Answers
Answer:
[tex]\displaystyle \frac{dy}{dx} \bigg| \limit_{(1, 4)} = 2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Coordinates (x, y)Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Implicit Differentiation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \sqrt{x} - \sqrt{y} = -1[/tex]
Point (1, 4)
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle x^{\frac{1}{2}} - y^{\frac{1}{2}} = -1[/tex][Implicit Differentiation] Basic Power Rule: [tex]\displaystyle \frac{1}{2}x^{\frac{1}{2} - 1} - \frac{1}{2}y^{\frac{1}{2} - 1}\frac{dy}{dx} = 0[/tex][Implicit Differentiation] Simplify Exponents: [tex]\displaystyle \frac{1}{2}x^{\frac{-1}{2}} - \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0[/tex][Implicit Differentiation] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0[/tex][Implicit Differentiation] Isolate y terms: [tex]\displaystyle -\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}[/tex][Implicit Differentiation] Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}[/tex][Implicit Differentiation] Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}[/tex]Step 3: Evaluate
Substitute in point [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{(4)^{\frac{1}{2}}}{(1)^{\frac{1}{2}}}[/tex]Exponents: [tex]\displaystyle \frac{dy}{dx} = \frac{2}{1}[/tex]Division: [tex]\displaystyle \frac{dy}{dx} = 2[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Implicit Differentiation
Book: College Calculus 10e
Related Questions
HELP!! i will vote brainlest answer
Answers
Answer:
D. 18
Step-by-step explanation:
The polygon given is a 5-sided polygon (pentagon). Sum of all interior angles of a 5-sided polygon = (n - 2) * 180°
= (5 - 2) * 180 = 540°
Therefore:
95° + (7x - 4)° + (3x + 23)° + (9x - 6)° + 90° = 540°
Solve for x
95 + 7x - 4 + 3x + 23 + 9x - 6 + 90 = 540
Add like terms
198 + 19x = 540
19x = 540 - 198
19x = 342
x = 342/19
x = 18
49:51
What does PIN stand for?
a.
Principal Investment Number
b.
Permission Initiating Number
c.
Percent Increase Number
d.
Personal Identification Number
Answers
Answer:
Personal Identification Number
Hope this helped and brainliest please
What is the value of the expression 12.25 + (-17.75)?
Answers
Answer:
-5.5
Step-by-step explanation:
7
T
S
U
The triangle STU has been drawn on to a centimetre grid.
Calculate the area of triangle STU *
(2 Points)
Enter your answer
Answers
Answer:
12 square units
Step-by-step explanation:
The area of a given figure is the measure of space occupied by the figure on a 2 dimensional plane.
Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
From the given grid, the following can be observed for triangle STU.
base SU = 6 units
height = 4 units
Thus,
area of triangle STU = [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 6 x 4
= 3 x 4
area of triangle STU = 12 square units
The required area of triangle STU is 12 square units.
The results that follow were obtained from an analysis of data obtained in a study to assess the relationship between percent increase in yield (Y) and base saturation (x1, pounds/acre), phosphate saturation (x2, BEC%), and soil pH (x3). Fifteen responses were analyzed in the study. The least-squares equation and other useful information follow.
y^=38.83-0.0092x1-0.92x2-11.56x3, Syy=10965.46, SSE=1107.01
a. Is there sufficient evidence that, with all independent variables in the model, β2 < 0? Test at the α = .05 level of significance.
b. Give a 95% confidence interval for the mean percent increase in yield if x1 = 914, x2 = 65 and x3 = 6.
Answers
Answer:
a. yes there is enough evidence
B. -22.83, 102.79
Step-by-step explanation:
H0: B2 >= 0
H1: B2 < 0
Alpha = 0.05
T critical is calculated to be -1.79
If t is less than -1.79 we reject the null hypothesis
Test statistic
S = √1107.01/15-3-1
= 10.032
T stat = -0.92 - 0/10.032√0.00081
= -3.222
-3.222 is less than -1.79
So we Reject the null hypothesis and conclude that enough evidence exists that B2<0
B. At 95% confidence
38.83 - 0.0092x1 - 0.92x2 + 11.56x3
= 38.83 - 0.0092x914 - 0.92x65 + 11.56x6
= 38.83 - 8.4088 - 59.8 + 69.36
= 39.98
39.98-2.2*28.55,39.85+2.2*28.55
= 39.98 - 62.81, 39.98 + 62.81
= -22.83, 102.79
A prism has a length of 8 meters, height of 14 meters, and width of 6 meters. What is the volume of the prism? m3
Answers
Answer:
672 m^3
Step-by-step explanation:
The formula to find the volume of a prism is V = l x w x h, where l is length, w is width, and h is height. You are given the length, width, and height in the problem so you just plug it into the formula.
