Answer:
A
Step-by-step explanation:
We are given the equation:
[tex]x^2+xy-3y=3[/tex]
And we want to find dy/dx at the point (2, 1).
Find dy/dx. We can take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}[x^2+xy-3y]=\frac{d}{dx}[3][/tex]
Implicitly differentiate:
[tex]\displaystyle 2x+y+x\frac{dy}{dx}-3\frac{dy}{dx}=0[/tex]
Solve for dy/dx:
[tex]\displaystyle \begin{aligned} x \frac{dy}{dx} - 3\frac{dy}{dx} & = -2x - y \\ \\ \frac{dy}{dx}(x - 3) & = -2x - y \\ \\ \frac{dy}{dx} & = \frac{-2x-y}{x-3} \\ \\ & = \frac{2x+y}{3-x} \end{aligned}[/tex]
To find dy/dx at (2, 1), evaluate dy/dx for x = 2 and y = 1. Hence:
[tex]\displaystyle \frac{dy}{dx}\Big|_{(2, 1)}=\frac{2(2)+1}{3 - (2)}=\frac{5}{1}=5[/tex]
Hence, our answer is A.
We want to find the differential dy/dx for the given expression at the given point. We will see that the correct option is A.
How to differentiate the expression?
We have:
x^2 + xy - 3y = 3
First, we need to isolate the variable y in one side of the equation, so we get:
xy - 3y = 3 - x^2
y*(x - 3) = 3 - x^2
y = (x - x^2)/(x - 3)
Now we can differentiate this, remember that if:
f(x) = g(x)*h(x)
then:
f'(x) = g(x)*h'(x) + g'(x)*h'(x)
Using that rule.
dy/dx = (1 - 2x)/(x - 3) - (x - x^2)/(x - 3)^2
Now we need to evaluate this in x = 2 (the x-value of the point) so we get:
(1 - 2*2)/(2 - 3) - (2 - 2^2)/(2 - 3)^2
= (-3)/(-1) - (-2)/(1) = 5
So the correct option is A.
If you want to learn more about differentiation, you can read:
https://brainly.com/question/24898810
Find the length of line segment UV.
Answer:
The length of the line segment UV is 76 units
Step-by-step explanation:
In a triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length
In Δ ONT
∵ U is the mid-point of ON
∵ V is the mid-point of TN
→ That means UV is joining the mid-points of two sides
∴ UV // OT
∴ UV = [tex]\frac{1}{2}[/tex] OT
∵ UV = 7x - 8
∵ OT = 12x + 8
∴ 7x - 8 = [tex]\frac{1}{2}[/tex] (12x + 8)
→ Multiply the bracket by [tex]\frac{1}{2}[/tex]
∵ [tex]\frac{1}{2}[/tex] (12x + 8) = [tex]\frac{1}{2}[/tex] (12x) + [tex]\frac{1}{2}[/tex] (8) = 6x + 4
∴ 7x - 8 = 6x + 4
→ Add 8 to both sides
∴ 7x - 8 + 8 = 6x + 4 + 8
∴ 7x = 6x + 12
→ Subtract 6x from both sides
∴ 7x - 6x = 6x - 6x + 12
∴ x = 12
→ Substitute the value of x in the expression of UV to find it
∵ UV = 7(12) - 8 = 84 - 8
∴ UV = 76
∴ The length of the line segment UV is 76 units
Find the mean and the median of the data set. 31,32,36,31,30,35,33,30.
Answer:
Mean = 32.25
median = 31.5
Answer:
Median = 31.5
Mean = 32.25
Step-by-step explanation:
Number of data = 8
Ascending order:
30 , 30 , 31 , 31 , 32 , 33 , 35, 36
Median = Average of 4th and 5th term
= (31 + 32) / 2
= 63/2
= 31.5
Mean = Sum of all the observations /number of observations
= (31 + 32 + 36 +31 + 30 + 35 + 33 +30) / 8
= 258/8
= 32.25
A classmate tells you that there are two Fahrenheit temperature that is the same as the Celsius temperature. They tell you it is 50 degrees and -40 degrees. Is your classmate correct or incorrect explain your reasoning.
Answer:
Step-by-step explanation:
the conversion for farenheit to celsius is to subtract 32 and multiply by 5/9.
-40-32 is -72. multiply that by 5/9 and that is -40
50-32 is 18. multiply that by 5/9 and you get 10. so no she's wrong
-4(5x - 3) + 15
Solved please!
Answer:
Step-by-step explanation:
-20x + 12 + 15
-20x + 27
The figure below shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A triangle ABC is shown with vertex A on ordered pair 4, 1, vertex B on ordered pair 3, 1, and vertex C on ordered pair 3, 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 4, 4, vertex B prime on ordered pair negative 3, 4, and vertex C prime on ordered pair negative 3, 1. What set of transformations is performed on triangle ABC to form triangle A′B′C′? (5 points) A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin A translation 5 units down, followed by a 270-degree counterclockwise rotation about the origin A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units down
Answer:
A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin
Step-by-step explanation:
Plz mark as Brainliest!
