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
1. Allen had 12 goals on the season. If he
played in 8 games, how many goals did
he average per game? Round your answer
to the nearest hundredth.
A. 0.67
B. 1.5
C. 2.3
D. 3.2
WILL MARK Brainlyest
Answers
Answer:
B. 1.5
Step-by-step explanation:
12/8 = 1.5
6x + 4 = X + 24
Can some one plz help me with this problem
Answers
Answer:
x=4
Step-by-step explanation:
you have to get x on one side so x=4
Answer:
x=4
Step-by-step explanation:
combine the like terms beside eachother so it would be
6x-x=24-4
5x=20
then move the 5 and divide
x=20/5
x=4
Help please this is urgent
Answers
Hope this helps!!!!
Answer:
25 - 5a
Step-by-step explanation:
5(5 - a)
25 - 5a
Hope this helps, thank you !!
how to Evaluate the expression, given functions f and g: f(x) = 3x - 2, g(x) = 7 – x^2. 3f(1) – 2g(-2)
Answers
3 7/8- 3/8 I really need help!
Answers
Answer:
[tex]3\frac{1}{2}[/tex]
Step-by-step explanation:
3 1/2
It would get you 3 4/8 then you simplify it to 3 1/2
James bought a PS5 game. The original price was $90, but it
was on sale for 30% off. What was the sale price?
Please help!!
Answers
Answer:
The correct answer is 27
Step-by-step explanation:
i took the test and its right please amrk brainliest i need it ;c
Answer:
63
Step-by-step explanation:
That's a cheap PS5.
are 4/5 and 1/2 equivalent explain
Answers
Answer:
They are not
Step-by-step explanation:
4/5 cannot be simplified, plus 1/2 indicates half of a fraction but 4/5 is not half if a fraction, therefore they are not equivalent.
3x + 1/3y=12
2y=18x+72
Show all work
A no solution
B one solution
C infinity solutions
Answers
Answer:
B one solution
Step-by-step explanation:
3x + 1/3y=12
2y=18x+72; y = 18x/2 +72/2; y =9x+36
3x + 1/3y=12
multiply all through by 3
9x + y = 36
9x + 9x+36 = 36
18x =36-36= 0
x= 0/18 = 0
y =9x+36
y = 9(0) +36 = 0+36= 36
Liam opened a savings account with a $400 deposit and a simple interest rate of 7.5%. If the balance of the account is now $670 and there are no deposits or withdraws, how long ago did he open the account?
Answers
Answer:
If he deposited weekly, he would be depositing 9 dollars each week.
Step-by-step explanation:
Just thank me later and click the crown at the top of this answer if it helped ;)
which equation best matches the graph ?
Answers
Suppose f(x)=x+2. Find the graph of f(1/3x)
Answers
Answer:
f(x)=x+2.
f(1/3x)=1/3 x+2=(x+6)/3or x/3+2
Answer:
graph 3
Step-by-step explanation:
Is $20.29 with $4 dollar shipping more, or is $23.09 with 3 dollar shipping more? Help please, ASAP! :(
Answers
Answer:
23.09 w/ 3 dollar shipping is more.
Step-by-step explanation:
20.29 + 4 = 24.29
23.09 + 3 = 26.09
hope this helps :)
Answer:
23.09 dollars and 3 dollar shipping is more than 20.29 with 4 dollar shipping
Step-by-step explanation:
if you add the shipping and price together 23.09 dollars and 3 dollar shipping is 26.09 in total
And the 20.29 with 4 dollar shipping is 24.29 in total
and 26.09 is greater than 24.29, so 23.09 dollars and 3 dollar shipping is more than 20.29 with 4 dollar shipping
2y = 2x = 8 y = x + 4
Answers
Answer:
I love algebra anyways
the ans is in the picture with the steps how i got it
(hope that helps can i plz have brainlist it will make my day :D hehe)
Step-by-step explanation:
Find an equation in point slope form for the line haveing the slope m=-3 and containing the point (6 7)
Answers
Answer:
7-y=-3(6-x)
Step-by-step explanation:
Point slope form:
[tex]y-y_{1} = m(x-x_{1} )[/tex]Substitute y in for 7. Substitute x in for 6. Substitute m in for -3.
