Answer:
A) [tex]\frac{d^2y}{dx^2}=\frac{2y}{x^2}[/tex]
Step-by-step explanation:
Use implicit differentiation to find dy/dx
[tex]x^2y^2=1\\\\\frac{d}{dx}(x^2y^2)=\frac{d}{dx}(1)\\ \\x^2(\frac{d}{dx}y^2)+(\frac{d}{dx}(x^2))y^2 =0\\\\2yx^2\frac{dy}{dx}+2xy^2=0\\\\2xy(x\frac{dy}{dx}+y)=0\\ \\x\frac{dy}{dx}+y=0\\ \\x\frac{dy}{dx}=-y\\ \\\frac{dy}{dx}=-\frac{y}{x}[/tex]
Determine d²y/dx² using dy/dx
[tex]\frac{dy}{dx}=\frac{-y}{x}\\ \\ \frac{d^2y}{dx^2}=\frac{(x)[\frac{d}{dx}(-y)]-(-y)[\frac{d}{dx}(x)] }{x^2}\\ \\ \frac{d^2y}{dx^2}=\frac{-x\frac{dy}{dx}+y}{x^2}\\ \\ \frac{d^2y}{dx^2}=\frac{-x(\frac{-y}{x})+y}{x^2}\\\\ \frac{d^2y}{dx^2}=\frac{-(-y)+y}{x^2}\\\\ \frac{d^2y}{dx^2}=\frac{y+y}{x^2}\\\\ \frac{d^2y}{dx^2}=\frac{2y}{x^2}[/tex]
Helpful tips
When doing implicit differentiation, make sure to treat "y" as a constant and write dy/dx next to the y-term because it's differentiated with respect to xThe product rule is [tex]\frac{d}{dx}[f(x)g(x)]=f(x)[\frac{d}{dx}g(x)]+[\frac{d}{dx}f(x)]g(x)[/tex]The quotient rule is [tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{f(x)[\frac{d}{dx}g(x)]-g(x)[\frac{d}{dx}f(x)]}{(g(x))^2}[/tex][tex]\frac{dy}{dx}[/tex] represents the first derivative of y with respect to x and [tex]\frac{d^2y}{dx^2}[/tex] represents the second derivative of y with respect to xLet me know if you have any more questions!
WILL GIVE BRAINLY 15 points as well
The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
Enter your answer in the box.
A prism with a volume of 270 m³ is dilated by a factor of 3. What is the volume of the dilated prism? Enter your answer in the box. M³.
The volume of the prism, when it is dilated by a scale factor of 3 changed as 7290 meter cube.
What is dilation of solids?The dilation of the solids is the change of the size of it with a factor, by which it is bigger or smaller from original shape.
Given information-
The volume of the prism is 270 meter cube.
The scale factor of dilation is 3.
As the volume of the prism is 270. The dilation is done by the scale factor of 3. Thus the change in the shape for three dimensions is,
[tex]\Delta =3^3\\\Delta=27[/tex]
Now the volume of the prism is 270. To find the volume of the dilated prism, multiplied 27 by the volume of given prism. Thus the volume of the dilated prism is,
[tex]V_d=27\times270\\V_d=7290\rm m^3[/tex]
Hence, The volume of the prism, when it is dilated by a scale factor of 3 is 7290 meter cube.
Learn more about the dilation of solids here;
https://brainly.com/question/24760202
if not able to awnser say it in the comments
What is the solution to the equation
x-5/6=-1
I Enter your answer as a fraction in simplest form in the box
Answer:
x= -1/6
Step-by-step explanation:
x-5/6 = -1
Add 5/6 to both sides
x = - 1/6
a construction worker has a ladder against the side of a building. the building is 10 feet tall, and the ladder is 15 feet long. how far is the base of the ladder from the building
Answer:
5
Step-by-step explanation:
So bad at this someone help
Answer:
Volume of a cylinder : πr^2h
: π = 22/7
: r = 9
: h = 20
: 22/7 × 9^2 × 20
: 5091.4 (corrected to 1.dp )
Answer:
5089.4 cm³
Step-by-step explanation:
You want the volume of a cylinder with radius 9 cm and height 20 cm.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
ApplicationFor r = 9 cm and h = 20 cm, the volume is ...
V = π(9 cm)²(20 cm) = 1620π cm³
The value you get for this depends on the value you use for π. The attachment shows the three common choices: "π button", 3.14, 22/7.
