The derivative y′y′ at the point [tex]y'(-sqrt(e^(8-64))) = 7e^84/4097.[/tex]
To find the derivative of y with respect to x, we need to use the chain rule and the partial derivative of y with respect to x and y.
Let's begin by taking the partial derivative of y with respect to x:
[tex]∂y/∂x = 2x/(x^2 + y^2)[/tex]
Now, let's take the partial derivative of y with respect to y:
[tex]∂y/∂y = 2y/(x^2 + y^2)[/tex]Using the chain rule, the derivative of y with respect to x can be found as:
[tex]dy/dx = (dy/dt) / (dx/dt)[/tex], where t is a parameter such that x = f(t) and y = g(t).
Let's set[tex]t = x^2 + y^2[/tex], then we have:
[tex]dy/dt = 1/t * (∂y/∂x + ∂y/∂y)[/tex]
[tex]= 1/(x^2 + y^2) * (2x/(x^2 + y^2) + 2y/(x^2 + y^2))[/tex]
[tex]= 2(x+y)/(x^2 + y^2)^2[/tex]
dx/dt = 2x
Therefore, the derivative of y with respect to x is:
dy/dx = (dy/dt) / (dx/dt)
[tex]= (2(x+y)/(x^2 + y^2)^2) / 2x[/tex]
[tex]= (x+y)/(x^2 + y^2)^2[/tex]
Now, we can evaluate the derivative at the point [tex](-sqrt(e^(8-64)), 8)[/tex]:
[tex]x = -sqrt(e^(8-64)) = -sqrt(e^-56) = -1/e^28[/tex]
y = 8
Therefore, we have:
[tex]dy/dx = (x+y)/(x^2 + y^2)^2[/tex]
[tex]= (-1/e^28 + 8)/(1/e^56 + 64)^2[/tex]
[tex]= (-1/e^28 + 8)/(1/e^112 + 4096)[/tex]
We can simplify the denominator by using a common denominator:
[tex]1/e^112 + 4096 = 4096/e^112 + 1/e^112 = (4097/e^112)[/tex]
So, the derivative at the point (-sqrt(e^(8-64)), 8) is:
[tex]dy/dx = (-1/e^28 + 8)/(4097/e^112)[/tex]
[tex]= (-e^84 + 8e^84)/4097[/tex]
[tex]= (8e^84 - e^84)/4097[/tex]
[tex]= 7e^84/4097[/tex]
Therefore,the derivative y′y′ at the point [tex]y'(-sqrt(e^(8-64))) = 7e^84/4097.[/tex]
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To determine the derivative y′ of y=ln(x2+y2) at the point (−√e8−64,8)(−e8−64,8), we first need to find the partial derivatives of y with respect to x and y. Using the chain rule, we get: ∂y/∂x = 2x/(x2+y2) ∂y/∂y = 2y/(x2+y2)
Then, we can find the derivative y′ using the formula: y′ = (∂y/∂x) * x' + (∂y/∂y) * y'
Therefore, the derivative y′ at the point (−√e8−64,8)(−e8−64,8) is (8-√e8−64)/(32-e8).
Given the function y = ln(x^2 + y^2), we want to find the derivative y′ at the point (-√(e^8 - 64), 8).
1. Differentiate the function with respect to x using the chain rule:
y′ = (1 / (x^2 + y^2)) * (2x + 2yy′)
2. Solve for y′:
y′(1 - y^2) = 2x
y′ = 2x / (1 - y^2)
3. Substitute the given point into the expression for y′:
y′(-√(e^8 - 64)) = 2(-√(e^8 - 64)) / (1 - 8^2)
4. Calculate the derivative:
y′(-√(e^8 - 64)) = -2√(e^8 - 64) / -63
Thus, the derivative y′ at the point (-√(e^8 - 64), 8) is y′(-√(e^8 - 64)) = 2√(e^8 - 64) / 63.
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Select all the correct systems of equations. Which systems of equations have infinite solutions? 2x + 5y = 31 6x - y = 13 y = 14 - 2x 6x + 3y = 42 2x + y = 14 x = 13-2y Reset 2x + y = 10 -6x = 3y + 7 y = 13-2x 4x - 3y = -19 2x + y = 17 Next -6x = 3y - 51
Answer:
The system of equations y=14-2x and 6x+3y=42.
Step-by-step explanation:
Please see attachment to see the answer as a graph.
