APPLICATION
3. Use the first principle of derivatives to determine the equation of tangent to the
curve y = 1/radical7x at
x = 5
Answers
Answer:
[tex]\displaystyle y - \frac{\sqrt{35}}{35} = \frac{-\sqrt{35}}{350}(x - 5)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Coordinates (x, y)
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinatey₁ - y coordinatem - slopeAlgebra II
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
The definition of a derivative is the slope of the tangent line.Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Chain Rule: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{\sqrt{7x}} \\x = 5[/tex]
Step 2: Differentiate
[Function] Rewrite: [tex]\displaystyle y = \frac{1}{(7x)^\frac{1}{2}}[/tex][Function] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y = (7x)^{-\frac{1}{2}}[/tex][Derivative] Chain Rule [Function]: [tex]\displaystyle y' = \frac{-1}{2}(7x)^{-\frac{1}{2} - 1} \cdot \frac{d}{dx}[7x][/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{-1}{2}(7x)^{-\frac{3}{2}} \cdot \frac{d}{dx}[7x][/tex][Derivative] Basic Power Rule: [tex]\displaystyle y' = \frac{-1}{2}(7x)^{-\frac{3}{2}} \cdot 1 \cdot 7x^{1 - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{-7}{2}(7x)^{-\frac{3}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{-7}{2(7x)^{\frac{3}{2}}}[/tex]Step 3: Find Slope of Tangent Line
Substitute in x [Derivative]: [tex]\displaystyle y'(5) = \frac{-7}{2[7(5)]^{\frac{3}{2}}}[/tex][Tangent Slope] [Brackets] Multiply: [tex]\displaystyle y'(5) = \frac{-7}{2[35]^{\frac{3}{2}}}[/tex][Tangent Slope] Evaluate exponents: [tex]\displaystyle y'(5) = \frac{-7}{2(35\sqrt{35})}[/tex][Tangent Slope] Multiply: [tex]\displaystyle y'(5) = \frac{-7}{70\sqrt{35}}[/tex][Tangent Slope] Simplify: [tex]\displaystyle y'(5) = \frac{-1}{10\sqrt{35}}[/tex][Tangent Slope] Rationalize: [tex]\displaystyle y'(5) = \frac{-\sqrt{35}}{350}[/tex]Step 4: Find Tangent Line Equation
Point (x, y)
Substitute in x [Function]: [tex]\displaystyle y(5) = \frac{1}{\sqrt{7(5)}}[/tex][Function] [√Radical] Multiply: [tex]\displaystyle y(5) = \frac{1}{\sqrt{35}}[/tex][Function] Rationalize: [tex]\displaystyle y(5) = \frac{\sqrt{35}}{35}[/tex]Define point: [tex]\displaystyle (5, \frac{\sqrt{35}}{35})[/tex]Equation
Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - \frac{\sqrt{35}}{35} = \frac{-\sqrt{35}}{350}(x - 5)[/tex]Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e
Related Questions
Find the number that makes the ratio equivalent to 12:1.
?:6
Answers
A group of researchers was interested in the effect of music on the behavior of dogs. Specifcally, they wanted to
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the following study on a group of 400 Jack Russell Terriers.
Every day for 4 months, the researchers would play Beethoven's Moonlight Sonata for 1 hour occurring
randomly between 9 a.m. and 12 p.m. During the entire 3 hours observers would record the times in which
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Is the study appropriate for the statistical questions it's supposed to answer?
Answers
Answer:
Step-by-step explanation:
The first part of the question would be: B) Experiment
The second part would be: C) No, because the sample the study used isn't representative of all dogs.
The independent variable is a variable that represents a quantity being manipulated in an experiment, the control group will be the group that did not hear the music, and the experimental group the group that heard the song.
What is Independent variable?An independent variable is a variable that represents a quantity being manipulated in an experiment.
xxx is often the variable used to represent the independent variable in an equation.
Dependent variables
A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.
yyy is often the variable used to represent the dependent variable in an equation.
Confounding variable
It is a variable that influences both the dependent variable and the independent variable, causing a spurious association. The confounding variable is a causal concept and as such cannot be described in terms of correlations or associations.
With this information, we can conclude that, The control group are people who have not heard the music, the experimental group are those who heard the music, and the hypothesis is that music can change people's heart rate.
Learn more about Independent variables in brainly.com/question/900187
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bader ginsbury is 5 feet and 1 inch. how tall is she in inches?
Answers
Answer: 61 inches
Step-by-step explanation:
Answer:
61 inches
Step-by-step explanation:
units digit in (126^2)
Answers
Answer:
The unit digit of (126²) is 6
Answer:
That would be 6.
Step-by-step explanation:
Here it is.
What is the greatest common factor (GCF) of 24 and 42?
Answers
Answer:
6
Step-by-step explanation:
. The industrial output of an automobile factory increases by 5% of what it had been in the beginning of
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Answers
If the factor increases output by 5% yearly than the end output will be 92,610
Write the missing decimal so that each pair adds to 1/2 + ...= 1
Answers
Answer:
0.5
Step-by-step explanation:
1/2 + 0.5 = 1
6 R
;\: ; _6
-2
4 6
4 2
4
Help❗️❗️
Answers
Answer:
drop the 0 then add the 0 o. the top or I think
what is |-2|+|4| help ill do anything!
