5. (3.5pts) Given the equation y = y²x+2 cos(x) find . Show each step of your work.
dx
Answers
Answer:
[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=y^2x+2 \cos(x)[/tex]
To find the derivative of the given equation, use implicit differentiation.
Add d/dx in front of each term:
[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x+\dfrac{d}{dx}\:2 \cos(x)[/tex]
Differentiate terms in x only (and constant terms) with respect to x:
[tex]\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]
Use the chain rule to differentiate terms in y only:
(in practice this means to differentiate with respect to y then place dy/dx on the end)
[tex]\dfrac{dy}{dx}\: =\dfrac{d}{dx}\:y^2x-2 \sin(x)[/tex]
Use the product rule on the term in x and y:
[tex]\textsf{let }u=y^2 \implies \dfrac{du}{dx}=2y \dfrac{dy}{dx}[/tex]
[tex]\textsf{let }v=x \implies \dfrac{dv}{dx}=1[/tex]
[tex]\implies u\dfrac{dv}{dx}+v\dfrac{du}{dx}=y^2+2xy \dfrac{dy}{dx}[/tex]
Therefore:
[tex]\dfrac{dy}{dx} =y^2+2xy \dfrac{dy}{dx}-2 \sin(x)[/tex]
Rearrange to make dy/dx the subject:
[tex]\dfrac{dy}{dx}-2xy \dfrac{dy}{dx} =y^2-2 \sin(x)[/tex]
[tex]\dfrac{dy}{dx}(1-2xy)=y^2-2 \sin(x)[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}[/tex]
Related Questions
Use the digits 1-9 without repeating, to create two prisms with the same volume
Answers
Two prisms with the same volume are rectangular prisms of the dimensions 1 by 4 by 9 and 2 by 3 by 6
How to create the prisms?To do this, we start by determining the type of prism to create.
Assume that we want to create a rectangular prism.
The volume of a rectangular prism is:
Volume = Length * Width * Height
Using the digits 1 - 9, we have:
Prism 1
Length = 1
Width = 4
Height = 9
The volume is
Volume = 1 * 4 * 9 = 36
This means that the second prism must have a volume of 36.
Using the digits 1 - 9, we have:
Prism 2
Length = 2
Width = 3
Height = 6
The volume is
Volume = 2 * 3 * 6 = 36
Notice that the digits are not repeated.
Hence, two prisms with the same volume are rectangular prisms of the dimensions 1 by 4 by 9 and 2 by 3 by 6
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opposite of expanded form
Answers
Answer:
factored form
Step-by-step explanation:
example
(x + 2)(x + 3) ← is an expression in factored form
= x² + 5x + 6 ← in expanded form
Answer:
factored formStep-by-step explanation:
Factored form is opposite of expanded form.
More info:-
Expanded form:
[tex]\sf{5(x+7)=5x+35}[/tex]Factored form:
[tex]\sf{5x+35=5(x+7)}[/tex]If the diameter of a youth baseball is 2. 8 inches and the diameter of an adult softball is 3. 8 inches, what is the approximate difference in their volumes? use 3. 14 for pi. round to the nearest tenth. recall the formula sphere volume = four-thirds pi r cubed. 1. 0 cubic inch 17. 2 cubic inches 40. 2 cubic inches 137. 8 cubic inches.
Answers
The approximate difference in their volumes is 17.2 cubic inches
How to determine the difference in the volume?The given parameters are:
Diameter, d = 2.8
Diameter, D = 3.8
The radii are the half of the diameter.
So, we have:
r = 1.4
R = 1.9
The volume of the balls is then calculated using:
[tex]V = \frac{4}{3}\pi r^3[/tex]
The difference is then represented as:
[tex]D = \frac{4}{3}\pi (R^3 - r^3)[/tex]
Substitute known values
[tex]D = \frac{4}{3}* 3.14* (1.9^3 - 1.4^3)[/tex]
Evaluate
D = 17.2
Hence, the approximate difference in their volumes is 17.2 cubic inches
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Which function is increasing and has a domain of (1, )?
