.
a. Given the equation of the function as, [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex], this means that, the value of C is dependent on the value of F, therefore, the answer is, Yes, C is a function of F.
b. Since no mathematical restriction was stated, therefore:
Domain of the function is: ( - ∞ , + ∞)
c. Temperature of water in its liquid state ranges between 0 and 100°C, therefore:
Range of function C is: (0, 100)
To find the domain, substitute C = 0 and C = 100, respectively, into [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex].
Thus:
[tex]0 = \frac{5}{9}(F) - \frac{160}{9}\\\\F = 32[/tex]
[tex]100 = \frac{5}{9}(F) - \frac{160}{9}\\\\F = 212[/tex]
Therefore, the domain of function C is: (32, 212).
d. To find C when F = 71°, substitute F = 71° into [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex].
Thus:
[tex]C(71) = \frac{5}{9}(71) - \frac{160}{9}\\\\C(71) = \frac{65}{3} \\\\\mathbf{C(71) = 21.67^{\circ}C}[/tex]
Learn more about domain and range of function on:
https://brainly.com/question/10197594
Jack has a saving account of value $65,550 at the start. The saving account has an interest rate of 3% that is compounded every six months. How long will it take Jack to have $100,000 in his account?
Given:
Principal value = $65,550
Rate of interest = 3% compounded every six month
To find:
The taken to have $100,000 in Jack's account.
Solution:
The formula for amount is
[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]
where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is time in number of years.
Interest compounded every six month. It means, interest compounded 2 times in an year.
Substitute A=100000, r=0.03 and n=2 in the above formula.
[tex]100000=65550(1+\dfrac{0.03}{2})^{2t}[/tex]
[tex]\dfrac{100000}{65550}=(1+0.015)^{2t}[/tex]
[tex]1.525553=(1.015)^{2t}[/tex]
Taking log on both sides.
[tex]\log (1.525553)=\log (1.015)^{2t}[/tex]
[tex]\log (1.525553)=2t\log (1.015)[/tex]
[tex]\dfrac{\log (1.525553)}{2\log (1.015)}=t[/tex]
[tex]t=14.1838928[/tex]
[tex]t\approx 14.18[/tex]
Therefore, after 14.18 year the amount will reach at $100,000 or we can say that in 15th year the amount will reach at $100,000.
please help me with the question.
Answer:
Step-by-step explanation:
∠a is corresponding to ∠f
∠b is alternate interior angle to ∠e
∠g is alternate exterior to ∠d
∠f is vertical to ∠h
∠b is consecutive( same side) interior with ∠f
what is an equation for the translation of y=|x| left 7 units?
Answer:
y=|x+7|
Step-by-step explanation:
to move an absolute value equation to the left, all you have to do is add 7 to the inside of the absolute value:
y=|x+7|
We can check that this works, because the x-intercept moved from (0, 0) to (0, -7), meaning that the whole graph got translated 7 units to the left.
You have found the following ages in years of 4 gorillas at your local zoo. What is the average age of the gorillas at your zoo? What is the variance? 7, 10, 15,21
Answer:
your answer is 7
Step-by-step explanation:
i may be wrong but i think that is the correct answer oh and Have a good thanksgiving everyone
Answer:
13.3 and 28.2 years
Step-by-step explanation:
from Khan academy
The BHS band needs to make T-shirts for its 35 members and has set aside some money in their budget to pay for them. The members of the band decided to order from a printing company that charges $3 per shirt, plus a $50 fee for each color to be printed on the shirts.
Write an equation that represents the relationship between the number of T-shirts ordered, the number of colors on the shirts, and the total cost of the order. If you use a variable, specify what it represents.