Hope this helps!
explain how the following problem could be solved. then, solve the problem. a full-grown dog is about one-eighth as heavy as a cow. together, they weigh 360 kg.
The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
The weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
We assume the weight of the cow to be x kg.
The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.
Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.
But, we are given that together, they weigh 360 kg.
This can be shown as the linear equation in the one variable:
x/8 + x = 360.
Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
To solve the problem, we solve the equation as follows:
x/8 + x = 360,
or, (9/8)x = 360 {Simplifying},
or, x = 360*8/9 {Cross-Multiplying},
or, = 320.
Thus, the weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
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What is the slope?
Please help!! Thankss
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0,2) ← 2 points on the line
m = [tex]\frac{2-0}{0-(-1)}[/tex] = [tex]\frac{2}{0+1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
Choose the equation that satisfies the data in the table.
X -1
0 1
Y
0
-4 -8
-
OA. y = 4x - 4
OB.y = -x +4
Oc.y=x+4
D. y = -4x - 4
The equation that satisfies the data in the table is,
y = -4x - 4 [Option D]
Definition of an Equation:
An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.
The (x, y) coordinates from the given table are,
(-1,0), (0, -4), (1, -8)
Now, these points must satisfy the required equation.
Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.
Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.
Taking the fourth equation, y = -4x - 4
Putting x = -1 in this equation, we get,
y = -4(-1) - 4
y = 4 - 4
y = 0
Likewise, this equation satisfies the rest of the data in the table too.
Therefore, y = -4x - 4 is the required equation.
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Graph and label each of the ordered pairs in the coordinate plane. Then state the quadrant
or axis in/on which the point is located.
55. A(2, 4)
56. B(0, -3)
57. C(1, -1)
59. E(-4,1)
61. G(-3,-2)
63. I(0, 2)
58. D(3, 3)
60. F(2,0)
62. H(-2, 3)
64. J(-1,-4)
The quadrants of the points are
Quadrant 1: Points A and DQuadrant 2: Points E and HQuadrant 3: Points G and JQuadrant 4: Points Cx-axis: Point Fy-axis: Point B and IHow to determine the quadrants?The points are given as:
A(2, 4) B(0, -3) C(1, -1)
E(-4,1) G(-3,-2) I(0, 2)
D(3, 3) F(2,0) H(-2, 3)
J(-1,-4)
Next, we plot each coordinate on a graph (see attachment)
From the attached graph, we have the following categories
Quadrant 1: Points A and D
Quadrant 2: Points E and H
Quadrant 3: Points G and J
Quadrant 4: Points C
x-axis: Point F
y-axis: Point B and I
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Find the digits x and y such that number 90x0y07 is divisble by 2017
No digit with the format 90x0y07 is divisible by 2017
How do determine the digits x and y?The given parameters are:
Dividend = 90x0y07
Divisor = 2017
The dividend is a 7-digit number, and the divisor is a 4-digit number
So, the quotient must be 3 to 4 digits.
Comparing the first and last digits of 90x0y07 and 2017;
The first and last digits of the quotient must be 4 and 1, respectively
So, we have:
90x0y07 = 2017 * 4a1
Assume a = 9.
So, we have:
90x0y07 = 2017 * 491
90x0y07 = 990347
The above is 6-digit.
So, we make use of a 4-digit quotient
This gives
90x0y07 = 2017 * 4ab1
Next, we make use of trial by error.
After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017
The closest attempt is
90x0y07 = 2017 * 4471
90x0y07 = 9018007
Where:
x = 1, y = 0 and the digit between x and y is 8, not 0
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How do I get started on the second part
The function to calculate the speed is S = 260.52/t.
How to illustrate the information?From the information given, there are 78 laps through the Monte Carlo and each lap has a distance of 3.34 km. Therefore, the total length of the race will be:
= 78 × 3.34
= 260.52km
The function to calculate the speed will be:
Speed = Distance/Time
S = 260.52/t
Complete question:
The famous Grand Prix has 78 laps through the Monte Carlo and each lap has a distance of 3.34 km.
a. What is the total length of the race?
b. Write a function that can be used to model the race where the independent variable represent the average speed.
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If the probability that the person A will be alive for 30 years is 0.7 and the probability that the person B will be alive for 30 years is 0.5, what is the probability that they both will be alive for 30 years?