A. -log(x − 2) + 1 B. -log(x − 1) + 2 C. log(x − 1) + 2 D. log(x − 2) + 1
Answers
Answer:
B . it was right when I picked it
Mr. Rodrigo pours himself a glass of orange juice every morning. Yesterday he drank 5/6 of his glass. Today he drank 7/12 of his glass. On which day did drink more
Answers
Exp: if you make the denominators equal, 5/6 becomes 10/12 which is more than 7/12
A piece of card, 1200 cm² in area, will make a tube 13 cm long. How long is a similar
tube made from a similar piece of card with an area of 500 cm³?
Answers
The length of the similar tube will be 5041 cm.
What is the area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Given that:-
A piece of card, 1200 cm² in area, will make a tube 13 cm long. How long is a similar?Tube made from a similar piece of card with an area of 500square centimetres.The radius of the first tube will be calculated as:-
1200 = 2πr ( 13 )
r = 12 / 2π x 113
r = 14.7 cm
Now the length of the second tube will be:-
500 = 2π x 14.7 x L
L = 500 / 2π x 14.7
L = 5.41 cm.
Therefore the length of a similar tube will be 5041 cm.
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help solve these algebraic fractions please with explanation would be great <3
Answers
Answer:
7/ Ans;
[tex] \frac{x + 2}{ x + 4} \div \frac{ {x }^{2} - 2x - 8}{ {x}^{2} + 2x - 8} \\ \\ \\ \frac{x + 2}{x + 4} \times \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 2x - 8} \\ \\ \\ \frac{x + 2}{x + 4} \times \frac{(x - 2)(x + 4)}{(x - 4)(x + 2)} \\ \\ \\ =1 \times \frac{x - 2}{x - 4} \\ \\ \\ = \frac{x - 2}{x - 4} [/tex]
___o__o__
9/Ans;
[tex] \frac{ {x}^{2} - 9}{ {x}^{2} - 6x + 9} \div \frac{x + 4}{x - 3} \\ \\ \frac{ {x}^{2} - 9 }{ {x}^{2} - 6x + 9} \times \frac{x - 3}{x + 4} \\ \\ \\ \frac{(x + 3)(x - 3)}{(x - 3)(x - 3)} \times \frac{x - 3}{x + 4} \\ \\ \\ = \frac{(x + 3)}{1} \times \frac{1}{(x + 4)} \\ \\ \\ = \frac{x + 3}{x + 4} [/tex]
__o__o__
In the two questions, we first replace the division with multiplication with flipping the fraction after the division sign, secondly we analyze any equation that needs analysis to simplify it, thirdly, to simplify the fraction by deleting the numerator and the similar denominator .
Sean counts by 2s from 15 to 35. which number does Sean count?
HELP ME ASAP!!!
Answers
The number that Sean counts is 27.
What number does Sean count?
When Sean counts by 2s from 15 to 35, he would be counting odd numbers. An odd number is a number that cannot be perfectly divided by 2. There would always be a remainder.
Here are the options:
13
27
16
22
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(Refer to the attached image)
Answers
Answer:
missing side: 133 cm
Explanation:
Provided 2 length sides and one angle also need to find one missing side.
So, use cosine rule:
⇒ a² = b² + c² - 2bc cos(A)
Insert values
⇒ g² = 166² + 147² - 2(166)(147) cos(50)
⇒ g² = 17794.3935
⇒ g = √17794.3935
⇒ g = 133.3956
⇒ g = 133 (rounded to nearest whole number)
the hcf of 12x^2-4xy+15x-5y
Answers
Answer:
-1
Step-by-step explanation:
We have 2 letters, x and y. what letter is in all of them? none of them. that means the HCF can't contain a letter. let's take away the letters, we have 12, -4, 15, -5. Since -5 is a prime number. the answer is -1
Pleaseeeee helpppppp
Please help me evaluate this in terms of sin/cos/sec etc. (trigonometric form)
tan2θ-(1-tan2θ)=?
Answers
The evaluation is (2sin2∅-cos2∅)sec2∅.
What are trigonometric functions?Trigonometric functions are functions used to relate the sides of a triangle with its angles.
