If x² + xy – 3y = 3, then at the point (2, 1), dy/dx
(A) 5
(B) 4
(C) 7/3 (D) 2
Answers
Answer:
A
Step-by-step explanation:
We are given the equation:
\(x^2+xy-3y=3\)
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:
\(\displaystyle \frac{d}{dx}[x^2+xy-3y]=\frac{d}{dx}[3]\)
Implicitly differentiate:
\(\displaystyle 2x+y+x\frac{dy}{dx}-3\frac{dy}{dx}=0\)
Solve for dy/dx:
\(\displaystyle \begin{aligned} x \frac{dy}{dx} - 3\frac{dy}{dx} & = -2x - y \\ \\ \frac{dy}{dx}(x - 3) & = -2x - y \\ \\ \frac{dy}{dx} & = \frac{-2x-y}{x-3} \\ \\ & = \frac{2x+y}{3-x} \end{aligned}\)
To find dy/dx at (2, 1), evaluate dy/dx for x = 2 and y = 1. Hence:
\(\displaystyle \frac{dy}{dx}\Big|_{(2, 1)}=\frac{2(2)+1}{3 - (2)}=\frac{5}{1}=5\)
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.
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Related Questions
Only the bottom one please help solve and check
Answers
Answer:
3
Step-by-step explanation:
16+5f=31
5f=31-16
5f=15
f=3
CHECK:
16+5(3)=31
16+15=31
31=31
since e=-14 in the first equation, the last one is
-14-3=-17, which is correct
The total revenue for Jane's Vacation Rentals is given as the function R(x)=400x−0.4x2
, where x is the number of apartments booked. What number of apartments booked produces the maximum revenue?
Answers
The vertex of a quadratic function in the form ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, a = -0.4, b = 400, and c = 0.
Using the formula, we can calculate the x-coordinate of the vertex:
x = -b / (2a)
= -(400) / (2 * (-0.4))
= -400 / (-0.8)
= 500
Therefore, the number of apartments booked that produces the maximum revenue is 500.
Given the point with Cartesian coordinates, (−7√3/2,7/2), find the polar coordinates of the point.
Select the correct answer below:
(7,4π/3)
(7,11π/6)
(3,4π/3)
(3,5π/6)
(3,11π/6)
(7,5π/6)
Answers
Answer: the last option is correct
Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.
Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:
r = √((-7√3/2)^2 + (7/2)^2)
θ = atan2(7/2, -7√3/2)
Simplifying the expressions:
r = √(147/4 + 49/4) = √(196/4) = √49 = 7
θ = atan2(7/2, -7√3/2)
Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:
θ ≈ 5π/6
So the correct answer is: (7, 5π/6), which is option (6).
ALGEBRAA!! HELP!!
Wich one is an identity, wich one is an equation, wich one is an expression and wich one is a formula?
3x+4y
3+2=5
A=bh
3x=15
Answers
3x+4y. is expression
3+2=5. is an identity
A=bh is a formula
3x=15 is equation
2. Identity
3. Formula
4. Equation
Which expressions are completely factored?
Select each correct answer.
Responses
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
Answers
Hello!
12a³ + 8a = 4(3a³+2a) = 4a(3a² + 2)
30a⁶ - 24a² = 6(5a⁶ - 4a²) = 6a²(5a⁴ - 4)
24a⁴ + 18 = 6(4a⁴ + 3)
16a⁵ - 20a³ = 4a³(4a² - 5)
So the correct answers are:24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
…aniwwjwwjaoqkqwgahw qjauaaj
Answers
Answer:
Undefined
Step-by-step explanation:
Lim x - - > 1(1 /In(2-x) + 1/(x-1))
To find the limit as x tends to 1
Substitute x = 1 into the function ;
(1 / In(2 - 1) + 1 / (1 - 1))
(1 / In 1) + (1 / 0)
1 / 0 + 1 / 0
Undefined
What inequality is shown by the graph?
Answers
6 sin =5 solve to the nearest 0.1
Answers
Step-by-step explanation:
sin Φ = 5/6 = .8333
Arcsin ( sin Φ) = arcsin (.8333)
Φ = 56.4 degrees
the volume of a pyramid is given by the formula V=1/, where B is the area of the base and h is the height?
Answers
Answer:
Step-by-step explanation:
The volume of this pyramid in cubic inches is 16.
Given that,
The base and height is 8 and 6.
Based on the above information, the calculation is as follows:
The volume is
= 16
Find the value of x. You may assume triangle ABC is similar to triangle STU.