0.24
1.2
0.15
0.35
Answer:
[tex]0,35[/tex]
Step-by-step explanation:
In view of the fact that our events are independent of each other, we should multiply their probabilities: [tex]P(A \cap B) = P(A) * P(B) = 0,7 * 0,5 = 0,35[/tex].
round to the hundredths pl[tex]2÷6.3[/tex]ace
The value of the expression [tex]2 \div 6.3[/tex] is 0.32
How to solve the expression?The expression is given as:
[tex]2 \div 6.3[/tex]
Rewrite as:
[tex]2 \div 6.3= \frac{2}{6.3}[/tex]
Multiply the expression by 10/10
[tex]2 \div 6.3= \frac{20}{63}[/tex]
Divide 20 by 63
[tex]2 \div 6.3= 0.31746031746[/tex]
Approximate to the nearest hundredth
[tex]2 \div 6.3= 0.32[/tex]
Hence, the value of the expression [tex]2 \div 6.3[/tex] is 0.32
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Find the area of a circle with radius, r =
6.05m.
Give your answer rounded to 2 DP.
r
The diagram is not drawn to scale.
m²
Answer:
Step-by-step explanation:
The area of a circle is πr²
so your area is 114.99
identify and shade the following regions on separate venn diagram
The attached figures represent the shaded areas of the given set operations
How to identify the shaded regions?To shade the given regions of the sets, we need to highlight the following set operations
Intersection: This represents the elements that are common between two or more setsUnion: This represents the totality of all elements in two or more sets (without repetition of elements)Complement: This represents the elements that are not present in the given setUsing the above definition of set operations and the Venn diagram, we have the following values:
X U Y' = Y'X n Y' = ∅ i.e an empty set(X U Y)' = X' n Y'(X n Y)' = U i.e. the universal setX' U Y' = X' n Y'X' n Y' = X' U Y'(X' U Y)' = X(X U Y')' = YSee attachment for the shaded areas of the above set operations
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Your dad says you can have a new puppy if you build the dog house. Before building, you need to determine the dimensions. Choose the dimensions of the base, the length, and the width of the dog house. Choose dimensions that you think are reasonable for whatever type of puppy you would get. Once you plan the base and walls, you need to decide on the height of the roof (represented by the dotted line in the image below). The roof is a triangle with two sides that are the same length.
Find the height of the roof using the dimensions you chose. You are hoping to put shingles on the roof and need to know what the square footage of the roof will be. Use the dimensions to calculate the area of the roof.
Hint: Remember to find the area of the entire roof.
The area of Entire roof is 12 feet².
What is Pythagorean theorem?The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)
Given:
As, the roof peak with a 3 and the roof overhang the sides is 4.
Now, Using Pythagorean theorem.
a² + b² = c ²
15² + 13² = c²
c² = 225+ 169
c = 19.8 (or 20)
So, the length of diagonal is 24.
Roof Dimension 36 x 24 or (
Area of Roof = 3 x 2
= 6 unit²
and, area of the entire roof = 2 x6 = 12 ft²
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2. If you use AB as the base to find the area of ABCD shown at the right, what should you use as the height?
The height that should be used is DE
Area of a parallelogramFrom the question, we are to determine what should be used as the height
The area of a parallelogram is given by the formula,
A = b × h
Where A is the area
b is the base
and h is the perpendicular height
In the given diagram, if AB is used as the base, then the height that would be used will be DE. This is because DE is perpendicular to AB
Hence, the height that should be used is DE
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please help me.--------------------------------
Answer:
tan 33° = 0.6494
C = 65°
Step-by-step explanation:
Use a calculator.
tan 33° = 0.6494
cos C = 0.4226
Use the inverse cosine function on a calculator.
C = 65°
Hi Guys!
I need help ASAP
Answer:
8.
Step-by-step explanation:
P/Q = 3.125 = 3 1/8
- looks like the denominator Q could be 8.
It could not be any of the other choices.
25/8 = 3.125.
The tree diagram represents an experiment consisting of two trials. P(C) = [?]