What is 71283922222 E Times 78232 E Divide by 8326.291213?
Answer:
4333.23777
Step-by-step explanation:
.just type it in the calculator
Find x for each of the problems;
1) 2x+5=12+x
2)5x=30+3x
3)2+x/3=7
4)15-x=17-2x
5)6x= -42-x
6)36-4x=26-3x
7) -2+x=15
Answer:
1) x = 7
2) x = 15
3) x = 19
4) x = 2
5) x = - 6
6) x = 10
7) x = 17
Step-by-step explanation:
1) 2x + 5= 12 +x
-x -x
2x -x + 5 = 12
-5 -5
x = 7
2) 5x = 30 + 3x
-3x -3x
2x = 30
x = 15
3) 2 + x/3 = 7
3(2 + x/3) = (7) 3
2 + x = 21
-2 -2
x = 19
4) 15 - x = 17 - 2x
+2x +2x
15 - x + 2x = 17
-15 -15
x = 2
5) 6x = - 42 - x
+x +x
7x = -42
x = - 6
6) 36 - 4x = 26 - 3x
+3x +3x
36 - x = 26
-36 -36
-x = -10
x = 10
7) -2 + x = 15
+2 +2
x = 17
hope this helps!
What is the value of h(2)?
-2
-1 0 3
Answer:
103 is ur answer hope this helps
Answer:
The answer is 0 or C on Edge.
Step-by-step explanation:
Got it right. 2021.
Resuelve la ecuación de la recta
que pasa por el punto (2 , 8 ) y tiene una pendiente de -3.
ayudaaaa
Answer:
SPANISH TALK ENGLISH OK
Step-by-step explanation:
OKKK
Write a like term to: -5y
Answer:
-7y
Step-by-step explanation:
As long as the variable and exponent is the same, they are like terms
Answer: 68y
There are infinitely many ways to answer this. All you need to do is pick your favorite number and then stick y at the end of it. The terms -5y and 68y are like terms because they have the same variable attached.
You can think of 68y-5y as having 68 yoyos and then subtracting off 5 yoyos to get 63 yoyos when all is said and done. In terms of algebra, we would write 68y-5y = 63y.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
113
Step-by-step explanation:
Answer:
diameter =6 cm
radius =3cm
shaded area =area of square- area of circle
= a^2 - πr^2
=(6)^2-3.142(3)^2
=36-3.142×9
=36-28.278
=7.622
I need help with this question please
Answer:
It's A
Step-by-step explanation:
A parallelogram only has 4 sides, but pentagon has 5. Also like the name, a parallelogram opposite sides are parallel to each other.
Cereal. A dietician obtains the amounts of sugar (incentigrams) from 100 centigrams (or 1 gram) in each of 10 differentcereals, including Cheerios, Corn Flakes, Fruit Loops, and 7others. These values are listed below. Is thestandard deviation of those values likely to be a good estimate ofthe standard deviation of the amounts of sugar in each gram ofcereal consumbed by the population of all Americans who eatcereal? Why or why not?
3, 24, 30, 47, 43, 7, 47, 13, 44, 39
Find the range, variance, standard deviation
Answer:
Range is 44
mean is 29.7
variance is 289.56
standard deviation is 17.016
Step-by-step explanation:
The data given as follows
3, 24, 30, 47, 43, 7, 47,13, 44, 39
Range = maximum - minimum
= 47 -3 = 44
mean = [tex]\frac{3+24+30+47+43+7+47+13+44+39}{10}[/tex] = 297/10 = 29.7
variance = [tex]\frac{sum xi^2 }{N} - mean^2 }[/tex]
= 289.56
SD = [tex]\sqrt{variance}[/tex] = 17.016
The standard deviation of the given data is not a good measure as the range and standard deviation are far apart. The standard deviation gives how the given data is dispersed from the mean or expected value, while the range gives a rough idea of variability of the data.
Please help me I’m really dumb
Answer:
d So yah plz tell me if I am right it has Ben a while since I have done this
Step-by-step explanation:
it is d so yah
There are 6 triangles and 2 circles. What is the simplest ratio of circles to triangles?
Answer:
6:2
Step-by-step explanation:
This simply means for every 6 triangles there are going to be 2 circles, so if you had 12 triangles there would be 4 circles.
So think of it kinda like:
6 triangles = 2 circles and so on.
Answer:
1:3
Step-by-step explanation:
Since the question says ratio of circles to triangles , we will arrange the answer in that order
So,
2:6
Breaking it down,
1:3
A pound of ground beef costs $5 At this rate, what is the cost of 3 pounds
Answer:
$15
Step-by-step explanation:
if one pound is $5 and we need 3, then we can multiply the price of one pound by 3. (3×$5) This gives $15
Miss Kito is building a rectangular pen for her lea.She will use the side of her house for one wall of the pen;therefore she will not need any fencing on that side.On the other three sides, she will use special fencing that costs $12 per foot . She wants the entire enclosed area to be 2400 square feet. Lastly,she needs four corner that costs $5 each ?