2. In this situation, which quantities do you think can vary? Which might be fixed?
Answer:
C = 105 + 50x
2) variable unit = Numbe of color
Fixed unit = number of shirt
Step-by-step explanation:
Given that :
Number of members = 35
Charge per shirt = $3
Charge per color = $50
relationship between the number of T-shirts ordered, the number of colors on the shirts, and the total cost of the order
Let cost of order = C
Number of color = x
Number of Tshirt ordered = 35
Cost = (charge per shirt * number of shirts) + charge per color * number of colors)
C = (3 * 35) + ($50 * x)
C = 105 + 50x
Number of shirts to be ordered has been fixed tnd this includes it's 35 members
The number of color to be used hasn't been adopted and can thus be varied
46% of the students that were surveyed like to eat at McDonald's if 351 students do not like to eat at McDonald's how many people were surveyed
Answer:650 people were surveyed
What is the first thing you do before solving an adding fraction problem
Pls help
Answer:
The first thing you do is make the denominators equal on both sides.
Step-by-step explanation:
As a example if you have the equation:
[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex] =
you would multiply the denominator by the smallest multiple. I would do 2 * 5= 10
this would make the equation
[tex]\frac{x}{10} + \frac{x}{10} = ...[/tex]
next you have to do the same with the numerator.
so sence you multiplied the [tex]\frac{1}{2}[/tex] by five you will get [tex]\frac{5}{10}[/tex]
same with the other fraction except you multiplied it by two.[tex]\frac{2}{5}[/tex] x 2 = [tex]\frac{4}{10}[/tex]
next you add and simplify if needed
Answer:
3 simple steps
Step-by-step explanation:
1. Make sure the bottom numbers ( the denominators ) are the same
IF DIFFERENT find the LCD
2. Add the top numbers (the numerators )
3. simplify the fraction if needed
ex: 1/4 +1/4 = 2/4 (bottoms were the same) simplify 1/2
1/3 + 1/6 LCD of 3 and 6 so make the bottom numbers 6
so multiply 1/3 x 2 = 2/6
now you have 2/6 + 1/6 = 3/6 simplify 1/2
Julie is trying to choose between two packs of cookies. Pack A has 36 cookies for $5.90. Pack B has 24 cookies for $4.10. Which pack has cheaper cookies
Answer:
b
Step-by-step explanation:
I really need help can someone please understand
sure what’s the problem
for every house there is one and only one street address is it a function
Answer:
No
Step-by-step explanation:
No, it is not a function it would instead be a constant since the result will always be the same street address regardless of the input that is being given. With a function, a specific input is given to the function which is applied to the function itself, and output is provided based on the results generated from the input. Therefore, with a function, the input determines the output which is almost always different when different inputs get provided.
If 200 men can make a road 5 km long in 25 days ,how much overtime per day must 60 men can work to finish an road 2 km in 32 days , 12 hours being a day's work ?
Answer:
Solution with step by step explanation is the image attached below
Sean has some candy bars that he wants to give away. He is going to give each person 1/8 of a bar, and he has 2 3/4 bars to give away
how many people will get candy?
Answer:
jdfsddudnfdhujskvbusduyhd
Step-by-step explanation:
habdaerfukhdskfsubfa
Maria needs to be at the airport terminal at 15:20. It will take 2 hours to
drive to the airport from her home, and a further 30 minutes to park and get
to the terminal.
What is the latest time she should leave home?
Give
your answer as a time in the 24-hour clock.
Answer:
12:50
Step-by-step explanation:
15:20 - 2h= 13:20
13:20-30 min= 12:50
Answer:
12:50
Step-by-step explanation:
If it takes 2 hours to get there, you subtract 2 hours from 15:20 which gives you 13:20. It also says that she needs 30 minutes to park so you subtract that from 13:20 giving you 12:50
Explain to me in words how you would find the slope of this line and explain your answer
Answer: m=7/3
Step-by-step explanation:
the point were at (4,3)(1,-4)
m=y2-y1/ x2-x1
m= -4-3/ 1-4
m= -7/-3
m=7/3
PLZ HELP!!!
