Answers
Answer:
See explanation.
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringAlgebra II
Polynomial Long DivisionPre-Calculus
ParametricsCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Parametric Differentiation: [tex]\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle x = 2t - \frac{1}{t}[/tex]
[tex]\displaystyle y = t + \frac{4}{t}[/tex]
Step 2: Find Derivative
[x] Differentiate [Basic Power Rule and Quotient Rule]: [tex]\displaystyle \frac{dx}{dt} = 2 + \frac{1}{t^2}[/tex][y] Differentiate [Basic Power Rule and Quotient Rule]: [tex]\displaystyle \frac{dy}{dt} = 1 - \frac{4}{t^2}[/tex]Substitute in variables [Parametric Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{1 - \frac{4}{t^2}}{2 + \frac{1}{t^2}}[/tex][Parametric Derivative] Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{t^2 - 4}{2t^2 + 1}[/tex][Parametric Derivative] Polynomial Long Division: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{2} - \frac{7}{2(2t^2 - 1)}[/tex] [Parametric Derivative] Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{2} \bigg( 1 - \frac{9}{2t^2 + 1} \bigg)[/tex]Here we see that if we increase our values for t, our derivative would get closer and closer to 0.5 but never actually reaching it. Another way to approach it is to take the limit of the derivative as t approaches to infinity. Hence [tex]\displaystyle \frac{dy}{dx} < \frac{1}{2}[/tex].
Topic: AP Calculus BC (Calculus I + II)
Unit: Parametrics
Book: College Calculus 10e
Related Questions
PLEASE HELP THIS IS DUE ASAP!!!!!!!!!!
Answers
Answer:
1/36
Step-by-step explanation:
When you roll a die the possible outcomes are 1,2,3,4,5,6
P(1) = number of outcomes that are 1 / total outcomes
=1/6
The events are independent so we can multiply the probabilities
P(1,1) = 1/6*1/6 = 1/36
radius is 21 5/8 incercepted by 5Pi/6? What is arc lenght?
Answers
9514 1404 393
Answer:
(18 1/48)π ≈ 56.61 units
Step-by-step explanation:
Arc length is the product of radius and intercepted arc in radians:
s = rθ
s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units
Question 1 of 10
What is the value of n?
144
O A. 36
O B. 23
O C. 95°
D. 590
Answers
Answer:
Option C, 95°
Step-by-step explanation:
180-121 = 59
180-144 = 36
third angle of the triangle is, 180-59-36 = 85,
missing angle n = 180-85 = 95°
Answered by GAUTHMATH
Savannah used 2 quarts of paint on a summer project. She still had 5.
quarts of paint left when she was finished. How much paint did Savannah
have at first?
la cloud
Answers
Answer:
7 quarts
Step-by-step explanation:
total paint = paint used + paint left
total paint = 2 +5
total paint 7
I need helpppp please I don’t understand this question at alll
Answers
Answer:
17000
Step-by-step explanation:
17^1 * 10^3
17 * 10*10*10
17*1000
17000
the answer is 17,000
the exponent shows how many times you multiply the number by itself
here is an image for an explanation
hope I helped ❤
build and sketch 2x2+7x+6)
Answers
Answer:
Step-by-step explanation:
Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
[infinity]Σ n =1 (-1)^n - 1/n√n
Answers
Answer: hello your question is poorly written attached below is the complete question
answer:
The series is absolutely convergent
Step-by-step explanation:
To determine whether the series is absolutely or conditionally convergent or divergent. apply the Root Test
The series is absolutely convergent
attached below is the solution
Question 3 (5 points)
Draw a right isosceles triangle.
Answers
Answer:
Step-by-step explanation:
Vẽ góc vuông. - Trên hai canh góc vuô dùng thước thước có chia khoảng vẽ hai đoạn thẳng bằng nhau có chung một điểm và nối hai điểm còn lại.
What is the volume of a pyramid below?
600 cm^3
750 cm^3
900 cm^3
1800 cm^3
Answers
Answer: 600 cm³
Step-by-step explanation:
Volume of square pyramid = (1/3) · b² · h
b = base edge length = 10 cmh = height = 18 cmTherefore, the volume can be calculated as
[tex]\frac{1}{3} *10^{2}*18=\frac{1}{3}*100*18=\frac{1}{3}*1800=\frac{1800}{3}=600[/tex]
Answer
900
Step-by-step explanation:
it is pyramid and finding its volume we use the 3 components that is length, with and the height
1/2 base x width x height
5 x 18 x 10 = 900cm³
Water is flowing into a tank at a rate of 20 cm3/min. At the start, there is 250 cm3 of water in the tank.