Let x represent the length of each side of the pen perpendicular to the house and let y represent the length of the side of the pen parallel to the house.Write a function c(x) for the cost of the materials for the llama pen in terms of x. Simplify
Please explain and thank you
Answer:
The answer is "[tex]=24x+ \frac{28800}{x}+20[/tex]"
Step-by-step explanation:
The perimeter of the fence [tex]=2x+y[/tex]
cost of fence[tex]=12(2x+y)[/tex]
cost of corner ports[tex]= 4 \times 5=20[/tex]
cost of pen[tex]= 24x+12y+80.............(1)[/tex]
area of pen[tex]=2400[/tex]
[tex]xy=2400\\\\y=\frac{2400}{x}[/tex]
cost c(x)[tex]=24x+ \frac{12 \times 2400}{x}+20[/tex]
[tex]=24x+ \frac{28800}{x}+20[/tex]
A company has Liabilities of $23,500 and Stockholders' Equity of $56,500. How much
does the company have in Assets?
Which best describes the error in solving the system of linear equations?
Only the x-value is given.
The wrong value for x is given.
The blue line is graphed incorrectly.
The red line is graphed incorrectly.
Answer:
a. Only the x-value is given.
Step-by-step explanation:
Taking a look at the graph of both equations, both equations are graphed correctly, because the slope (m) and y-intercept (b) values corresponds of each equation corresponds with what we have on the graph representing each equation.
The solution of two linear equations ought to be in a coordinate pair, (x, y). This means the x-value and it's correaponding y-value of the solution needs to be stated, not just the x-value.
Thus, the correct solution. Of the two linear equations are x = 4, when y = 3.
Solution in coordinate pair form is (4, 3).
Therefore, the statement that describes the error is:
a. Only the x-value is given.
how to find a inequality
vitamin c is 3/4 cup of orange juice
Answer:
Step-by-step explanation:
Vitamin c=3/4×cup of orange juice
hiii my dudeeeeeeeeeeee
Answer:hi how’s it going
Step-by-step explanation:
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
don’t understand sb help
Answer:
the 3rd one
Step-by-step explanation:
Answer:
It is the second one
Step-by-step explanation:
PLEASE ANSWERRRRRRRRRRRR
Answer:
Bertha picked up more than anica.
Step-by-step explanation:
10 1/3 = 10.33333 which is greater than anica
Compare using <,> or = 5 3/4 _ 6 1/4
Answer:
5 3/4 > 6 1/4
Step-by-step explanation:
When the following quadratic equation is written in standard form, what is the value of "c"?
Answer:
it's 2
Step-by-step explanation:
a= -3/4
b=0
c=2
An annual pass to a park costs $120. Use a percent model to find 200% of the full price of the annual pass.
200% of the full price is $____
Given:
An annual pass to a park costs $120.
To find:
The 200% of the full price using percent model.
Solution:
In the percent model,
100% = 1 box
It means 1 box represents park costs $120.
200% = 2 box
[tex]120+120=240[/tex]
It means 2 box represents park costs $240.
Therefore, 200% of the full price is $240.
BROOO HELP what is the slope of the line through (-3,3) and (-1,-1)?
A. 1/2
B. -1/2
C. -2
D. 2
Answer:
C
Step-by-step explanation:
We are given a line that contains the two points (-3, 3) and (-1, -1) and we want to determine the slope of the line.
To find the slope of a line given any two points, we can consider using the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are the two points.
We have the two points (-3, 3) and (-1, -1).
So, let (-3, 3) be (x₁, y₁) and let (-1, -1) be (x₂, y₂).
Substitute and evaluate:
[tex]\displaystyle\begin{aligned} m&=\frac{(-1)-(3)}{(-1)-(-3)}\\ \\ &= \frac{-1 -3 }{-1 + 3} \\ \\ &= \frac{-4}{2} \\ \\ &= -2\end{aligned}[/tex]
So, the slope of the line is -2.
In conclusion, our answer is C.
Answer:
m=-2
Step-by-step explanation:
Its just -2 I cant explain sorry
There are 279 middle school students signed up for a field trip. An adult needs to be assigned to guide every 8 students. Mr. Corcoran determines that 34 adults are needed for the field trip. Explain whether or not Mr. Corcoran is correct.
Answer:
No, because 3 students would be left over and we have to make an extra so 35. Mr.Smith is wrong.
Step-by-step explanation:
PLEASE HELP!!!!
IT IS NOT A
A. Yes; 20 hours/painter
B. Yes; 8 hours/painter
C. No; Does not pass through the origin
D. None of the above
Answer:
C
Step-by-step explanation:
Answer:
Pretty sure it's
D. None of the above