V = 8 x 6 x 14
After multiplying all three numbers together, you should get the answer 672 m^3.
Please answer I need help
Answers
I think the inequality is right
The graph of f(x) = 2^x + 4 shifts five units to the right when it is replaced with the graph of f(x) = 2^x - k. what is the value of k?
A. 5
B. -1
C. 1
D. 4
Answers
==============================================================
Work Shown:
I'm assuming you meant to write [tex]f(x) = 2^{x+4}[/tex] where all of the "x+4" is the exponent.
If we shift f(x) 5 units to the right to end up with g(x), then,
[tex]g(x) = f(x-5)\\\\g(x) = 2^{x-5+4}\\\\g(x) = 2^{x-1}\\\\[/tex]
In the second step, I replaced every copy of x with x-5 so that I could apply the translation of 5 units to the right.
The exponent for g(x) is x-1, which matches up with x-k. We see that k = 1.
The height of a standard kitchen
counter top would be about
Hurry please
A 1 foot
B 1yard
C 1 mile
D1inch
Do not need explanation
Answers
Match each statement (term) with its value in relation to 0 (definition)
Match
Term
Definition
A building is 35 feet tall.
A) -35
The scuba diver was 35 feet below sea level.
B) 2.3
The basement is 7.6 feet below ground.
C) -23
Oliver owes his sister $23.
D) 35
Erica jumped 2.3 feet above ground.
E) -7.6
Answers
Answer: D. 35
The scuba diver was 35 feet below sea level.
Answer: A. -35
The basement is 7.6 feet below ground
Answer: E. -7.6
Oliver owes his sister $23
Answer: C. -23
Erica jumped 2.3 feet above ground.
Answer: B. 2.3
convert 3 hrs 20 min
into fraction
Answers
Answer:
Step-by-step explanation:
0.050/0.333
Answer:
3 and 1/3 or 10/3
Step-by-step explanation:
5 = y + x and 2y + x = 7 Answer Fast please.
Answers
Answer:
sorry i dont know it
Step-by-step explanation:
sorry
Can someone please give me step by step using pemdas I will give I brilliant
Answers
Answer: 24
Step-by-step explanation: so you calculate everything in the parenthesis fist so you do (5-1+3) to (4+3) then you do (4+3=7)
so this is how your equation is going to look 10+4÷2×7 then your going to do 4 divied by 2=2 then your going to do 2*7=14 and 14+10=24
STEP ONE- 10+4÷2(4+3)
STEP TWO- 10+4÷2×7
STEP THREE-10+2×7
STEP FOUR-10+14
ANSWER is 24
hope this helps :)
Write two ordered pairs that are solutions.
Answers
Answer:
(-1,-4)
(0,-2)
The answer is
(-1,-4)
(0,-2)
This is correct because im not in 2nd grade
Volume of a cone is 48 pi and have a radius of 8 what is the height
Answers
Answer:
Step-by-step explanation:
the answer is in the pic open it
hope it help mark me as a brill please
mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answers
Answer:
interior
Step-by-step explanation:
exterior would be located outside the triangle.(10)
vertex is the point of the connected lines (12)
Jodie ran at an average speed of 8 km/h for 45 minutes.
How far did she run in km?
Answers
Answer:
6 km.
Step-by-step explanation:
A quadrilateral has angle measures of 50°, 72°, and 78°. What is the measure of the fourth angle?
160°
60°
50°
100°
Answers
Answer:
160°
Step-by-step explanation:
Quadrilateral's angles add up to 360 degrees.
So:
x = fourth angle measure (unknown currently)
50° + 72° + 78° + x = 360°
200° + x = 360°
x = 160°
Jordan typed 40 words a minute and he spends 1 minute typing a ending how many minute did it take him to write a sentence
i also heard that you can get points for answering questions.
