Answer:
Part A)
[tex]\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}[/tex]
Part B)
[tex]\displaystyle y=-\frac{5}{8}x+\frac{9}{4}[/tex]
Step-by-step explanation:
We have the equation:
[tex]\displaystyle x^2y+y^2x=6[/tex]
Part A)
We want to find the derivative of our function, dy/dx.
So, we will take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\Big[x^2y+y^2x\Big]=\frac{d}{dx}\big[6\big][/tex]
The derivative of a constant is 0. We can expand the left:
[tex]\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0[/tex]
Differentiate using the product rule:
[tex]\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0[/tex]
Implicitly differentiate:
[tex]\displaystyle (2xy+x^2\frac{dy}{dx})+(2y\frac{dy}{dx}x+y^2)=0[/tex]
Rearrange:
[tex]\displaystyle \Big(x^2\frac{dy}{dx}+2xy\frac{dy}{dx}\Big)+(2xy+y^2)=0[/tex]
Isolate the dy/dx:
[tex]\displaystyle \frac{dy}{dx}(x^2+2xy)=-(2xy+y^2)[/tex]
Hence, our derivative is:
[tex]\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}[/tex]
Part B)
We want to find the equation of the tangent line at (2, 1).
So, let's find the slope of the tangent line using the derivative. Substitute:
[tex]\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{2(2)(1)+(1)^2}{(2)^2+2(2)(1)}[/tex]
Evaluate:
[tex]\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{4+1}{4+4}=-\frac{5}{8}[/tex]
Then by the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Yields:
[tex]\displaystyle y-1=-\frac{5}{8}(x-2)[/tex]
Distribute:
[tex]\displaystyle y-1=-\frac{5}{8}x+\frac{5}{4}[/tex]
Hence, our equation is:
[tex]\displaystyle y=-\frac{5}{8}x+\frac{9}{4}[/tex]
Believe it or not, there are some people who don't think that Duke will win the NCAA tournament this year. Let's say that you want to measure the average intelligence of Duke Doubters. Problem is you could only find 28 DDs on this whole campus. The mean of your sample was 90 and the standard deviation was 60. Calculate the 90% Confidence Interval for the IQ of DDs
Answer:
The 90% confidence interval is [tex] 87.95 < \mu < 92.05 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 28[/tex]
The sample mean is [tex]\= x = 90[/tex]
The standard deviation is [tex]s= 60[/tex]
Generally given that the sample size is not large enough i.e n < 28 then we will make use of the t distribution table
Generally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 28 - 1[/tex]
=> [tex]df = 2 7[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the student t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 2 7[/tex] is
[tex]t_{\frac{\alpha }{2} , 27 } = 2.052[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]90 - 2.052 < \mu < 90 + 2.052 [/tex]
=> [tex] 87.95 < \mu < 92.05 [/tex]
What is this answer????
Answer:
im pretty sure its c
Step-by-step explanation:
A 10 pound bag of grapes costs $14.00. How many pounds of grapes can you get for $7.00?
A hummingbird's heart rate while resting is about 7,500 beats every 30 minutes. How many more beats does a hummingbird's heart beat in 60 minutes than a human baby's heart? It was on the last question
Answer:
This is what I got, hope u get it right
Step-by-step explanation:
The Giant Hummingbird beats its wings 10-15 times per second. The fastest recorded rate is about 80 beats per second on an Amethyst Wood- star Hummingbird.
85 is the answer........
what are ratios? and how do you multiply them? someone help please
Answer:
ratio is a comparison of two or more numbers that indicates their sizes in relation to each other
Step-by-step explanation: how to multiply
sixteen less than 3 times a number is seventeen.
Answer:
the number is 11
Step-by-step explanation:
3x-16=17
3x=33
x=11
At an electronics store, the price of a tablet is marked down 15% to $212.50
What was the price of the tablet before the markdown?
Enter your answer in the box.
Please ai need answers fast!!!!
Answer:
$250
Step-by-step explanation:
$212.50 is 85% of the original price.
Therefore use the equation below to find out original price.
(original price) * 0.85 = 212.50
original price = 212.50 / 0.85 = 250
Answer:
250
Step-by-step explanation:
hope this helps
Which is the coefficient in the expression 7x + 14?
Answer:
7
Step-by-step explanation:
A coefficient is the number before a variable (x, y, z...etc).
Which set of numbers represents a Pythagorean triple?
Answer:
52 , 165 , 173 is Pythagorean triple.
Step-by-step explanation:
Pythagorean triple;
a² + b² = c²
Computation:
88² + 105² ≠ 139²
39² + 80² ≠ 119²
38² + 198² ≠ 202²
52² + 165² = 173²
So,
52 , 165 , 173 is Pythagorean triple.
