Answer:
Please check this image for the answer.
Answer:
(x - 5)² + (y -6)² = 9Step-by-step explanation:
Formula for the circle is
(x – h)² + (y – k)² = r²Using the center (5, 6) and radius of 3
(x - 5)² + (y - 6)² = 3²(x - 5)² + (y -6)² = 9please help this is so confusing.
Answer:
6 ÷ 3 = -6/-3
(-3)/6 = 3 ÷ (-6) = -(3/6)
6/(-3) = -(6/3)
leftover: -3/-6
Given the following program, write a C (user-defined) function that returns the sum of the following series x+2mx2+3mx3+4mx4+⋯+nmxn
The function in C (user-defined) that returns the sum of the given series is shown below:```cint series_sum(int x, int m, int n){ int i, j = 1, sum = 0, term = 0; for(i = x; i <= n; i++){ term = j * m * i; sum += term; j++; } return sum;}```.
Here, `x`, `m`, and `n` are the integer inputs of the function, and `j` is a variable whose value gets incremented by 1 in each iteration of the for loop. The for loop runs from the `xth` term to the `nth` term of the series and calculates the `ith` term of the series as `j*m*i` and adds it to the variable `sum`. Finally, the variable `sum` is returned as the output of the function.
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Five less than twice a number is 7
Answer:
2X-5=7
x=6 im mostly sure
The value of the required number will be 6.
What is an expression?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that a number is five less than twice a number is 7. The value of the unknown number will be:-
2n - 5 = 7
2 x ( n ) = 12
n = 12 / 2
n = 6
Therefore, the value of the required number will be 6.
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I need help with this story problem it very confusing can explain this step by step instructions so I understand. Huh, low battery again?! Samantha had just charged her phone up to 76%, and now it was already down to 16%. She had only streamed... oh... oops...three whole episodes of The Haunted Cave this morning (each episode is exactly thirty minutes). That afternoon, after having her phone plugged in for the past hour, she hopped on a bus to meet her friend Jorge at zoo. During the 24-minute ride, she listened to her favorite playlist, Top Pop, noticing her charge had only dropped from 63% to 59%. Not bad!At the edge of the monkey habitat, Samantha pulled out her phone to snap a photo. Suddenly, the monkeys started doing amazing flips and tricks. It was as if they were creating a distraction... "Wait! No!" One of those crafty monkeys swiped her phone right out of her hand! The other monkeys gathered around, guffawing, as the first monkey begin tapping the screen.When Samantha finally got her phone back, the monkey had drained the battery all the way to 31%, boo!On the bus home, Samantha turned on Top Pop to calm herself. " Too bad your battery's at 29% now. I'm still at 55%," Jorge said, while watching The Haunted Cave. Samantha eyed their phones thoughtfully.If Jorge's phone battery drains at the same rate as Samantha's, and they continue playing their current media, how many minutes will it be before the two phones have the same battery level?
When Samantha was streaming "The Haunted Cave" the cellphone went from a level of battery charge of 76% to 16%. We need to calculate the rate at which the battery of the phone is drained while streaming this show. She watched three episodes of the show, each with 30 minutes. So the first step is to calculate the time she spent streaming it. Since she watched 3 episodes of 30 minutes each, the total time is the product between the number of episodes and the elapsed time.
\(\text{time}_{\text{haunted}}=3\cdot30=90\text{ minutes}\)Then we need to calculate how much of the battery was spent on that time. This is the difference between the charge when she started and the charge when she finished.
\(\text{charge}_{\text{dif}}=76-16=60\text{ \%}\)Now we can calculate the rate at which her battery is drained while watching that show, this is done by dividing the total battery spent by the elapsed time.
\(\text{rate}_{\text{haunted}}=\frac{60}{90}=\frac{2}{3}\text{ \% per minute}\)This rate means that for every minute watching this show she spends 2/3 of a % of battery.
She then charged the battery to 63% and went on a 24 minute bus ride while listening to Top Pop, this resulted on her battery dropping all the way to 59%. We need to do the same as above to find how much batter per minute this playlist consumes. We have:
\(\text{charge}_{\text{dif}}=63-59=4\text{ \%}\)The playlist spent 4% in 24 minutes, so the rate is:
\(\text{rate}_{\text{playtop}}=\frac{4}{24}=\frac{1}{6}\text{ \% per minute}\)While listening to Top Pop the cellphone discharges at a rate of 1/6 of a % per minute.