Using the "pi button" value provided by a calculator, the volume is ...
5089.4 cm³
<95141404393>
Help me pleasee guyss
Answer:
9.5 mm
Step-by-step explanation:
They gave the diameter, and we needed to find the radius
r = d × 1/2
r = 19 × 1/2
r = 9.5 mm
A car starts 40 meters away from home and every minute the car travels an additional 1000 meters. What
equation can represent this word problem?
Y=Mx+b
The question is in the picture please help fast
Answer:
y = 4x - 57
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~
( 15 , 3 )
( 19 , 19 )
m = [tex]\frac{19-3}{19-15}[/tex] = 4
y - 3 = 4 ( x - 15 )
y = 4x - 57
If 120% is £360, what is 100%?
Answer:
300
Step-by-step explanation:
To get from 120% to 100% you divide by 1.2 360/1.2=300 :)
How many cúbic centímeters are in the completéd display?
Answer:
machikne up girls i will help you 4 cubic centimeter are in the completed display
Find the number that makes the ratio equivalent to 1:7.
Answer:
So 2:14 and 3:21 are two ratios that are equal to 1:7. Students are also asked to determine whether two given ratios are equal, by first writing each ratio as a fraction, then writing each fraction in lowest terms. If the two fractions are the same when written in lowest terms, then the ratios are equal.
Step-by-step explanation:
Above
Please Mark brainliest if this helped i need 3 more!
Answer:
2:14 or 3:21
Step-by-step explanation:
because u multiply
will give brainlist plus will give brianlist plus 20 points
Answer: 8 60 70 i think if i am wrong pls let me know ty :D
Step-by-step explanation:
Please help all questions shown
Answer:
27. x=7/20; 28. m= 3.7; 29. a= 5.8
30. x= 6; 31.x= 46
Step-by-step explanation:
27.
[tex]x + \frac{2}{3} = \frac{9}{ 10} [/tex]
you are going to carry the 2/3 over the equal sign. This will make the 2/3 negative so...
[tex]x = \frac{9}{10} - \frac{2}{3} [/tex]
now calculate it by finding the LCM of 10 and 3 ....this will be 30....you can just multiply the 10 and 3
now
30 into 10 goes 3 times....you will multiply this 3 with the 9 to get 27
30 into 3 goes 10 times...you will multiply this 10 with the 2 to get 20
[tex]x = \frac{27 - 20}{30}[/tex]
[tex]x = \frac{7}{30} [/tex]
Hopefully you understand
28.
[tex]1.2 = m - 2.5[/tex]
[tex]1.2 + 2.5 = m[/tex]
carry the 2.5 over the equal sign to get the m by itself...this is because you are trying to find m
when the negative number goes over the equal sign it will become positive...this is why you add it to the 1.2
m= 3.7
you can do the other on your own
the error in 30 is that the 7 should not be added to the 13 but subtracted
..this is because when you carry the positive number over the equal sign it will become negative..hence you subtract it
[tex]x + 7 = 13[/tex]
[tex]x = 13 - 7[/tex]
[tex]x = 6[/tex]
and for 31...the 12 should not be subtracted but added since when it goes over the equal sign it will become positive.
[tex]34= y - 12[/tex]
[tex]34 + 12 = y[/tex]
[tex]y = 46[/tex]
A recipe requires 2 eggs 500 grams of flour and two teaspoons of salt how many eggs are needed if you use 2 kg of flour?
the temperature in Austria one morning is -5 degrees Celsius at 8:00 and increased by 2 degrees Celsius every hour until 12:00. wht will the temperature be
at 11:30
The equation illustrates that the temperature by 11:30 am will be 2 degree Celcius.
How to solve the equationIt should be noted that there are 3 hours and 30 minutes from 8 am to 11.30 am.
Therefore, the temperature by 11:30 will be:
= -5 + 2(3.5)
= -5 + 7
= 2°
In conclusion, the correct option is 2°.