Use the quadratic formula to solve the zero(s) of the quadratic equation 3x^2-4x-6=0. Round to the nearest 10th.
Answer:
so Is because you do 3x2=6 so is
Step-by-step explanation:
3x2=6
x=(o,-6) ok
is c or d
what is the difference of the fractions? 5/6 - 4/6
Answer
[tex]--------------------------------------------[/tex]
[tex]\frac{5}{6}-\frac{4}{6}[/tex] = [tex]\frac{1}{6}[/tex]
[tex]0.8333333333[/tex] - [tex]0.6666666667[/tex] = [tex]0.1666666666[/tex]
[tex]\frac{1}{6}[/tex] = [tex]0.1666666666[/tex]
[tex]It's[/tex] [tex]\frac{1}{6}[/tex] [tex]because[/tex] [tex]5-4[/tex] = [tex]1[/tex]
[tex]and[/tex] [tex]the[/tex] [tex]denominator[/tex] [tex]is[/tex] [tex]the[/tex] [tex]same.[/tex]
[tex]So[/tex], [tex]it's[/tex] [tex]\frac{1}{6}[/tex]
[tex]--------------------------------------------[/tex]
Hope this helps! <3
[tex]--------------------------------------------[/tex]
A(n) _____ transition shows that one event happened before another. Some examples of this type of transition are "so," "therefore," "hence," and "as a result. "A.contras tB.cause-and-effect C.order-of-importance
D.summary
What describes θ when an ellipse is created from an intersection of a plane and double-napped cone?
θ = α
θ = 90⁰
α < θ < 90⁰
0⁰ ≤ θ < α
Answer:
C: a < θ < 90%
Step-by-step explanation:
WHAT IS 5/6 TIMES 15
Answer:
12.5
Step-by-step explanation:
it's the awnser. I need to explain why
The average time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. You run an experiment to verify if the new product is better. You test out the new aspirin on 70 people. Those seventy people had a mean time of 24 minutes and 12 seconds with a standard deviation of 3 mins. Find the test statisic and p-value for your experiment.
Answer:
-2.23 ; 0.012874
Step-by-step explanation:
Given that :
Population mean (μ) = 25 minutes
Same mean (x) = 24min 12 seconds = 24.2 minutes
Standard deviation σ = 3
Sample size (n) = 70
Test statistic :
Using the relation :
Tstatistic = (x - m) / σ/sqrt(n)
Tstatistic = (24.2 - 25) / (3/sqrt(70)
Tstatistic = - 0.8 / 0.3585685
Tstatistic = - 2.2310939
= - 2.23
The P value can be obtained using a. P value Calculator :
P at α = 95% and test statistic = - 2.23
Hence, p = 0.012874 using calculator
Triangle ABC has the following vertices:
A(-8,7)
B(0, -5)
C(9,1)
Is triangle ABC a right triangle, and why?
Answer:
Yes because AB ⊥ BC
Step-by-step explanation:
Answer: Yes because AB ⊥ BC
Step-by-step explanation: Khan Academy
I need help with this question thanks!
Answer:
n= -10
Step-by-step explanation:
50-20= 30 so -3n=30. So n= -10.
Answer:
n=-10
Step-by-step explanation:
-3n+20=50 move constant to the right hand side
-3n=50-20 subtract the numbers
-3n=30 divide both sides by -3 and the answer is n=-10
help now fast i will mark brainlest and please don't just put the answer work it out
Answer:
a. 6276
b. 5590
c. 23128
d. 17325
e. 15090
f. 40419
g. 10496
h. 15000
i. 15648
99% sure
If u can help me with this and have any social media please let me know ;-;
Answer:
I can't
Step-by-step explanation: I have every social
A rectangular prism is made up of 36 unit cubes and is 3 unit cubes high choose two possible combinations of width and length for the prism
A) 2 cubes wide and 6 cubes long
B) 3 cubes wide and 12 cubes long
C) 4 cubes wide and 3 cubes long
D) 5 cubes wide and 7 cubes long
E) 6 cubes wide and 6 cubes long
I think (i said think) the answer is E
quadrilateral ABCD is dilated by a scale factor of 2 centered around (2,2). Which statement is true about the dilation?