When she was on the bus home with her friend her battery was at a level of 29%, while his was at 55%. He then went to watch the haunted show, while she went to listen Play Top. If the rate is the same as we calculated above, then the level of battery of each person can be calculated by the starting level subtracted by the rate at which each app consumes the battery multiplied by the time they are using the app. So for each person we have:
\(\begin{gathered} \text{samantha}=29-\frac{1}{6}\cdot t \\ \text{jorge}=55-\frac{2}{3}\cdot t \end{gathered}\)To find the time it will take before the level of battery is the same on each device we need to make both equations equal and solve for t.
\(\begin{gathered} 29-\frac{1}{6}\cdot t=55-\frac{2}{3}\cdot t \\ \frac{2}{3}t-\frac{1}{6}t=55-29 \\ \frac{2\cdot2t-t}{6}=26 \\ \frac{4t-t}{6}=26 \\ \frac{3t}{6}=26 \\ \frac{t}{3}=26 \\ t=26\cdot3=78\text{ minutes} \end{gathered}\)For both phones to achieve the same level of battery they'll need to use it for 78 minutes.
Eemil is training for a marathon. The ratio of the number of minutes to the number of miles they run is 30 to 3. At this rate, how many minutes will it take Eemil to run the race (26.2 miles)?
Please help will give Brain!!
yes i think because i think so
Answer:
Yes
Step-by-step explanation:
Their sides are similar proportionally and the 60 degrees + 120 degrees makes 180 degrees meaning the OTHER angles match
dx = ax + by 45.1. Consider dt dy =cx + dy, dt for the following cases: O b= 1 b= 3 c I4 (а) а %3 1 d= 0 c 1 c = 1 c =1 c = -1 c = 1 c =0 1c=1 c 1 c 1 c =-2 c = 1 (6) a= 2 d= -1 b= 1 d= 2 (с) а %3 b= -2 d= -5 a = a = 1 f) (g) b 2 d= -2 b=-1 d 2 a= 3 b=0 = -2 d= -3 b 1 0 d= -3 (h) a= b = 3 d 1 b= -3 4 (i) a (k) a=-1 2 d = 0 b 2 d -1 b -1 () а — d= 0 3 b 2 (m) a= d 4 C = = -3 d 1 n a = 1 b C = (0) а — 4 b C= Determine x and y as functions of time. # 2, 3 and 4: Use conditions of questions d), e) and f), respectively, of Problem 45.1 on page 199 and the same initial condition x(0) 1, y(0) = 0 in all three cases: Find the general solution; Find the particular solution corresponding to the given initial values; Describe the asymptotic behavior of the particular solution
The given system of differential equations is dx = ax + by and dy = cx + dy. To determine the functions x(t) and y(t) as a function of time, we need to solve the system for different values of the coefficients a, b, c, and d. We will consider three cases: (a) b = 1, c = 4, (b) a = 2, d = -1, and (c) a = -2, b = -1. We will find the general solutions, particular solutions with the given initial conditions, and describe their asymptotic behavior.
Case (a): For b = 1 and c = 4, we have dx = ax + y and dy = 4x + y. Solving these equations yields the general solutions x(t) = Ce^(at) - t - 1 and y(t) = De^(at) + 4t - 3, where C and D are constants. Applying the initial conditions x(0) = 1 and y(0) = 0, we can determine the particular solutions x(t) = e^(at) - t - 1 and y(t) = 4t - 3.
Case (b): For a = 2 and d = -1, the system becomes dx = 2x + by and dy = cx - y. The general solutions are x(t) = Ce^(2t) - (b + 1)y and y(t) = De^(2t) + cx - y, where C and D are constants. Substituting the initial conditions x(0) = 1 and y(0) = 0, we find the particular solutions x(t) = e^(2t) - (b + 1)y and y(t) = (c - 1)e^(2t) + cx.
Case (c): In this case, a = -2 and b = -1, resulting in dx = -2x - y and dy = cx - y. The general solutions are x(t) = Ce^(-2t) + (1 - c)y and y(t) = De^(-2t) + cx - y, where C and D are constants. Using the initial conditions x(0) = 1 and y(0) = 0, we obtain the particular solutions x(t) = e^(-2t) + (1 - c)y and y(t) = (2c - 1)e^(-2t) + cx.
The asymptotic behavior of the particular solutions can be described by examining the exponential terms in the general solutions. If the coefficients in front of the exponential terms are positive, the solutions will approach infinity as t approaches infinity. Conversely, if the coefficients are negative, the solutions will approach zero. Additionally, the presence of linear terms (such as -t or 4t) will affect the overall behavior of the solutions.
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Calculate the slope
Answer:
Undefined
Step-by-step explanation:
Slope us (y2-y1)/(x2-x1)
(9-4)/(3-3)
Cant divide by zero
What decimal is the closest to 80
Answer: it would .08 then if you multiply by ten you would get 80
Step-by-step explanation:
PLEASE HELP ASAP!!