The value of the probability P(A and C) is 0.18
How to determine the probability?The complete question is added as an attachment
From the attached tree diagram, we have:
P(A) = 0.6
P(C) = 0.3
The required probability is then calculated as:
P(A and C) = P(A) * P(C)
This gives
P(A and C) = 0.6 * 0.3
Evaluate
P(A and C) = 0.18
Hence, the value of the probability P(A and C) is 0.18
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Write an expression, of the type A log(x B), for the transformed logarithmic function shown below:
The equation of the logarithmic function is y = log(x - 1)
How to write the equation of the transformed function?The points are given as:
(0,3) and (2,0)
The equation is represented as:
y = A log(x + B)
Substitute (2,0) in y = A log(x + B)
y = A log(x + B)
This means that:
0 = A log(2 + B)
This means that:
A = 0 or log(2 + B) = 0
Take the antilog of both sides of log(2 + B) = 0
2 + B = 1
Solve for B in 2 + B = 1
B = -1
Substitute B = -1 in y = A log(x + B)
y = A log(x - 1)
Substitute (0,3) in y = A log(x - 1)
3 = A log(0 - 1)
So, we have:
3 = A log(-1)
The above equation is undefined.
Hence, the equation of the logarithmic function is y = log(x - 1)
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Complete question
Write an expression, of the type A log(x + B), for the transformed logarithmic function shown below:
(0,3) and (2,0)
The number of bagels sold daily for two bakeries is shown in the table.
Bakery A Bakery B
53 34
52 40
50 36
48 38
53 41
47 44
55 40
51 39
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below. (5 points)
Group of answer choices
A) Mean, because there are no outliers to affect the data
B) Mean, because the distribution is perfectly symmetric for both bakeries
C) Median, because the distribution for Bakery B is not symmetric
D) Median, because there are outliers that affect both data sets
The correct statement based on the data is: A. Mean, because there are no outliers to affect the data.
What are Outliers?Outliers are data point that appears extreme from other data values of a data distribution. When there is an outlier in a data distribution, the median is a better measure of center, while the mean is best when outliers are absent.
From the data distribution for both bakeries, no data seem extreme from the rest of the data, therefore, the mean is a better measure of center.
The answer is: A. Mean, because there are no outliers to affect the data.
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Ed records the temperature of two pots of water. The pots are the same size and material. Pot X has a temperature of 56 degrees Fahrenheit, and pot Y has a temperature of 49 degrees Fahrenheit. What conclusion can Ed make about the pots of water
Answer:
The water in pot X is hoter than that of pot Y
Answer:
A is the answer
Step-by-step explanation:
Which equation represents a direct variation?
A.y = 0.5 x
B.x minus y = 5
C.x y = 5
D.y = x + 5
Answer:
A.
Step-by-step explanation:
i'm 99% sure
Answer:
A. y = 0.5x
Step-by-step explanation:
i got it right
write the slope-intercept form of the equation of each line
1. x-3y = 6
2. 4x-y = 1
3. 6x+5y = -15
4. 13x- 11y =-12
Answer:
y = [tex]\frac{1}{3}[/tex]x - 2y = 4x - 1y = -[tex]\frac{6}{5}[/tex]x - 3y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]Step-by-step explanation:
The slope-intercept form is y = mx + b, where m represents the slope and b represents the intercept.
x - 3y = 6
3y = x - 6
y = [tex]\frac{1}{3}[/tex]x - 2
4x - y = 1
y = 4x - 1
6x + 5y = -15
5y = -6x - 15
y = -[tex]\frac{6}{5}[/tex]x - 3
13x - 11y = -12
11y = 13x + 12
y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]
Help ASAP!!! Geometry, “fill in the blanks”
Skew lines and parallel lines do not intersect
How to determine the skew lines?As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect
Using the above definition as a guide, the skew lines in the figure are:
CG and BDAE and FHEG and DHThe difference between skew lines and parallel linesParallel lines and skew lines are different in the following ways:
Skew lines are on different planesParallel lines are on the same planeThe likeness between skew lines and parallel linesParallel lines and skew lines are alike in the following way:
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PLEASE HELP QUICK!!!!!!!
The Science Club arranged a trip tot he Smithsonian. Only 2/3 of the members were able to attend, which left one seat empty on the 25-passenger bus. How many members does the Science Club have?
Answer:
There are 36 members in the Science Club.
Step-by-step explanation:
25 minus one is 24 and half of 24 is 12. 12 times 3 is 36, which is the full 3/3 of the Science Club.
