Differentiate both sides with respect to x and solve for the derivative dy/dx :
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[x^2y^2+xy\right] = \dfrac{\mathrm d}{\mathrm dx}[2] \\\\ \dfrac{\mathrm d}{\mathrm dx}\left[x^2\right]y^2 + x^2\dfrac{\mathrm d}{\mathrm dx}\left[y^2\right] + \dfrac{\mathrm d}{\mathrm dx}\left[x\right]y + x\dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ 2xy^2 + x^2(2y)\dfrac{\mathrm dy}{\mathrm dx} + y + x\dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ (2x^2y+x)\dfrac{\mathrm dy}{\mathrm dx} = -2xy^2-y \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{2xy^2+y}{2x^2y+x}[/tex]
This gives the slope of the tangent to the curve at the point (x, y).
If the slope of some tangent line is -1, then
[tex]-\dfrac{2xy^2+y}{2x^2y+x} = -1 \\\\ \dfrac{2xy^2+y}{2x^2y+x} = 1 \\\\ 2xy^2+y = 2x^2y+x \\\\ 2xy^2-2x^2y + y - x = 0 \\\\ 2xy(y-x)+y-x = 0 \\\\ (2xy+1)(y-x) = 0[/tex]
Then either
[tex]2xy+1 = 0\text{ or }y-x=0 \\\\ \implies y=-\dfrac1{2x} \text{ or }y=x[/tex]
In the first case, we'd have
[tex]x^2\left(-\dfrac1{2x}\right)^2+x\left(-\dfrac1{2x}\right) = \dfrac14-\dfrac12 = -\dfrac14\neq2[/tex]
so this case is junk.
In the second case,
[tex]x^2\times x^2+x\times x=x^4+x^2=2 \\\\ x^4+x^2-2 = (x^2-1)(x^2+2)=0[/tex]
which means either
[tex]x^2-1 = 0 \text{ or }x^2+2 = 0 \\\\ x^2 = 1 \text{ or }x^2 = - 2[/tex]
The second case here leads to non-real solutions, so we ignore it. The other case leads to [tex]x=\pm1[/tex].
Find the y-coordinates of the points with x = ±1 :
[tex]x=1 \implies y^2+y=2 \implies y=-2 \text{ or }y=1 \\\\ x=-1\implies y^2-y=2\implies y=-1\text{ or }y=2[/tex]
so the points of interest are (1, -2), (1, 1), (-1, -1), and (-1, 2).
can anyone help me out with this one?
help me plz now plz help me asap
[tex]\\ \sf\longmapsto 0.49=\dfrac{49}{100}[/tex]
[tex]\\ \sf\longmapsto 0.093=\dfrac{93}{1000}[/tex]
[tex]\\ \sf\longmapsto 0.021=\dfrac{21}{1000}[/tex]
[tex]\\ \sf\longmapsto 0.103=\dfrac{103}{1000}[/tex]
Jungwon has $15. Notepads cost $2.50 each. How many notepads can Jungwon buy?
Order the numbers from least to greatest
Answer:
B
Step-by-step explanation:
It just is
Plz help me with this
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) A table and graph are attached.
__
b) The relationship is NOT PROPORTIONAL. The line does not go through the origin (0, 0).
The midpoint of AB is (1, 2). The coordinates of A are (-3,6).Find the coordinates of B.
Midpoint has coordinates [tex](x_m,y_m)[/tex] which equal to,
[tex]x_m=\frac{x_1+x_2}{2}[/tex]
[tex]y_m=\frac{y_1+y_2}{2}[/tex]
We know the coordinates of a midpoint as well as the coordinates of [tex]A(x_1,y_1)[/tex] so we should be able to find coordinates of [tex]B(x_2,y_2)[/tex].
First solve both equations for [tex]x_2[/tex] and [tex]y_2[/tex] respectively,
[tex]x_2=2x_m-x_1[/tex]
[tex]y_2=2y_m-y_1[/tex]
Now insert the data,
[tex]x_2=2\cdot1-(-3)=\boxed{5}[/tex]
[tex]y_2=2\cdot2-6=\boxed{-2}[/tex]
The coordinates of B are therefore [tex](5,-2)[/tex].
Hope this helps :)
The midpoint of AB is (1, 2) the coordinates of A are (-3,6) coordinates of B coordinates of point B are (5, -2).
To find the coordinates of point B given that the midpoint of AB is (1, 2) and the coordinates of A are (-3, 6), use the midpoint formula:
Midpoint formula: M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that M is the midpoint (1, 2) and A is (-3, 6), we have:
(1, 2) = ((-3 + x2) / 2, (6 + y2) / 2)
Solve for x2 and y2:
For x-coordinate:
1 = (-3 + x2) / 2
2 = -3 + x2
x2 = 2 + 3
x2 = 5
For y-coordinate:
2 = (6 + y2) / 2
4 = 6 + y2
y2 = 4 - 6
y2 = -2
To know more about coordinates here
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What is this number sentence equal to?
If you could help, thank you so much!
Answer:
18.63
Step-by-step explanation:
[tex] \frac{6}{10} = 0.6 \\ \frac{3}{100} = 0.03[/tex]
[tex]10 + 8 + 0.6 + 0.03 = 18.63[/tex]
Which of the h values are solutions to the following equation?
h^2=0.36
Choose all answers that apply:
A: h= square root of 0.6
B: h = square root of -0.6
C: h = 0.18
D:h = -0.18
E: None of the above
Answer:
a:h=square root of 0.6
Step-by-step explanation:
thank you for your time today
Answer:
none of the above
Step-by-step explanation:
KHAN
what times we subtract the number 80 by 8
Answer:
Question unclear
Step-by-step explanation:Your probally asking what times 8 gives us 80. If you are than 10!