Analysis:
2tan2∅ -(1- tan2∅)
2tan2∅ - 1 + tan2∅
3tan2∅ - 1
3([tex]\frac{sin2\alpha }{cos2\alpha }[/tex]) - 1
(3sin2∅/cos2∅) - 1
(3sin2∅ - cos2∅)/cos2∅
but 1/cos2∅ = sec2∅
(3sin2∅ - cos2∅)/sec2∅
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Hunter picked three quarts of blueberries. some of the blueberries are ripe and some are not ripe. If he takes one blueberry from the basket without looking, what are the outcomes
Answers
Answer:
Berries with any blush of red are not ripe, yet may ripen further once picked if kept at room temperature. That said though, you really want to ...
A map shows that the vertices of a backyard are W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) . The coordinates are measured in feet. The line segment XZ separates the backyard into a lawn and a garden. The area of the lawn is greater than the area of the garden. How many times larger is the lawn than the garden?
Answers
The area of the lawn is 2.5 times greater than the area of the garden.
What is Heron's formula in math?Heron's formula for finding the area of a triangle in terms of the lengths of its sides.
In symbols, if a, b, and c are the lengths of the sides: Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given vertices W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) of a backyard,
We have to find distances WX, XY, YZ, ZW and XZ:
1. WX= √(-100+100)²+(0+70)²
=√0+4900
=70
2. XY= √(0+100)²+(0-0)²
=100 units.
3. YZ= √(-60-0)²+(-70-0)²
=√3600+4900
= √8500= 10√85
4. ZW= √(-60+100)²+(-70+70)²
=√40²+0
=40 units
5. XZ= √(-60+100)²+(-70+0)²
=√40²+70²
=√6500=10√65
Then:
1. the area of WXZ
[tex]\sqrt{(70+40+10\sqrt{65}) /2 * ({70+40+10\sqrt{65}) /2 -70* {(70+40+10\sqrt{65}) /2 -40[/tex]*[tex]\sqrt{(70+40+10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=1400 feet²
Area of XYZ= [tex]\sqrt{(100+10\sqrt{65}+10\sqrt{85}) /2 * (100+10\sqrt{65}+10\sqrt{85}) /2 -100* {(100+10\sqrt{85}+10\sqrt{65}) /2[/tex]-[tex]\sqrt{-10\sqrt{85}*(10+10\sqrt{85} +10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=3500 feet²
Then, ar(WXZ)/ ar (XYZ)= 3500/1400=2.5 times.
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Identify coordinate point C.
(1, 5)
(6, 7)
(7, 3)
(0, 2)
Answers
Answer: (6,7)
Step-by-step explanation:
Answer:
(7,6)
Step-by-step explanation:
look above as your axis x it's 7, and then down is axis y is 6.
What is the equation of the line that passes through the point (-6, -7) and has a
slope of1/2?
Answers
Answer:
y = x/2 - 4
Step-by-step explanation:
Determine whether each set of side lengths could be the sides of a right triangle. drag and drop each set of side lengths to the correct box. right triangle not a right triangle
Answers
The set of side lengths that could be the sides of a right triangle must follow the Pythagoras theorem
How to determine the side lengths?The rule of the side lengths of a right triangle is:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the longest side, and a and b represent the lengths of the triangle
This in other words mean that:
All right triangles obey the Pythagoras theorem
Note that I gave a general explanation because the question is incomplete
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Given the circle has a radius of 9 and a center of (-6,4) what is the equation of the
circle?
Answers
Answer:
(x+6)2 + (y-4)2 = 81
Step-by-step explanation:
The equation of the circle is in the for (x-a)2 + (y-b)2 = c2
At a music academy, a randomly selected group of people were asked which type of musical instrument they are learning to play. The results are displayed, by age, in the two-way frequency table.
String Woodwind Piano Total
Ages 15-19 11 3 7 21
Ages 20-24 9 10 17 36
Ages 25-29 16 6 7 29
Total 36 19 31 86
Based on the data in the table, which statement is true?
A.
P(learning a string instrument) ≠ P(ages 20-24)
B.
P(playing piano|ages 25-29) = P(ages 15-19|learning piano)
C.
P(ages 15-19|learning piano) ≠ P(ages 15-19)
D.
P(learning piano|ages 20-24) = P(learning piano)
Answers
P(ages 15-19|learning piano) = P(playing piano|ages 25-29) so option (B) must be correct.
What is a frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.
The quantity of times that an event or value occurs is its frequency.
In other words, a frequency table is a table in which we have some data and their frequency.
