In problems 1 - 10 find dy/dx by differentiating implicitly then find the value of dy/dx at th given point 1. x2 + y2 = 100, point (6, 8) 2. x² + 5y = 45, point (5,2) 3. x2 – 3xy + 7y=5 , point (2,1) 5. B + = 1 , point (0,4) 7. In(y) + 3x – 7 = 0 , point (2,e) 4. Vx + Vy = 5 , point (4,9) 0B + B = 1, point (3,0) 8. x2 - y2 = 16 , point (5,3) 9. x2 - y2 = 16 , point (5, -3) 10.y2 + 7x3 - 3x = 8 , point (1,2) x = 4y-y 11. Find the slopes of the lines tangent to the graph in shown at the points (3,1), (3,3), and (4,2). (4,2) 12. Find the slopes of the lines tangent to the graph in shown where the graph crosses the y-axis. (31)
Answers
The differentiation of function x^2 + y^2 = 100 is -3/4. The differentiation of function x^2 + 5y = 45 is -2. The differentiation of function x^2 - 3xy + 7y = 5 is 4/11.
Differentiating both sides of x^2 + y^2 = 100 with respect to x using implicit differentiation, we get:
2x + 2y(dy/dx) = 0
Solving for dy/dx, we get:
dy/dx = -x/y
At point (6,8), x = 6 and y = 8, so:
dy/dx = -6/8 = -3/4
Differentiating both sides of x^2 + 5y = 45 with respect to x using implicit differentiation, we get:
2x + 5(dy/dx) = 0
Solving for dy/dx, we get:
dy/dx = -2x/5
At point (5,2), x = 5, so:
dy/dx = -2(5)/5 = -2
Differentiating both sides of x^2 - 3xy + 7y = 5 with respect to x using implicit differentiation, we get:
2x - 3y - 3x(dy/dx) + 7(dy/dx) = 0
Solving for dy/dx, we get:
dy/dx = (3x - 2y)/7x - 3y
At point (2,1), x = 2 and y = 1, so:
dy/dx = (3(2) - 2(1))/[7(2) - 3(1)] = 4/11
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--The complete question is, Find dy/dx by implicit differentiation and then evaluate at the given point:
a. x^2 + y^2 = 100, point (6,8)
b. x^2 + 5y = 45, point (5,2)
c. x^2 - 3xy + 7y = 5, point (2,1)--
Related Questions
In ΔOPQ, q = 6.5 inches, o = 8.6 inches and ∠P=55°. Find ∠Q, to the nearest 10th of an degree.
Answers
Answer:
∠Q = 35.5°
Step-by-step explanation:
We are given;
q = 6.5 inches
o = 8.6 inches
∠P = 55°
Let's first use cosine rule to find p.
p² = q² + o² - 2qo cos P
Plugging in the relevant values;
p² = 6.5² + 8.6² - (2 × 6.5 × 8.6 × cos 55)
p² = 42.25 + 73.96 - 32.0629
p² = 84.1471
p = √84.1471
p = 9.17 inches
Using sine rule, we can find ∠Q;
p/sin P = q/sin Q
sin Q = (q•sinP)/p
sin Q = (6.5 × sin 55)/9.17
sin Q = 0.5806
Q = sin^(-1) 0.5806
Q ≈ 35.5°
Answer:
47.5
Step-by-step explanation:
From delta math
Each of the following is a sugar EXCEPT:
А
Lactose
B
Maltose
C
Fructose
D
Sucralose
Answers
Lola's school is 2.8 kilometers west of her house and 8.4 kilometers south of her friend Deion's house. Every day, Lola bicycles from her house to her school. After school, she bicycles from her school to Deion's house. Before dinner, she bicycles home on a bike path that goes straight from Deion's house to her own house. How far does Lola bicycle each day? If necessary, round to the nearest tenth.
Answers
The distance that Lola bicycles each day totals to the nearest tenth to 20.1 km.
Given that,
Lola's school is 2.8 kilometers west of her house and 8.4 kilometers south of her friend Deion's house.
Using the Pythagoras theorem,
Distance between Lola's house and her friend Deion's house is,
D = √(2.8)² + (8.4)² = √78.4 = 8.854
Total distance she travels in a day = 2.8 + 8.4 + 8.854
= 20.054 km ≈ 20.1 km to the nearest tenth.
Hence the total distance is 20.1 km.