(i) How much water will be in the tank after 30 minutes?
(ii) Find the time when there is 1210 cm3 of water in the tank.
Answers
Answer:
i) 410 cm³
ii) 48 min
Step-by-step explanation:
we start with 250 cm³.
and then we fill in 20 cm³ per minute.
i)
after 30 minutes we have
250 + 8×20 = 250 + 160 = 410 cm³
ii)
how long (how many minutes) does it take to reach 1210 cm³ in the tank ?
well, first we subtract the start amount (250).
and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.
1210 - 250 = 960 cm³
so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.
and
960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =
= 960 min / 20 = 48 min
Leena is arranging 3 different books in a row on a shelf. Create a sample space for the arrangement of a detective story (D), a mystery story (M), and a comic book (C).
Source
StylesNormal
Answers
There are 6 DIFFERENT POSSIBLE arrangements as obtained using the factorial method and they are :
DMC, CMD, DCM, MDC, CDM, MCD
Given :
DETECTIVE STORY = D
MYSTERY STORY = M
COMIC BOOK = C
To use the factorial method, we find the factorial value of the number of books to be arranged
Number of different possible arrangements = (number of books)!
Number of books = 3
Hence, 3! = 3 * 2 * 1 = 6 ways
The sample space :
DMC
CMD
DCM
MDC
CDM
MCD
THEREFORE, there are 6 different samples on the SAMPLE SPACE.
learn more :
https://brainly.com/question/13041664
What is the solution to this system of equations?
a - b + c = -6
b - c = 5
2a - 2c = 4
A) 2
B) -1
C) -3
D) 1
Answers
(-1;2;-3)
а, b, c
~~~~~~
I NEED HELP ON MATH PLS
Answers
Answer:
5/2 or 2½ or 2.5
Step-by-step explanation:
20/8 = 2.5
10/4 = 2.5
What is the equation of the line in the following graph?
Answers
Answer:
2 . y=-1
Step-by-step explanation:
m=0 (it is a straight line)
use (-6,-1) in y=mx+b
-1=0(-6)+b
-1=b
equation is now
y=0(x)-1
y=-1
Please help brainliest will be given
Complete the equation describing how
x and y are related.
x
-1
5
0 1 2 3 4
3 8
V 2
13
18
23
28
y = 5x + [?]
Enter the answer that belongs in [?].
Answers
y = 5x + 3
Step-by-step explanation:
When x = 0 y = 3 so the y-intercept will be 3
And the equation is y = 5x + 3 where the slope is 5
The number line shows the record low temperatures for four states.. what is the difference, between the low temperature in Hawaii and the low temperatures In south Dakota
A -70°F
B -46°F
C 46°F
D 70°F
Answers
Answer:
D 70°F
Step-by-step explanation:
Difference between temperature in Hawaii and in South Dakota is 12°F - (-58°F) = 12°F + 58°F = 70 °F
An advertiser goes to a printer and is charged $36 for 80 copies of one flyer and $46 for 242 copies of another flyer. The printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if xx is the number of copies made.
Answers
Answer:
ytre
Step-by-step explanation:
Find the sum of the geometric sequence.
1, 1/2, 1/4, 1/8, 1/16.
Answers
Answer:
2
Step-by-step explanation:
a1= 1
r= a2/a1
r= (1/2)/1
r=0.5
s= a1/1-r
s= 1/1-0.5
s=2
If 2L of solution needs to be administered through an IV over 24hours, then how many mililitres of solution needs to be provided per hour, rounded to two decimal places?
Answers
Answer:
83.33 milliliters
Step by step explanation:
2L = 2000 ml Change the liters to milliliters first
2000 ml : 24 hours
x ml : 1 hour
Next you cross multiply : 2000 × 1 hour = 2000 and 24 × x = 24x
Then you divide:
[tex]\frac{24x}{24} : \frac{2000}{24}[/tex]
x : 83.3333333...
When this is rounded off it is equal to 83.33
HOPE THIS HELPED
áp dụng quy tắc khai phương 1 tích hãy tính
Answers
Answer:
Please write out in english
Step-by-step explanation:
I cannot help unless you can translate.
please help answer question
Answers
Answer:
Mark me brainlist please please please please
Answer:
Step-by-step explanation:
Simply this rational expression.