(click on the photo to make it better quality) PLEASE HELP!!!
Answers
By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.
In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.
Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:
angle BAC = angle STU
4x = 100
To find the value of x, we divide both sides of the equation by 4:
x = 100/4
x = 25
Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.
For more such questions on triangle
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A plumber charges $50 to make a house call. He also charges $25 per hour for labor. If the bill from the plumber is $162.50.
How many hours did the plumber work at your house?
Answers
112.50/25= 4.5
The largest frog in the world is the goliath, It can grow to be 12 inches long. The smallest frog in the world is about 2.5% as log as the goliath. About how long is the smallest frog in the world
Answers
Answer:
0.3 inches
Step-by-step explanation:
2.5% = 0.025
The smallest frog is 12 * 0.025 inches, which is 0.3 inches.
PLEASE HELP EASY!!!!!!
Answers
Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.
What salary will workers have in each salary?Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.
On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.
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The phrase "linear regression" pertains to regression models with normal equations that can be expressed in matrix form using linear algebra to determine coefficient estimates.
A. True
B. False
Answers
Answer:
TRUE ( A )
Step-by-step explanation:
linear regression represents/ models the linear relationship between a dependent/scalar variable and an independent variable or one or more independent variables
Linear regression pertains to regression models with normal equations because Linear regressions can be calculated using a linear equation/algebra
example : Y= a + bX
Solve for the unknown. q- 5/6=1 5/6
Answers
Answer:
q=8/3
Step-by-step explanation:
First, add 5/6 to both sides to get rid of -5/6 to get q=16/6 then simplify to q=8/3.
Answer:
\(q=2\frac{2}{3}\)
Step-by-step explanation:
The given equation consists of a fraction and a mixed number.
First, convert the mixed number into an improper fraction by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
\(q-\dfrac{5}{6}=1 \frac{5}{6}\)
\(q-\dfrac{5}{6}=\dfrac{1 \cdot 6+5}{6}\)
\(q-\dfrac{5}{6}=\dfrac{11}{6}\)
Now, add 5/6 to both sides of the equation to isolate q:
\(q-\dfrac{5}{6}+\dfrac{5}{6}=\dfrac{11}{6}+\dfrac{5}{6}\)
\(q=\dfrac{11}{6}+\dfrac{5}{6}\)
As the fractions have the same denominator, we can carry out the addition by simply adding the numerators:
\(q=\dfrac{11+5}{6}\)
\(q=\dfrac{16}{6}\)
Reduce the improper fraction to its simplest form by dividing the numerator and denominator by the greatest common factor (GCF).
The GCF of 16 and 6 is 2, therefore:
\(q=\dfrac{16\div 2}{6 \div 2}\)
\(q=\dfrac{8}{3}\)
Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:
\(q=2 \; \textsf{remainder}\;2\)
The mixed number answer is the whole number and the remainder divided by the denominator:
\(q=2\frac{2}{3}\)
I need help with this please
Answers
Answer:
30°
Step-by-step explanation:
cos Ф = 35/38
arccos (.92105) = 30°
how many solutions does the eqaution below have? 4x-3-2x+5=6-3x+2+5x
Answers
Answer:
4x - 3 - 2x + 5 = 6 - 3x + 2 + 5x
2x + 2 = 2x + 8
2 ≠ 8, so this equation has no solutions.
Answer:
No solution
Step-by-step explanation:
Given:
\(4x-3-2x+5=6-3x+2+5x\)
rearrange terms so like terms are together
\(4x-2x-3+5=6+2-3x+5x\)
combine like terms
\(2x+2=8+2x\)
subtract 2x to both sides
\(2\neq 8\)
2 doesn't equal 8, meaning that there are 0 solutions to this problem.
Hope this helps! :)
Solve for x. Please help me!!
Answers
Answer:
64 degrees
Step-by-step explanation:
90-32=58
180-58-58=64
Answer:
x = 64°
Step-by-step explanation:
supplementary angles is two angles whose sum is 180° (straight line)
90 + 32 = 122°
To find angle A,
A + 122 = 180
subtract 122 from both sides,
A + 122 - 122 = 180 - 122
A = 58°
This is an isosceles triangle, two angles are equal in measure (A and B). These angles lie opposite to the equal sides.
A triangles angles add up to 180°
58° + 58° + x° = 180°
116° + x = 180°
116 - 116 + x = 180 - 116
x = 64°
Ten canoeing teams are racing downriver. Five teams have silver canoes and 2 teams have brown canoes.what Fraction of the canoes are either silver or/ and brown?