Answer:
The vertices of the image will have the coordinates
A(-5, 1) → A'(2x-2, 2y-2) → A'(-12, 0)
B(-4, 3) → B'(2x-2, 2y-2) → B'(-10, 4)
C(1, 2) → C'(2x-2, 2y-2) → C'(0, 2)
D(-3, 0) → D'(2x-2, 2y-2) → D'(-8, -2)
Step-by-step explanation:
Note: You missed to mention the vertices of a quadrilateral ABCD. So, I am assuming the following vertices. It would anyways clear your concept.
Let us suppose
A(-5, 1)B(-4, 3)C(1, 2)D(-3, 0)We know that the rule of the dilation with the center of dilation at (2,2) by a scale factor of 2 is:
(x, y) → (2x-2, 2y-2)Therefore, the vertices of the image will have the coordinates
A(-5, 1) → A'(2x-2, 2y-2) → A'(-12, 0)
B(-4, 3) → B'(2x-2, 2y-2) → B'(-10, 4)
C(1, 2) → C'(2x-2, 2y-2) → C'(0, 2)
D(-3, 0) → D'(2x-2, 2y-2) → D'(-8, -2)
Find the slope of the line passing through the points (8,-8) and (4, -2).
Answer:
-6/4
Step-by-step explanation:
m=y2-y1/x2-x1
m=-2--8/4-8=6/-4
-6/4
Answer:
The answer m= -3/2 , hope this helps you.
Wayne has a recipe on an index card with a length of 3 inches and a width of 5 inches. He wants to enlarge to 15 inches long. How wide will the enlargement be?
A 9 inches
B 13 inches
C 25 inches
D 45 inches
Answer:
a) 9 inches
is correct answer for you
Answer:
C, 25
Step-by-step explanation:
3 x 5 = 15
5 x 5 = 25
In 2011, the population of Mali was about 1.584 x 107 people. What is this number written in standard
notation?
HURRY UP WILL GIVE BRAINLYEST AND 20 POINTS What is the value of
O -4
O -2
O 2
O 4
Answer:
4
Step-by-step explanation:
you multiply -2 and 7 which makes a negative then you subtract from 15 and get 1 so then you divide 1 by 4 which gives you 4
Answer:
u do edg2020 just like me
4 is corrrrect answerrrrr
4(3 + 5) - 3 x 9² ?
Answer:
- 211Step-by-step explanation:
4(3 + 5) - 3 x 9² =4(8) - 3(81) =32 - 243 =- 211tor. Factor each expression. 2x + 8
Answer:
The factorized form of 2x + 8 is 2(x+4).
Step-by-step explanation:
Given the expression
2x + 8Let us factorize the expression
2x + 8
Rewrite 8 as 2·4
[tex]2x\:+\:8=2x+2\cdot \:\:4[/tex]
Factor out common term 2
= 2(x+4)
Therefore, factorized form of 2x + 8 is 2(x+4).
You are getting a car wash for $45.50. You have to pay 5% sales tax and you want to tip the person who washed your car 20%. How much will you spend in total?
Answer:
$56.88
Step-by-step explanation:
amount paying for sales tax---> $2.28
amount paying for tip---> $9.1
amount paying for car wash---> $45.50
$2.28 + $9.1 + $45.50= $56.88
The money we will spend in total will be $56.875. iIt is the sum of all expenses
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
money to get the car washed= $45.50
the 5% of $45.50= (5 x 45.50)/100
= $2.275
The 20% of $45.50 for the tip= (20 x 45.50)/100
= $9.1
The total amount we will be the sum of all expenditures = the money for car wash + the money for sales tax + the money for tip
= 45.50 + 2.275 + 9.1
= 56.875
the total amount to be paid= $56.875
Learn more about percent here:
https://brainly.com/question/11549320
#SPJ6
use distributive property to simplify -1(4+x)=6
Answer:
[tex]\huge\boxed{\boxed{x=-10}}[/tex]
Step-by-step explanation:
Hello.
The Distributive Property states that
a(b+c)=ab+ac
Simplify:
-1(4+x)=6
-4-x=6
Add 4 to both sides:
-4+4-x=6+4
-x=10
Divide both sides by -1 in order to get rid of the minus sign:
x=-10
And we're done!
I hope it helps & have an outstanding day!
~ST2710 :)
3. For each literal, make a Venn diagram with three nonempty sets A; B and C, which satisfy simulta-
neously the given conditions:
a)A ⊂ B, C ⊂ B, A ∩ C = ∅ b)A ⊂ C, A 6= B, B ∩ C = ∅
c)A ⊂ B, C * B, A ∩ C 6= ∅ d)A ⊂ (B ∩ C), B ⊂ C, C 6= B, A 6= C.
Answer:
c is the right answer
Answer:
A
Step-by-step explanation:
I say a because it's supposed to bring the Venn diagram alone