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Solve for X show your work
Answers
Answer:
Step-by-step explanation:
Using the side proportionality rule of triangles, we can see that the side with length 6 has a \(\frac{2}{3}\) ratio to the side with length 9. We can use the same principle to determine that the side length of 2 is two thirds to side length x. We can set up an algebraic equation to find the value of x: \(\frac{2}{3} x=2\). If we multiply both sides by 3, we get \(2x=6\), therefore x = 3
PLEASE HELP!! WILL GIVE BRAINLEST ANSWERS
Answers
Answer:
4th one
Step-by-step explanation:
it is the 4th one
Use the drawing tool(s) to form the correct answers on the provided number line.
Yeast, a key ingredient in bread, thrives within the temperature range of 90°F to 95°FWrite and graph an inequality that represents the temperatures where yeast will NOT thrive.
Answers
The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F
Writing an inequality of the temperatures where yeast will NOT thrive.from the question, we have the following parameters that can be used in our computation:
Yeast thrives between 90°F to 95°F
For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range
Using the above as a guide, we have the following:
T < 90°F or T > 95°F.
Where
T = Temperature
Hence, the inequality is T < 90°F or T > 95°F.
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find the inverse
will mark brainliest
Answers
Answer:
\(f^{-1} (x) = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }\)
Step-by-step explanation:
Let f(x) = y
Interchange x and y so
\(x = \frac{1}{\sqrt{y^{3} + 9 } }\)
\(x\sqrt{y^{3} + 9} = 1\)
\(\sqrt{y^{3} + 9 } = \frac{1}{x}\)
\(y^{3} + 9 = \frac{1}{x^{2} }\)
\(y^{3} = \frac{1}{x^{2} } - 9\) = \(\frac{1 - 9x^{2} }{x^{2} }\)
\(y = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }\)
\(f^{-1} (x) = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }\)
help me out plzzzzzz
Answers
Answer:
A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Step-by-step explanation:
To factor this, you are looking for factors of 8×21 = 168 that have a sum of 34.
168 = 1×168 = 2×84 = 3×56 = 4×42 = 6×28 = 7×24 = 8×21 = 12×14
The sums of these factor pairs are 169, 86, 59, 46, 34, 31, 29, 26. The factor pair whose sum is 34 is 6×28. This means we can rewrite the expression as ...
8x² +28x +6x +21
Factoring by pairs gives ...
4x(2x +7) +3(2x +7)
(4x +3)(2x +7) ⇒ A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Answer:
......................
40 POINTS PLS HELP PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS /J IM LAZY NO PLS HELP
Answers
Answer:
y = -0.5x - 3.5
Explanation:
Take two points: (1, -4), (3, -5)
Find slope:
\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)
\(\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}\)
Equation:
\(\sf y- y_1 = m (x - x_1)\)
\(\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)\)
\(\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}\)
\(\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4\)
\(\rightarrow \sf y = -0.5 x -3.5\)
The formula of a line is:
\(f(x) = kx + b\)
k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.
We can see 2 points:
A (1, -4)
B (3, -5)
We can make a system of equations:
\(k*1+b=-4\\k*3+b=-5\\\)
From second equation:
\(b = -5 - 3k\)
Let's put b in first equation:
\(k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}\)
Now we can find b:
\(b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5\)
The answer is:
-0.5x -3.5
Grandma baked 96 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received c fewer cookies than she would have received had all of the cookies been evenly divided among the 8 grandchildren.How many cookies did Cindy receive
Answers
Answer:
12-c
Step-by-step explanation:
Let c be Cindy's cookies
Solution:
Each child should have gotten 12 cookies because 96/8 is 12 but Cindy got c less so the answer would be 12-c.
The vertices of triangle EFG are E(-3, 2), F(-3, 0), and G(0, 0). The
triangle will be reflected over the x-axis. What will be the vertices of the image triangle?