7-y=-3(6-x)What percent is 45 out of 70
I’m so sorry to bother you guys I have been stuck on this problem
Answers
plssssss someone help pls pls pls i dont get this look
Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) − 160°. Find m∠Y
Answers
Answer:
I think the answer is 50.
Step-by-step explanation:
Y + S = 90
S = 4 (Y) - 160
160 = 4 (Y)
Y = 40
90 - 40 = 50
Hope it's correct and helps!
the diameter of a circle is 7 m. find its area and perimeter.Answer fast!!!!!
Answers
Answer:
Area≈38.48m²
perimeter≈43.98
Ariel has $181 saved towards the purchase price of a laptop. The laptop she wants to purchase cost $599. Ariel earns $9.50 an hour as a lifeguard. (I have to write an in…
Answers
¿*=£×**€×¿¿==£÷€=4÷54
Plz I need help this is due at 7:10
Answers
Answer:
8units²
Step-by-step explanation:
Area of the trapezoid = 1/2(a+b)h
a and b are the opposite sides
h is the height
Take a square as 1 unit
a = 1 unit
b = 3 units
height h = 4 units
Substitute
A = 1/2(1+3)*4
A = 1/2 * 4 * 4
A = 16/2
A = 8units²
Hence the area of the trapezoid is 8units²
8. Paris used a semicircle, a rectangle, and a right triangle to form the figure shown.
Which is the best estimate of the area of the figure in square centimeters?
F 100 cm2
G 88 cm2
H 50 cm2
J 74 cm2
Answers
= option J
area of figure = 1/2 × 6× 4 + 8×6 + 3.14× 9/2
= 12+ 48 + 3.14× 4.5
= 60+ 14.13
= 74.13 cm²
option J
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you.
An angle turns through 60 one degree angles. What is the measure of the angle?
Answers
9514 1404 393
Answer:
60°
Step-by-step explanation:
60 × 1° = 60°
The angle measure is 60°.
What is the product of 148x27
Answers
Answer:
3996 :)
Step-by-step explanation:
Answer:
3,996
Step-by-step explanation:
Hope this right.but if it's not,im so sorry
Find the equation of a line which has:
slope of -2 and
crosses the y-axis at 5
in slope-intercept form
Answers
Answer:
y = -2x + 5
Step-by-step explanation:
Recall that slope-intercept form is y = mx + b where m is the slope and b is the y intercept
In this case our slope is m = -2
and, line crosses y-axis at 5 which is b = 5
thus, y = -2x + 5
What is the answer for (1-2g + 4h)•5?
Answers
Answer:
-10g +24 + 5 hope this helps
Step-by-step explanation:
1-2g+20h
You have to cancel out the factors
what is the mystery number 1,2,4,8,16,32
Answers
Answer:
64
2×32=64............
Solve this linear equation:
x/2 + 3/4 = x/8
Answers
Number of solutions found: 1
x1=-2
A fern grows 7/9 of a foot per year. How much will it grow in 5 years
Answers
Answer:
46.6 inches in 5 years
Step-by-step explanation:
Answer: 46.6 inches in five years
Step-by-step explanation:
SO you wanna multiply 7.9 by 5 to get your grand total
An infinite number of ratios are equivalent to 3:8. How
can that be possible, when the multiplication table only
goes to 9?
Answers
Answer:
See below, please!
Step-by-step explanation:
There are infinite number of ratios equivalent to 3:8 because both numbers can be multiplied by a common number or divided by a common number.
For example, 9:24 would still be equivalent to 3:8 because the common number in our case is 3. See what I mean?
Hope this helped!
This is classwork and i don't understand it at all PLEASE HELP
Answers
Answer:
The independent variable is the number of cars
the band washes and the dependent is the number of money they earn
Step-by-step explanation:
y = -2x + 3
4x - 5y = 13
Answers
Answer:
letters do not belong in math
Step-by-step explanation:
1=1-2=3