When a ball is dropped, the function () = 4(0.6)x models the ball’s height in feet after each bounce, where x is the bounce number. To the nearest hundredth, what is the height after the third bounce?
Answer:
7.2 feet
Step-by-step explanation:
plug in x = 3 since we are looking for the height after the 3rd bounce
4(0.6)(3)
4(1.8)
7.2
The height after the third bounce is 0.86 feet.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4 x \(0.6^x\) models the ball’s height in feet after each bounce.
Where x is the bounce number.
Now,
Substituting x = 3,
f(x) = 4 x \(0.6^x\)
f(x) = 4 x \(0.6^3\)
f(x) = 4 x 0.6 x 0.6 x 0.6
f(x) = 0.864
f(x) = 0.86
The height after the third bounce is 0.86 feet.
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Cam is making a party hat, shown at left, in the shape of a cone for his
birthday. The circumference of the part of his head where the hat will
rest is 56 centimeters (cm). If the height of the hat is 25 cm, which of
the following is closest to the volume of Cam's hat, measured in cubic
centimeters (cm)?
Answer:
V≈2,080cm^3 Hope I helped :)
Step-by-step explanation:
The volume of a cone of radius r and height h is:
V=1/3πr^2h
Since the circumference of Cam's head is 56
2πr=56
r=56/2π
r=28/π
The volume of the hat is therefore:
V=1/3π(28/π )^2(25)
V=1/3((28)^2/π)(25)
V=1/3(19,600/π)
V≈2,080cm^3
The volume of the Cam's hat measured in cubic centimetres is 2081 cm³
Volume of a cone:The volume of a cone is as follows:
v = 1 / 3 π r²hwhere
h = height
r = radius
The circumference of the part of his head where the hat will rest is 56 cm. Let's find the radius
circumference = 2πr56 = 2 × π × rr = 28 / πh = 25 cm
V = 1 / 3 × π × (28 / π )² × 25
V = 1 / 3 × π × 784 / π² × 25
V = 19600 / 3π
V = 19600 / 9.42
V = 2080.67940552
V ≈ 2081 cm³
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BRIDGE Arturo is designing a bridge for
science class using parallel supports for
the top and bottom beam. Find m_2if
m_1 = 60°
the measure of m_2 is 120°, making the two angles of the bridge Arturo 60° and 120° respectively.
Bridge Arturo is the name given to a bridge designed by Arturo for his science class. It consists of two parallel beams that are supported by two different angles, m_1 and m_2.
The bridge Arturo is designing requires two supports of different angles, m_1 and m_2. The measure of m_1 is given as 60°. To find the measure of m_2, we can use the fact that the sum of the angles of a triangle is 180°. Since m_1 is given as 60°, subtracting this from 180° gives us 120°. Therefore, the measure of m_2 is 120°.
Bridge Arturo is a bridge designed by Arturo for his science class. It consists of two parallel beams which are supported at two different angles, m_1 and m_2. The measure of m_1 is given as 60°, which means that m_2 must be 120°, as the sum of the angles of a triangle is 180°. Hence, the measure of m_2 is 120°, making the two angles of the bridge Arturo 60° and 120° respectively.
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Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). For what percentage of great lakes states would you expect the economic impact from fishing to be between $234.5 and $401.5 (in millions of dollars)? ( Hint use the empirical rule)
The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.
Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.
We have to calculate the percentage of great lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.
Because we have not given the sample size taken so we will use any test.We are using z test.
We know that,
z=X-μ/σ
where μ is population mean and σ is population standard deviation.
We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.
P value between $234.5 and $318:
z=234.5-318/83.5
=-83.5/83.5
=-1
p value of -1 is 0.1587
P value between $318 and $401.5:
z=401.5-318.5/83.5
=83.5/83.5
=1
p value of z=1 is 0.3413
Total p value=0.1587+0.3413
=0.5
Total percentage=0.5*100
=50%
Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.
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pls help...................................
The value of x found using the angle addition postulate is; x = 35°
What is the angle addition postulate?The angle addition postulate states that the measure of the angle formed by the non-common sides (rays) of two adjacent angles that have a common side is the sum of the two adjacent angles.
The measures of the angles in the document are;
The measure of angle STV is 75°
The measure of angle WTV is 40°
The measure of angle STW is x°
Please find attached a possible drawing representing the angles, obtained from the drawing in a similar question, and created with MS Word.
The angle addition postulate indicates that we get;
m∠STV = m∠STW + m∠WTV
Whereby angle ∠x is the same as the angle ∠STW, therefore, wse get;
m∠STV = x° + m∠WTV
Plugging in the values for the angles defined by the letters, we get the angles
75° = x° + 40°
x° = 75° - 40° = 35°
The measure of angle x is 35°
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what’s does 7 correspond to . please help .