A. E'(-2, -3), F'(0, 3), G'(0, 0)
B. E'(-3, -2), F'(-3, 0), G'(0, 0)
C. E'(3, 2), F'(3, 0), G'(0, 0)
D. E'(2,3), F'(0,3), G'(0, 0)
Answers
Answer:
B. E'(-3, -2), F'(-3, 0), G'(0, 0)
Step-by-step explanation:
When a point (x, y) is reflected over the x-axis the new coordinates will be
(x', y') where x'x = x and y' = -y
In other words, the transformation is
(x, y) ⇒ ((x, -y)
Point E is (-3, 2) . When transformed e' becomes (-3, -2)
The only choice where E' is (-3, -2) is choice B
You can test the others if you wish
Answer:
B. E'(-3, -2), F'(-3, 0), G'(0, 0)
Which graph represents the linear equation y equals one half times x plus 2 on the coordinate plane? graph of a line passing through the points 0 comma negative 2 and 2 comma negative 1 graph of a line passing through the points negative 4 comma 0 and 0 comma 2 graph of a line passing through the points negative 5 comma 0 and 0 comma 1 graph of a line passing through the points 0 comma 1 and negative 4 comma 0
Answers
The graph which represents the linear equation y = 1/2 x + 2 is the graph of a line passing through the points (-4, 0) and (0, 2).
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
The slope intercept form of a line is,
y = mx + c,
m : slope and c : y intercept
y intercept is the y coordinate of a point when x coordinate equals 0.
Given linear equation is y = 1/2 x + 2.
m = 1/2 and c = 2
Find the slope and y intercept of each of the line in the options given.
In the first option, we have the point (0, -2).
y intercept of this line = -2, which is not the required y intercept.
In the second option, points given are (-4, 0) and (0, 2).
Since we have the point (0, 2), y intercept = 2
m = (2 - 0) / (0 - -4) = 2 / 4 = 1/2
So the line in the second option is the required line.
Hence the graph of the line represented in the second option is the required line.
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Please help me!
A spinner and a fair number cube are used in a game. The spinner has an equal chance of landing on 1 of 6 colors: red, purple, blue, green, white, or orange. The faces of the cube are labeled 1 through 6. What is the probability of a player spinning the color green and then rolling an even number?
Answers
The probability of spinning green and then rolling an even number is 1/36
What is Probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
The probability of spinning green is 1/6 because there are 6 equally likely outcomes and 1 of them is green.
The probability of rolling an even number is 3/6 because there are 6 equally likely outcomes and 3 of them are even numbers (2, 4, and 6).
The probability of spinning green and then rolling an even number is the product of the probabilities of each event. To find this, we multiply the probability of spinning green (1/6) by the probability of rolling an even number (3/6):
(1/6) * (3/6) = 1/36
So, the probability of spinning green and then rolling an even number is 1/36.
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1.0000÷16
solution pls pls help me
Answers
Answer:
0.0625
Step-by-step explanation:
what is seven million written as numeral?
Answers
Answer: 7,000,000
A million= six zeroes
Ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions
Each place value represents an additional zero
Pls help and take your time cuz if I get this wrong I fail WILL MARK BRAINIEST
Answers
The figures above are examples of
Answers
Have a good day.
A recipe needs cup of butter for every 2 cups of flour. if you plan to use 3 cups of flour, how much butter will you need?
Answers
You will need amount of 1.5 cups of butter if you plan to use 3 cups of flour in your recipe.
To calculate how much butter is needed for 3 cups of flour in a recipe, start by identifying that the recipe requires a ratio of 1 cup of butter for every 2 cups of flour. To get the amount of butter needed for 3 cups of flour, multiply 1 cup of butter by 1.5. This will give you 1.5 cups of butter, which is the amount needed for 3 cups of flour. Therefore, you will need 1.5 cups of butter if you plan to use 3 cups of flour in your recipe. To ensure accuracy, it is recommended to measure the ingredients carefully and double check your calculations before proceeding.
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The clearinghouse and research center on servant leadership is now called a. The Center for Applied Ethics b. The Service and Leadership Center c. The Greenleaf Center for Servant Leadership d. The Center for Service and Ethical Behaviors
Answers
The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.
The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.
It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.
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The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.
The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.
The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.
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1. An accounting firm decided to conduct a survey among its past clients. A sample of 750 clients was randomly selected to receive a mail survey. A total of 260 clients responded to the survey; 70 of the mailing addresses were not valid. The response rate on the project would be correctly calculated as _______. g
Answers
The correct calculation of the response rate for the project is approximately 38.24% valid responses received compared to the total number of clients in the sample
To calculate the response rate for the survey, we need to consider the valid responses received compared to the total number of clients in the sample.
The total number of clients in the sample is 750.
The number of clients who responded to the survey is 260.
The number of invalid mailing addresses is 70.