Learn more about equations on:
https://brainly.com/question/13763238
Please answer this (who ever answers correctly gets brainlest)
Answer:
6
Step-by-step explanation:
[tex] \frac{2}{5} \times 15 = 6[/tex]
[tex]15\div5\times2=6\:or\:15\times\dfrac{2}{5}=6 \\\text{Answer: 6}[/tex]
Simplify the following expressions using the distributive property
-3(z-7)
Answer:
I think that the answer is d=-7
Step-by-step explanation:
-3(z-7)
-3z+21
z=-7
I'm on a time crunch and I need to get a lot of homework done TODAY. Can someone help?
ayooo im on a time crunch too, i get you man
the complete factors are (x+11)(x-11)
(x+11) (x-11)
11 and 11 make 121
Shikha has quiz scores of 27, 25, 24, 26 and 25 this term. If she gets a score of 25 and 28, which part of the data( mean, median, mode or range) will be affected? Explain your reasoning.
Answer:
mean and range
arrangement before: 24,25,25,26,27
arrangement after: 24,25,25,25,26,27,28
mean before: (27+25+24+26+25)/5 = 25.4
mean after: (27+25+24+26+25+25+28))/5 = 25.7
median before: 25
median after: 25
mode before: 25
mode after: 25
range before: 24 to 27
range after: 24 to 28
hence, the mean and range were affected while the median and mode remained unchanged.
Which number is greater and by how much? 600 or 600 decreased by 20% and then uncreased by 20% of the result
Answer:
600.
Step-by-step explanation:
Hope this helps!
George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request. He asked 500 students at his school the following questions: "Are you in the Art Club?" and "Did you get the art class you requested?" The results are shown in the table below:
Art Club Not in Art Club Total
Received art class requested 100 265 365
Did not get art class requested 65 70 135
Total 165 335 500
Help George determine if all students at his school have an equal opportunity to get into the art class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answer: Not fair
Step-by-step explanation: Since the fractions and rations are unbelievably rigid, this question is no doubt going to the creaser side.
When simplifying x3. x2, the exponents are added together.
True
False
Because of the commutative property of multiplication, it is true that 3 4 × 4 = 4 × 3 4 . However, these expressions can be calculated in different ways even though the solutions will be the same. Below, show two different ways of solving this problem. First, show how 3 4 × 4 can be solved using repeated addition, Then, show how 4x3/4 can be solved using multiplication and division.
the main one i need help with is the multiplication
Answer:
4x3/4=3
Step-by-step explanation:
Multiplication(Do the multiplication first): 4x3/4=12/4=3
Division(Do the division first): 4x0.75=3
Hope this helped! Please give Brainliest if possible.
please help me!!! 50 points
Answer:
b no solution
Step-by-step explanation:
there is no solution
Answer:
The answer is B
Step-by-step explanation:
And B is no solution.
Hope this helps!
ion need the work js gimme the answer thanks
Answer:
4) Subtract 7 - 6 because is shows the difference between the two numbers.
Please help me with this question.
======================================================
Explanation:
Focus on the outer ring of numbers only.
The left arm of the angle points at 140. The right arm points at 15. The difference of which is 140-15 = 125
---------------
Alternatively, focus on the inner ring of numbers only.
The left arm points at 40 and the right arm points at 165.
165-40 = 125
We get the same answer as before.
Answer:
Step-by-step explanation:
Hello!
140 -15 =>125°
Error Analysis A student added the rational
expressions as follows:
5x 7 5x 7(7) 5x + 49
+
+
x
x + 7
Describe and correct the error the student
12
x+7
Х
x+7
x+7
Rational expressions are expressions that can be represented as fractions
The solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
How to determine the errorThe student operation is given as:
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac { 5 x } { x + 7 } + \frac { 7 ( 7 ) } { x + 7 } = \frac{5x + 49}{x + 7}[/tex]
The student's error is that, he multiplied the numerator of 7/x by 7, and he added 7 to the denominator
The correction is as follows:
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x }[/tex]
Take the LCM
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7(x + 7)}{(x + 7)x}[/tex]
Open the brackets
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
Hence, the solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
Read more about rational expressions at:
https://brainly.com/question/21342
Andy, ben and Cathy have £177 between them. Cathy has 3 times as much as ben. andy has £12 more than ben
How do I do number 1
Answer:
try using a graphing calculator.
Step-by-step explanation:
I know this doesn't really answer your question, but it gets you closer to the answer. Just put your problem into go-ogle, and go-ogle should spit out a graph with the answers of x and y right on it.
You had a bag of fruit snacks that you shared with 4 friends. Each of you got at most 6 fruit snacks. The inequality x÷5≤6 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
Answer: The possible numbers of fruit snacks that were in the bag is x < 18
Step-by-step explanation: Good luck :D