URGENT! PICTURE INCLUDED
Answers
Answer:
35n/17r
Step-by-step explanation:
Please help me to find out the answer
Answers
9514 1404 393
Answer:
80.99 m
Step-by-step explanation:
The hypotenuse of the triangle is given, and the desired side length is the one adjacent to the angle marked. The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
Multiplying by the hypotenuse, we find ...
RY = (82 m)cos(9°) ≈ 80.99 m
On January 2, 2008, the American Idol website (www .americanidol) conducted an online poll that asked respondents which contestant they liked best among six former contestants. To become part of the sample, respondents simply clicked on a response. Of the 941,434 responses to this poll, 55% voted for Clay Aiken. We can conclude that _________________________________ .
a. the sample is too small.
b. a fraction of the millions of people who watched the TV show to draw any conclusion.
c. most Americans prefer Clay Aiken out of those former contestants.
d. the poll uses voluntary response, so the results tell us little about the population of all adults.
Answers
Answer:
Online Poll
We can conclude that
c. most Americans prefer Clay Aiken out of those former contestants.
Step-by-step explanation:
Sample responses received from the poll = 941,434
Proportion of voters for Clay Aiken = 55%
Computed proportion of voters for the other 5 contestants = 45% (100% - 55%)
This gives an average of 7.5% (45%/5) for the other 5 contestants.
Therefore, the conclusion is that "most Americans prefer Clay Aiken out of those former contestants" in the American Idol contest.
I need help finding what U stand for
Answers
Answer:
u = 18
Step-by-step explanation:
The two angles 3u and u+36 are equal so
3u = u+36
Subtract u from each side
3u -u = u+36-u
2u = 38
Divide by 2
2u/2 = 36/2
u = 18
Tuition. The tuition at a community college increased from $2,500 to $2,650 per semester. What was the percent of increase in the tuition?
Answers
Answer:
6 percent increase
Step-by-step explanation:
2650 divided by 2500 gives you 1.06 which means if 2500 is 100 percent 2650 would be 106 percent so the answer is a 6 percent increase
Answer:
6%
Step-by-step explanation:
another way of doing this type of calculation is...
NEW-OLD = 2650-2500 = 150 = .06 = 6%
OLD 2500 2500
4 + 1n(x-1)=3 solve for x
Answers
[tex]\\ \sf \longmapsto 4+10(x-1)=3[/tex]
[tex]\\ \sf \longmapsto 4+10x-10=3[/tex]
[tex]\\ \sf \longmapsto 10x-6=3[/tex]
[tex]\\ \sf \longmapsto 10x=3+6[/tex]
[tex]\\ \sf \longmapsto 10x=9[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{9}{10}[/tex]
Find the Antilog of 547.840
Answers
Answer:
It's impossible because the figure is greater than 10
Step-by-step explanation:
[tex]{ \boxed{ \bf{antilog \: of \: x = \frac{x}{ log} = {10}^{x} }}}[/tex]
Therefore:
[tex]{ \sf{anti(547.840) = {10}^{547.840} }} \\ { \tt{ \red{math \: error \: !}}}[/tex]
When is it appropriate to use the two-sample t-methods instead of the one sample t-methods? Choose the correct answer below. A. Use the two-sample t-methods when a sample was taken from each of two populations (i.e. two groups being compared) and the population standard deviations are not known. Use the one-sample t-methods when a sample was taken from one population. B. Use the two-sample t-methods when a random sample was not taken. Use the one-sample t-methods when a random sample was taken. C. Use the two-sample t-methods when the conditions for inference using the one-sample t-methods aren't satisfied. D. Use the two-sample t-methods when the population standard deviation is known. Use the one-sample t-methods when the population standard deviation is not known.
Answers
Answer:
A. Use the two-sample t-methods when a sample was taken from each of two populations (i.e. two groups being compared) and the population standard deviations are not known.
Step-by-step explanation:
T-distribution:
When the population standard deviation is not known, the t-distribution is used.
If a sample was taken from one population, we use the one-sample method, while if there is a comparison of two populations, the two-sample method is used, and thus, the correct answer is given by option A.
What is the conversion factor from meters to centimeters?
10,000 meters per centimeter
100 meters per centimeter
100 centimeters per meter
10,000 centimeters per meter
Answers
Answer: there are 100 centimeters in 1 meter. Meters to centimeters multiply by 100. Centimeters to meters divide by 100.
Step-by-step explanation:
Meters to centimeters multiply by 100
(10,000 m ) (100) = 1,000,000 cm.
(100 m) (100) = 10,000 cm.
Centimeters to meters divide by 100.
100 cm / 100 = 1 meter
10,000 cm /100 = 100 m