Given the problem has been attached below,
It is clear that
Number of playing piano in the age of 25 - 29 = Number of playing piano in the age of 15 - 19
Hence it should be the correct answer.
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Two similar triangles are shown below
Which two sets of angles are corresponding angles?
Answers
Answer:
I cant help unfortunately
Step-by-step explanation:
can you help me in the comprehension of the story uncle Marcos ?
My exam is in 4 hours btw
please help, i’ll give pointsssss :)
Answers
What is the equation of a line through the points (0,9) and (3,0)?
Answers
Answer:
The image has the ans.
Step-by-step explanation:
The image will help.
help me pls I need to get my grade up before July 11th so help ASAP
Answers
-7x^2+4x+2
How many solutions are there for the system of nonlinear equations represented by this graph?
Answers
The total solution for the system of nonlinear equations represented by this graph is 2 solutions
Graphs and FunctionsQuadratic function have a leading degree of 2. The graph of a quadratic function is parabolic in nature.
Since the given graph consists of a parabola, hence the total solution for the system of nonlinear equations represented by this graph is 2 solutions
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write an equation for a prabola with a vertex at the origin, passing through(5,6), and symmetric with respect to the x-axis
Answers
a parabola with symmetry or mirror image across the x-axis, will be a horizontal parabola, namely one that opens either to the right or left.
a horizontal parabola will be a parabola whose independent variable is the "y", so it'll be an x(y) type of equation.
[tex]~~~~~~\textit{horizontal parabola vertex form} \\\\ x=a(y- k)^2+ h\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\supset}\qquad \stackrel{"a"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies x=a(y-0)^2+0\qquad \textit{we also know that} \begin{cases} x=5\\ y=6 \end{cases} \\\\\\ 5=a(6-0)^2 +0\implies 5=36a\implies \cfrac{5}{36}=a~\hfill \boxed{x=\cfrac{5}{36}y^2}[/tex]
Find the volume of this rectangular pyramid.
length =5cm
width =6cm
hight =7cm
PLEASE HURRY
Answers
f(x) = x². What is g(x)?
Answers
Answer:
We want to get g(x) given that we know f(x) and the graphs for both functions. We will see ...
Step-by-step explanation:
How many inches around is the border if the diameter of the pizza is 8 inches?
Answers
Answer:
25.12
Step-by-step explanation:
Since it says around the pizza, we can assume it means circumference.
So, the formula to find circumference is C=2πr.
We have a diameter which is 8. We know that radius is half of the diameter. So, half of 8 is 4.
Now that we have the radius we can plug in the numbers for the formula C=2πr.
C=2πr
C=2*3.14*4
C=25.12
your answer is 25.12 inches.
Find the 14 term of the following geometric sequence.
10, 20, 40, 80,
Answers
Answer:
81920
Step-by-step explanation:
Finding the common ratio (r) :
20/102Finding the 14th term :
a₁₄ = ar¹⁴⁻¹a₁₄ = ar¹³a₁₄ = (10)(2)¹³a₁₄ = (10)(8192)a₁₄ = 81920Answer:
the 14th term in the sequence would be 81920.
Step-by-step explanation:
because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.
I need help on this please
Answers
Answer:
-22
Step-by-step explanation:
each mark decreases by three, two marks down from 16 would be 16+3+3; which equals 22, and it has to be negative
hope this helped!
But I’m not 100% sure, but why I think this is because 10…..16
So between those 2 numbers is 13
That means that it adds by 3
Which maybe 16+3=19
sorry tho I’m not that sure but I think it is ?
What is the volume of the rectangular prism?
A rectangular prism with dimensions 4 and 1 third feet by 3 and 1 third feet by 4 feet.
57 7/9ft3
11 2/3ft3
48 2/9ft3
28 2/3ft3
Answers
Answer:
A or 57 7/9ft3
Step-by-step explanation:
13/3x10/3x4/1 = 520/9=57 7/9
Answer:
The volume of the rectangle would be [tex]57\frac{7}{9}[/tex] ft^3. (The first answer).
Step-by-step explanation:
To solve you have to multiply [tex]4\frac{1}{3},3\frac{1}{2}, and, 4[/tex] to get an answer of [tex]57\frac{7}{9}[/tex].
I hope this helps! :)