Answers
Answer:
6
Step-by-step explanation:
The absolute value of -2 is 2 because that is it's distance from 0 on a number line.
Then do the math. 2 + 4 = 6
Answer: 6X HOPE THIS HELPS!
| − 2 | + | 4 |
|-2|+|4|
∣−2∣+∣4∣
Solve
1
Find the absolute value
| − 2 + | 4 |
2 +| 4 | 2
Find the absolute value
Add the numbers
Solution
6
Step-by-step explanation:
I really really really really really really really really need help please help
Answers
Answer:
129 degrees
Step-by-step explanation:
One circle is 360 degrees, so add up all the degrees, including x:
35 + 55 + 141 + x = 360
231 + x = 360
x = 360 - 231
x = 129 degrees
solution of 4x=400 lies between two consective integers
Answers
Answer:
100
Step-by-step explanation:
Given the equation 4x = 400, we are to find the value o x
4x = 400
Divide both sides by 4
4x/4 = 400/4
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Hence the value of x is 100
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Answer:
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Step-by-step explanation:
1/6+1/6+1/6+1/6=4/6
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56÷37?
Answers
Answer:
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Step-by-step explanation:
A bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The
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If necessary, round your answer to the nearest tenth.
Answers
Answer:
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Step-by-step explanation:
10
Which statement is true?
O A.
A triangle can be congruent to a square.
ов.
A rectangle can be congruent to a square.
C.
All circles are congruent.
OD
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Answers
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A certain standardized tests math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 105. Complete part (a) through (c). (a) what percentage of standardized test scores is between 215 and 845. (b) what percentage of standardized test scores is less than 215 or greater than 845. (c) what percentage of standardized test scores is greater than 740.
Answers
boole summation formula used in real life
Answers
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Answers
Answer:
x = 5/4 OR 1 1/4
Answer:
x = 5/4 or 1 1/4
Step-by-step explanation:
X-1/2=3/4
Add 1/2 to each side
X-1/2+1/2=3/4+1/2
x = 3/4 +1/2
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x = 1 1/4
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Answers
Step-by-step explanation:
8.4 - 8.41 - 8.485 - 8.538 - 8.55 - 8.566
Answer: least to greatest
8.4, 8.41, 8.485, 8.538, 8.55, 8.566
least to greatest
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Answer:
1. are
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Step-by-step explanation:
Imao
Step-by-step explanation:
1) are
2)like
3)love
4)jump
5)run
6)help
7)wears
8)spin
9)play
10)are
Hope you guys have a nice day!♡
Edgar earns $13 for each hour of yard work. How many hours in all will it take Edgar to earn $39? hours
Answers
HELP ITS LIKE AN IMPOSIBLE RIDDLE OF CONFUSION AND STRESS AND MADNESS IV BEEN STUCK ON FOR 7 YEARS, I WILL GIVE BRAINLIEST...5 POINTS...A THANKYOU, AND A 5 STARS PLS HELPPPPPPPPPP
what 1 + 1 :P
Answers
Answer:
2
Step-by-step explanation:
Answer:
The answer is 2
Step-by-step explanation:
1 + 1 is 2
HELP QUICK EASY Pi WORK PLEASE HELP QUICK
Answers
Answer:
3.998 km?
not exactly sure but good luck
Step-by-step explanation:
answer the following by setting up and following as a proporition
I need it quick
at a bad wolfs concert there are fifteen males for every twenty three people. if 23,675 people attend the concert how man males attend the concert?
Answers
£2,300 is invested for 4 years at 5% per year simple interest work out the total interest
Answers
Answer:
£460
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
then, solving our equation
I = 2300 × 0.05 × 4 = 460
I = £ 460.00
The simple interest accumulated
on a principal of £ 2,300.00
at a rate of 5% per year
for 4 years is £ 460.00.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer: 27°
Step-by-step explanation: Here, we're asked to find the missing angle measure in the triangle shown which is represented by the variable x.
To find the value of x, remember that the sum of the
measures of the angles in a triangle is 180°
So we can setup the equation 63 + 90 + x = 180.
Remember that a box indicates a 90° angle.
Now to solve for x, let's first simplify on the left side of the equation.
63 + 90 is 153 so we have 153 + x = 180.
Now to get x by itself, we subtract 153 from both sides of the equation.
On the left side of the equation, 153 - 153 cancels out and we have x
and on the right side of the equation, 180 - 153 is 27.
This means that the missing angle in the triangle is 27°.
find the slope of the line going through the points (3,2) and (8,27)
Answers
Answer:
5
Step-by-step explanation:
y²-y¹/x²-x¹
Where y²=27
y¹=2
x²=8
x¹=3
= 27-2/8-3
=5
Don’t use for points or I’ll take it back
Help
Answers
Answer:
answer is 27 degrees
Step-by-step explanation:
first of all complementary angles add up to 90 degrees and you were given one angle
63 + x = 90
63-63 +x =90 -63
x = 27
hope that helps
What is 0.7151 as a fraction?
Answers
Answer:
i think its this
Step-by-step explanation:
*look at le picture
Ming traveled to the town hall and back. The trip there took two hours and the trip back took three hours. She averaged 10 mph faster on the trip there than on the return trip. Find Ming's average speed on the outbound trip.
Answers
Answer:30mph
Step-by-step explanation:
We know that the ratio must be 2:3. We know that 30 is 10 more than 20, which also fits into the ratio, so 30mph is the answer.