Answers
Answer:
02920
Step-by-step explanation:
92823
Keiko, Dale, and Tony sent a total of 95 text messages during the weekend. Dale sent 7 fewer messages than Kelko. Tony sent 4 times as many messages as
Keiko. How many messages did they each send?
Answers
Answer:
Keiko sent 17 messages, Dale sent 10 messages, and Tony sent 68 messages
Step-by-step explanation:
Let x represent the number of messages that Keiko sent.
Since Dale sent 7 less than Keiko, his number can be represented by x - 7
Since Tony sent 4 times as many as Keiko, his number can be represented by 4x
Using these variables, create an equation:
(x) + (x - 7) + (4x) = 95
Add like terms and solve for x:
6x - 7 = 95
6x = 102
x = 17
So, Keiko sent 17 messages.
Subtract 7 from this to find how many Dale sent:
17 - 7
= 10
Multiply it by 4 to find how many Tony sent:
17(4)
= 68
So, Keiko sent 17 messages, Dale sent 10 messages, and Tony sent 68 messages
Hurry please!!!Assuming that each worker used the standard deduction and that none of the workers had any additional adjustments, which worker had the lowest taxable income last year?
Number of exemptions at $3650 each
Esther has 2
Frank has 2
Macy has 1
Penny has 3
Answers
Answer:
Frank
Step-by-step explanation:
The worker that had the lowest taxable income last year was Frank
What is Tax?This refers to the deductions that are made based on income and earnings where a certain percentage is remitted to the government.
Hence, we can see that based on the gross income and the standard deduction that was made between Esther, Frank, Macy, and Penny, and the exception of %$3,650, Frank had the lowest taxable income last year
Read more about taxable incomes here:
https://brainly.com/question/26316390
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Maya earned $104,000 last year. If the first $40,000 is taxed at 12% and income above that is taxed at
18%, how much does Maya owe in tax?
Answers
Answer:
16,320
Step-by-step explanation:
There are $18,720 Maya owe in tax.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Maya earned $104,000 last year.
The first $40,000 is taxed at 12% and income above that is taxed at 18%.
Hence, Tax pay by Maya is,
⇒ 18% of 104,000
⇒ 18/100 × $104,000
⇒ $18,720
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ6
help me please:) anyways have a good day
Answers
Answer: it’s the last one
Step-by-step explanation:
will give the BRAINLIEST pls helpppppp
Answers
Answer:
pretty sure youre right kiddo
Please help, PhotoMath isn’t helping and I don’t understand
Answers
Answer:
Option B
Step-by-step explanation:
As here,
In all the options processes in 3rd step .
As the bases are same exponents get added.
And in Option B 3rd step it has been correctly done form of,
[tex] { ({2}^{ \frac{1}{4} } )}^{4} = 4[/tex]
Is correct simplification.
outline three methods of sampling
Answers
Answer: See explanation
Step-by-step explanation:
The sampling methods include:
1. Simple random sampling: Here, the individuals in the population have an equal chance of being selected as the selection is done randomly and anyone can be picked from the population
2. Systematic sampling: This is when the selection of the individuals is done at regular intervals. For example from the population, every 10th person might be picked.
3. Stratified sampling: Here, the total population is first divided into a smaller group called the strata before the sampling is done.
4. Clustered sampling: Here, the sampling unit is the subgroups of the population and not the individuals.
203% of what number is 146.16
Answers
Answer:
72
Step-by-step explanation:
Since 203% is 2.03 in decimal form we can write an equation that looks like:
2.03x=146.16 (divide both sides by 2.03)
x=72
Answer:
72
Step-by-step explanation:
Call the unknown number (x), set up a proportion to model the situation;
[tex]\frac{value}{unknown}=\frac{percent}{100}[/tex]
Substitute
[tex]\frac{146.16}{x}=\frac{203}{100}[/tex]
Cross products,
[tex](146.16)(100)=(203)(x)\\\\14616=203x\\[/tex]
Inverse operations,
[tex]14616=203x\\/203\\\\72 = x[/tex]
...........................................................
Answers
Answer:
Top is A bottom is B. ........
please answer!! will give brainliest!
Answers
Answer:
Q1=38
Q3=88
IQR=50
Step-by-step explanation:
would this be a cone??
Answers
no that would NOT be a cone
That would not be a cone.