Answers
The fraction of silver or brown canoes is 7/10.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Total canoes team = 10
5 teams have silver canoes team.
2 teams have brown canoes team.
Now,
The fraction of silver and brown canoes.
= (5 + 2) / 10
= 7/10
Thus,
7/10
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A computer costs £968. A tax of 16.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.
Answers
The amount of tax that is added to the cost of the computer is 159.72
How to determine the amount of tax that is added to the cost of the computer.From the question, we have the following parameters that can be used in our computation:
Computer cost = 968
Tax percentage = 16.5%
Using the above as a guide, we have the following:
Tax amount = Computer cost * Tax percentage
substitute the known values in the above equation, so, we have the following representation
Tax amount = 968 * 16.5%
Evaluate
Tax amount = 159.72
Hence, the amount of tax that is added to the cost of the computer is 159.72
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I need a help with this hw
Answers
The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5 d ) -25/12
What is trigonometric ratio?
Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent. Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse
the give parameters are:
tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2
a) sin(α+β)
Using the trig ratios tan = opp/adj
but from pyth. rule, 4² + 3² = h²
16+9 = h²
h = √25 = 5
Now from trig Sin(α+β)
4/5 + 3/5
=- 7/5
b) cos(α+β)
cos = ad/hypo
4/5 + 3/5
= -7/5
c) Sin(α-β)
4/5 - 3/5
-1/5
d) tan(α-β)
= -4/3 - 3/4
= (-16 - 9)/ 12
-25/12
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a bus is traveling at a constant speed if the bus travels 15 1/2 miles in 1/3 of an hour how many miles will the bus travel in one hour
Answers
Answer:93/2 or 46 1/2
Step-by-step explanation:
15 1/2 ✖️3
The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.
Answers
Answer:
d. 25.25.
Step-by-step explanation:
A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.
Maria has 8 more scarves than Lucy Lucy has 8 scarves. How many scarves does Maria have, write an equation?
Answers
The equation M = 8 + 8 represents the given information. Maria has 16 scarves.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's let "M" represent the number of scarves that Maria has.
According to the problem, "Maria has 8 more scarves than Lucy." We know that Lucy has 8 scarves. So, Maria has 8 more than that.
We can represent this information in an equation:
M = 8 + 8
We add 8 to Lucy's 8 scarves to get the total number of scarves that Maria has, which is 16.
So, Maria has 16 scarves.
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The required Maria has 16 scarves, and the expression models the situation is given as M = 8 + L.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's use the variable "M" to represent the number of scarves that Maria has. Since Maria has 8 more scarves than Lucy, and Lucy has 8 scarves, we can write an equation as,
M = 8 + L
where L is the number of scarves that Lucy has. Substituting L = 8 into this equation, we get:
M = 8 + 8
M = 16
Therefore, Maria has 16 scarves.
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plz help me will br
Answers
16x=320
X=20
a local hamburger shop sold a combined total of 641 hamburgers and cheeseburgers on sunday. there were 59 fewer cheseburgers sold than hamburgers. how many hamburgers were sold on sunday?
Answers
Answer: 700 Hamburgers
Answer:
I believe the answer is 700
The Smith family pays a rate of 27 mills in property tax. The assessed value of their home is $98,000. What is their property tax?
Answers
Their property tax would be =$ 26,460
Calculation of property taxA mill is one-thousandth of a dollar, and in property tax terms is equal to $1.00 of tax for each.
Therefore 27 mills = $27 for every $1,000 of assessed value, or 2.7%.
To calculate the property tax would
= 27/100× 98,000
= 2646000/100
=$ 26,460
Therefore, Their property tax would be =$ 26,460
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learning task 5. identify what is asked item below.
1.what number i am between 21 and 31 a multiple of 4 and 7
Answers
A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the perimeter and the area
Answers
Answer:
Parameter= 98ft
Area=180ft^2
Step-by-step explanation:
Parameter= Length times 2 plus width times 2 or
L2+W2=P 4(2)+45(2)=8+90=98
Area= LxW=A^2
4x45=180^2
Perimeter = 2(45 + 4)
Perimeter = 2(49)
Perimeter = 98 feet
Area = length x width
Area = 45 x 4
Area = 180 square feet
Write the following numbers in order, putting the largest
first:
a)
31 009
31.53
31. 099
b)
0.007
0.03
0.009
Answers
Answer:
a)
31.53
31.099
31.009 ⬅ (I'm assuming this one is a decimal too)
b)
0.03
0.009
0.007
Explanation:
Here ya go.
Hope this helps :)