Will mark brainliest
44. Show that the quadrilateral with vertices A(0,0), B(a,0), C(a + b, c) and D(b, c) is a parallelogram.
Answer:
A=1
B=2
c=1
Step-by-step explanation:
In San Diego, the weather was sunny 90% of the says this past June. How many days was it sunny
Answer:
27 days
Step-by-step explanation:
June has 30 days, So our equation looks like this:
30*0.9=27 days.
A line passes through the point (2, -7) and has a slope of
21
Please help me with this
Answer:
$62.50
Step-by-step explanation: 250 divided by 4 equals $62.10
Matt bought 8 pie molds at a cost of $0.67 per mold. He also bought 8 pre-
made crusts at a cost of $0.63 per crust. How much did Matt spend on pie
molds?
Answer:
$5.36
Step-by-step explanation:
multiply 8 by .67
11 ÷ 924 in long division
Answer:
231 your welcome
Step-by-step explanation:
y = -4x – 5
y = 3.x – 2
Is (3, 7) a solution of the system?
Answer:
no
Step-by-step explanation:
this is because
-12-5=-17
-28-2= -30
A local little league has a total of 66 players, of whom 80 % are right-handed. How many right-handed players are there?
Answer:
The amount of right-handed players is 53
Hope this Helps :)
Turn the sentence into an expression
5.three times the sum of two consecutive
integers
3(x+x+1)
hope this helps
SOMEONE PLS HELP I WILL MARK BRAINLIEST
Answer:
Trina is closer to the ocean because she is only 85.6 meters away from the surface, while Jessie is 87.9 meters away. 85.6 is less than 87.9, which means that Trina is closer.
Step-by-step explanation:
Sea level is represented by the number 0. -85.6 is closer to the number 0 than 87.9 is, which tells us that Trina is closer.
Hope this helps :)
What are the partial products that result from multiplying 17*32?
Answer:
544
Step-by-step explanation:
What is the greatest possible error if Irina measured the weight of her dog as 13 pounds?
Answer:
0.5
Step-by-step explanation:
Given that:
Irina measured the weight of her dog to be 13 pounds.
The greatest possible error that could have to occur will be the maximum error.
Let assume that the 13th value obtained was rounded between the range of 12.5 → 13.49 to 13 pounds
Then;
The greatest possible error that could have to occur = 13.0 - 12.5 pounds
The greatest possible error that could have to occur = 0.5 pounds
Answer:
0.5
Step-by-step explanation:
EDGE 2020 Unit Test
pls help what is 1+2
A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What percent of the radios will function for more than 16 years? (b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X. (c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years? (d) If 10% of the radios will function for more than X years, find X.
Help, please!!
Answer:
(a) 5.48%
(b) 17.82 years
(c) 21.19%
(d) 15.21 years
Step-by-step explanation:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
µ=12 years and σ=2.5 years.
(a) What percent of the radios will function for more than 16 years?
For x = 16
z = 16 - 12/2.5
z = 1.6
Probability value from Z-Table:
P(x<16) = 0.9452
P(x>16) = 1 - P(x<16)
1 - 0.9452
= 0.054799
Converting to percentage = 0.054799 × 100
= 5.4799%
Approximately = 5.48%
(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.
find the z score of the 99th percentile = 2.326
Hence:z = (x-μ)/σ
2.326 = x - 12/2.5
Cross Multiply
2.326 × 2.5 = x - 12
5.815 = x - 12
x = 12 + 5.815
x = 17.815
Approximately = 17.82 years
(c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years?
When x < 10
Hence,
z = 10 - 12/2.5
z = -0.8
Probability value from Z-Table:
P(x<10) = 0.21186
Converting to percentage
0.21186 × 100
= 21.186%
Approximately = 21.19%
(d) If 10% of the radios will function for more than X years, find X.
The z score would be : 100 - 10%
= 90th percentile z score
We find the z score of the 90th percentile = 1.282
Hence:z = (x-μ)/σ
1.282 = x - 12/2.5
Cross Multiply
1.282 × 2.5 = x - 12
3.205 = x - 12
x = 12 + 3.205
x = 15.205
Approximately = 15.21 years