Equivalent ratios what’s the answer
3:6=
Step-by-step explanation:
you multiply both sides by the same factor, so that the main message or information, the ratio, stays the same :
3:6 × 2/2 = 6:12
3:6 × 1/3 / 1/3 = 1:2
3:6 × 4/3 / 4/3 = 4:8
3:6 × 100/100 = 300:600
so, these are all equivalent ratios. and there are infinitely more, as you can see.
If a researcher needs a sample that is representative of the population they are studying, they could utilize a _______.
The researchers could utilize a probability sample.
Meaning of a Probability Sample
Every member of a population must have an equal chance of being chosen for a study in order for a sample to be considered a probability sample, and the researcher must be aware of this likelihood. The most typical type of sampling used in public opinion research, election polling, and other studies whose findings will be generalized to a larger population is probability sampling in which probability samples are made use of.
Probability Sample as the Representative of Population Sample
Here, a sample that qualifies for a representative of the population the researchers are studying, must consist of members having equal chances to be chosen for the study. Thus, a probability sample is the best representative of their study population.
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Kawan buys some protein bars at $0.90 each and bottled water at $0.70 each for a group hike. He buys twice as many bottles of water as protein bars. If he spends $46 in total, how many bottles of water and protein bars does he buy? Let x= the number of protein bars
Answer:
he buts 20 protein bars and 40 water bottles
Step-by-step explanation:
so first u set up an equation like this
46=.90x+.70(2x)
next you multipy
46=.90x+1.4x
Then add
46=2.3x
then divide by 2.3 to solve for x
x=20 so u have 20 protein bars
and 20 times 2 to find the amount of water bottles
Answer:
20 Protein bars and 40 waters.
Step-by-step explanation:
Let x = protein bars and y = waters
y = 2x .9x + .7 y = 46
Looking at the second equation, I would rather not work with decimals, so I will multiple the whole equation through by ten. That now gives m
9x + 7y = 460 Substitute in 2x for y (from my first equation above)
9x + 7(2x) = 460
9x +14x = 460 Combine 9x and 14x
23x = 460 Divide both sides by 23
x = 20 This is the number of protein bars. To find y plug 20 into the first equation above.
y = 2x
y =20(2)
y = 40
An igloo can be modeled as a hemisphere. Its radius measures 6.3 m. Find its volume in cubic meters. Round your answer to the nearest tenth if necessary.
The volume of the igloo is 523.43 m^3
How to get the volume of the igloo?We know that the volume of a sphere of radius R is:
[tex]V = (4/3)*pi*R^3[/tex]
Where pi = 3.14
Then the volume of a hemisphere is half of that.
In this case, we have a hemisphere with a radius of 6.3m, then the volume will be:
[tex]V = (1/2)*(4/3)*3.14*(6.3m)^3 = 523.43 m^3[/tex]
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Find the center and radius of the circle with the equation: (x-0^2 + (y+1)^2 = 4
a.
center: (-5, 1)
radius: 4
c.
center: (-5, 1)
radius: 2
b.
center: (5, -1)
radius: 4
d.
center: (5, -1)
radius: 2
The center and radius of the circle is (b) center: (-5, 1) radius: 2
How to determine the center and the radius?The circle equation is given as:
(x-5)^2 + (y+1)^2 = 4
The circle equation is represented as:
(x-a)^2 + (y-b)^2 = r^2
Where:
Center = (a,b)
Radius = 4
By comparison, we have:
(a, b) = (-5, 1)
r^2 = 4
This gives
(a, b) = (-5, 1)
r = 2
Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2
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Plss help give brainiest if right!
the speed of the boat going with a current is 20 mph. when the
boat goes against the current, the speed is 16 mph. find the speed of
the boat in still water and the speed of the current.
Answer:
The speed of the boat in still water is 18 mph.
The speed of the current is 2 mph
Step-by-step explanation:
Let x constitute the charge of the boat in nonetheless water.
Let y constitute the rate of the contemporary.
When the boat is going against the modern-day, the rate is sixteen mph. Assuming it traveled against the modern at the equal time as going upstream, its general speed may be (x - y) mph. It way that
x - y = 16 (equation 1)
Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its standard pace would be (x + y) mph. It way that
x + y = 20 (equation 2)
Adding each equation, it becomes
2x = 36
x = 36/2
x = 18 mph
Substituting x = 18 into equation 1, it will become
18 - y = 16
y = 18 - 16
y = 2 mph
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pls help i’ll give brainliest
Answer: y=-1/5x+ 8/5 (Third one down)