What is the arc length of arc cd in the circle below. The circle has a radius of 6ft and an angle measure of 30
9514 1404 393
Answer:
π ft ≈ 3.14 ft
Step-by-step explanation:
The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.
C = 2πr
1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft
The arc length is about 3.14 feet.
Could use help on this math problem
Answer:
78
90
86
96
09
Step-by-step explanation:
80
90
90
OK LA sir I will complete my work as soon as possible LA thank you la madam My name is now signing off
Tom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he
make in July if he sold 12 cars? In August he made $6500, how many cars did he sell?
Answer:
Answer = he made 7,000 in July and sold 10 cars in august.
Step-by-step explanation:
3. Consider the multiplication operations below and choose whether the fosuit com
be rational, Inational, or both.
Irrational
Expressions
Rational
8. VE
О
tvo. V
V3.12
о
Answer:
1st expression= rational 2nd expression= rational 3rd expression = irrational
Step-by-step explanation:
The first and second expressions are rational because they both equal whole numbers (4 and 3) while the last expression equals a decimal that goes on forever with no end, thus making it irrational.
Is 0.03456 a rational number
Answer:
Yes. It is a rational number.
State the gradient of the line 2y = 3 – 2x.
Answer:
Step-by-step explanation:
2y = 3-2x
y = -x + 3/2
Slope of line = coefficient of x = -1
pls help! I need the answer quickly!
Step-by-step explanation:
The correct answer is 4 (option B)
Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart after 30 minutes?
Answer:
they travel 115 km/h long
Is [tex]2 \frac{2}{3} [/tex]
a rational number
(x3)(x-5)
Fududeey
X=2
Answer:
-18 is the right answer..
Can a set of data having two modes have two points of central tendency
Answer:
The Measure of Central Tendency are
1. Mean
2. Median and Quartiles
3. Mode
4. Geometric Mean
5. Harmonic Mean
→When all the five Measure of Dispersion are Same, it means the two data sets have Identical Variate.
→Now consider the two data sets,
A=3,4,4,5
B=1,4,4,7
Both the Data set have , same mean, median, and Mode,which is equal to 4.
→When you will consider, First three as Measure of central tendency ,then it becomes incorrect statement ,that Data Set are same.
Step-by-step explanation:
A measure of central tendency is a descriptive statistic
The correct response to the question is as follows;
Yes; A data having two modes can have two points of central tendency
The reason a dataset having two modes can have two points of central tendency is as follows:
A dataset having two modes is said to be bimodal
A dataset having three modes is said to be trimodal
A dataset having more than three modes is said to be multimodal
A measure of central tendency is a type of summary statistics that is a
single value representing the center point, or average of a set of data
thereby providing a description of the data by telling the middle value, the
average or the most common value which is the mode
As can be seen from the given example, by having two modes, a bimodal
data set describes a data that has two points of central tendency, thereby
giving a description of the data type, which for example may a collection
of the height of individuals, male and female, that have two most common
height values for each gender
Therefore, the correct response is yes, a dataset having two modes can
have two points of central tendency because the mode is a measure of
central tendency which is a descriptive statistics
Learn more about the measures of central tendency here:
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i’m genuinely confused, please help
Answer:
2x + 3 + 3x +12 + 90 = 180 (degree )
5x +105=180 (degree )
5x= 180-105 (degree )
5x = 75 (degree )
x = 75/5 (degree )
x = 15 #
therefore, 2x + 3= 2*15 + 3
=30+3
= 33#
3x + 12 = 3*15+12
= 45 +12
= 57#
Please help due tomorrow
The scaled factor is 3 for all of them.
Find the value of x 3(4x+3)
3(4x+3)=12x+9
i don't know what do you need,
if roots, let 12x+9=0
the root is x=-3/4
One number exceeds another by 12 and their sum is 44 find the two numbers you
Answer:
Step-by-step explanation:
x - first
x + 12 - second
x + (x + 12) = 44
2x=44-12
x=16
first number is 16
second number is 16+12=28
two numbers are 16 and 28
16 and 28 are the required two numbers when one number exceeds another by 12 and their sum is 44
One number exceeds another by 12 and their sum is 44
We need to find the two numbers
What is equation?Two expressions with equal sign is called equation.
Let x be the first number
x + 12 be the second number
x + (x + 12) = 44
2x=44-12
x=16
Therefore first number is 16
second number is 16+12=28
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Someone please help me with 13 and 14 I’m really struggling
Answer:
Step-by-step explanation:
Going into the final exam, which will count as two tests, has test scores of 77 , 82, 72 , 63 and 92 What score does need on the final in order to have an average score of 80?
Answer:
you either need to score a perfect on one exam and get a 80 on the second or get two 90s on both exams.
Step-by-step explanation:
How would you write 5x5x5x5x5x5 in exponential form
Answer:
5^6
Step-by-step explanation:
This is because the exponent is how many numbers are in the multiplication equation, in this case, five. Because there are six five's being multiplied together, our exponent is six.
Can someone help me solve these 3 trig identity problems? I am stuck on these last 3... I will give brainliest!
(calculators are allowed)
Answer:
1. 1,246
2. 0,545
3. 0,9539
Step-by-step explanation:
semoga membantu :)
Write the number in standard form.
ninety-two billion, seventy thousand,
one hundred eight
92.000.070.108
Step-by-step explanation:
Thousand has 3 zeros, a million has 6 and a billion has 9.
So for ninety-two billion, you take 92 and add 9 zeros behind it because a billion has 9 zeros
(92.000.000.000)
What is a rational number between -1/5 and -2/5?
Answer:
-1/4
Step-by-step explanation:
-0.25