To calculate the response rate, we first need to subtract the number of invalid addresses from the total number of clients in the sample:
Valid Clients = Total Clients - Invalid Addresses
Valid Clients = 750 - 70
Valid Clients = 680
The response rate can then be calculated by dividing the number of valid responses by the total number of valid clients and multiplying by 100 to express it as a percentage:
Response Rate = (Valid Responses / Valid Clients) * 100
Response Rate = (260 / 680) * 100
Response Rate ≈ 38.24%
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Can y’all tell me what all numbers are rational or irrational
Answers
The irrational numbers among these given are:
\(\sqrt{83}, 24\pi, 90.790170..., \sqrt{109}\)
The remaining numbers are all rational.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as terminating decimals.Irrational numbers are numbers that cannot be represented by fractions, such as non-terminating decimals and non-exact roots.The irrational numbers in this problem are:
Square root of 83, as it is a non-exact root.24π, as π is a non-terminating decimal.90.790170, which is a non-terminating decimal.Square root of 109, as it is a non-exact root.More can be learned about rational and irrational numbers at brainly.com/question/17232771
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What is the approximate value of k? use the law of sines to find the answer. 2.9 units 3.8 units 5.1 units 6.2 units
Answers
K is about worth 5.1. Value is the measure of what something is worth, either financially or in terms of importance.
What is value?Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It can mean "identify how much something is worth" like a reward valued at $200 or it can indicate "hold something in high esteem" like "I value our friendship." Value is the monetary, material, or estimated worth of a good, service, or asset. The word "value" is used to describe a wide range of ideas, including shareholder value, company value, fair value, and market value.The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important."Then, determine J's angle in degrees.
180 - (120 + 40) = 20
Second, complete the equation with all the knowledge you have.
sin(20) / 2 and sin(120) / k
Third, cross multiply
k x sin(20) = 2 x sin(120)
Fourth, solve for k
k × sin(20) / sin(20) = [2 × sin(120)] / sin(20)
k = [2 × sin(120)] / sin(20)
k = 5.0641777.....
Fifth, round to the nearest tenth
k = 5.1
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Answer: c)5.1
Step-by-step explanation:
just did it
There are 65,450 people under the age of 14 years old
There are 214,965 people age between 15 and 64 years old
There are 40,809 people over the age of 65 years old
What is the Old Age Dependency Ratio as a decimal rounded to the Thousandths place?
Answers
The old age dependency ratio as a decimal is 0.190.
What is old age dependency ratio ?
The old age dependency ratio is a measure of the number of people who are considered "dependent" on those who are of working age.
Specifically, it is the ratio of the number of people aged 65 years and over to the number of people aged 15 to 64 years old.
Old Age Dependency Ratio = (Number of people over 65) / (Number of people aged 15-64)
Old Age Dependency Ratio = 40,809 / 214,965 = 0.1895
Therefore, Rounding this to the thousandths place the Old Age Dependency Ratio as a decimal is 0.190.
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Britney work 35 hours at a rate of pay of 9.55 how much did she earn before taxes
Answers
Answer:
3.66
Step-by-step explanation:
35÷9.55=3.66
6(2x + 4)2 = (2x + 4) + 2
Answers
Answer:
the answer is x=-21/11.
Step-by-step explanation:
hope it helps
its probably easy but i dont want to do my work
Answers
Answer:
1. 537.1
2. 8.15
3. 9.77
4. 26.75
Step-by-step explanation:
d(t) ==_5925 x + 26,300
What is the depreciated value of the car after 10 years?
Answers
Answer:
26,300 yards is longer because 26,300 yard is equal to 14.94 miles ( 14 or 15 miles)
Step-by-step explanation:
Mathematics questions
Answers
Answer:
Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data. The two major areas of statistics are descriptive and inferential statistics. Statistics can be used to make better-informed business and investing decisions.
Step-by-step explanation:
i hope this helps you as well as others. :)
3x²+2x²+x-2 divided x+2
Answers
Answer:
3x^2-4x+9 remainder -20/x+2
Step-by-step explanation:
A figure is transformed according to the rule (x,y) = (x-1, y + 4). What transformation has taken place?
A. Translation of each point 1 unit to the left and 4 units up.
B. Translation of each point 1 unit to the right and 4 units up.
C. Dilation by a scale factor of -1/4.
D. Reflection over the x-axis, then translated up 4 units.
Answers
The answer is A because x-1 means moving left 1 on the x axis. As well, y+4 means moving 4 up on the y axis.