\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)
A. 21
ThanksHope it helps.*WILL GIVEE BRAINLIEST FOR THE BEST ANSWER* Which of the following is NOT a biased sample?
Question 3 options:
A. A cable television company randomly calls 200 customers and asks them if they are satisfied with their service.
B. A town official surveys 50 people in a library to decide if town residents want the library services and facilities expanded.
C. You ask 10 basketball players in a gym if they like watching basketball.
D. A grocery store asks 15 customers at the deli counter if they eat meat.
Answer:
A
Step-by-step explanation:
All other options are more biased
In B, the official wants to use 50 people from a library to represent the entire town's opinion on the library itself.... that's biased.
In C, it's the same. Of course basketball players would like to watch basketball.... right?? That's why the choice is biased.
In D, the location is a deli.... and from experience people order meat at a deli... cuz why else go there?
Answer the following question in *full sentences*
What does the equation 100+0.05p=0.25p represent?
The value of "p" will be "0.002".
Equation:According to the question,
\(100+0.05p=0.25p\)By subtracting "0.25p" from both sides, we get
→ \(100+0.05p-0.25p=0.25p-0.25p\)
\(100-0.2p=0\)
\(100=0.2p\)
\(p = \frac{0.2}{100}\)
\(= 0.002\)
Thus the above approach is right.
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a street has parallel curbs 4040 feet apart. a crosswalk bounded by two parallel stripes crosses the street at an angle. the length of the curb between the stripes is 1515 feet and each stripe is 5050 feet long. find the distance, in feet, between the stripes?
The distance between the stripes is 4040 feet (distance between curbs) minus 1515 feet (length of the curb between the stripes), which equals 2525 feet.
To find the distance between the two parallel stripes in the crosswalk, we can use the given information about the street. The distance between the parallel curbs of the street is 4040 feet. The length of the curb between the stripes is 1515 feet, and each stripe is 5050 feet long.
Since the crosswalk is bounded by two parallel stripes, the distance between the stripes can be calculated by subtracting the length of the curb between the stripes from the distance between the curbs of the street.
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Enter the amplitude of the function f (x).
f(x) = 2 cos (-x) - 4
Answer:
Amplitude= |A|= |2|=2
Step-by-step explanation:
comparing the function with F(x)= a cos bx
then a=2 and b =-4
so Amplitude=|A|= |2|=2
3.∆ABC is similar to ∆XYZ.AB = 15 and XY = 25.If YZ = 15, what is measure of bc
The measure of the side BC from the triangle 9 units.
Given that, ∆ABC is similar to ∆XYZ.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Here, AB = 15 units, XY = 25 units and YZ = 15 units.
Since, the given triangles are similar
AB/XY = BC/YZ
⇒ 15/25 = BC/15
⇒ BC = (15×15)/25
⇒ BC = 225/25
⇒ BC = 9 units
Therefore, the measure of the side BC from the triangle 9 units.
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\(=59(F−32)\)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59
A degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answer:
Think of the equation as an equation for a line y = m x + b where in this case C = 5 9 ( F − 32 ) or C = 5 9 F − 5 9 ( 32 ) You can see the slope of the graph is 5 9 , which means that for an increase of 1 degree Fahrenheit, the increase is 5 9 of 1 degree Celsius. C = 5 9 ( F ) C = 5 9 ( 1 ) = 5 9 Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9 5 degrees Fahrenheit. C = 5 9 ( F ) 1 = 5 9 ( F ) ( F ) = 9 5 Since 9 5 = 1.8, statement II is true. The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5 9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true: C = 5 9 ( F ) C = 5 9 ( 5 9 ) C = 25 81 ( which is ≠ 1 ) An increase of 5 9 degree Fahrenheit leads to an increase of 25 81 , not 1 degree, Celsius, and so Statement III is not true. The final answer is D.
In the figure, Line a is parallel to line b.
A. Which equation can be used to determine the value of x?
a
3x = 180 - 2x + 20
b
3x = 2x + 20
c
90 - 3x = 2x + 20
d
3x + 2x + 20 = 180
Answer:
b
Step-by-step explanation:
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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Solve 6(x-3) + 7 = -5.
OA. X = 2
OB. x= 3
OC. X= 4
O D. x = 1
Answer:
O D. x=1
Step-by-step explanation:
6(x-3)+7=-5
6x-18+7=-5
6x=-5+18-7
x=6|:6
x=1
The force,
F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them.
The force is 0.07 Newtons when the distance between the objects is 6 metres.
Work out F (rounded to 2 DP) when d=5.5 metres.
When the distance between the objects is 5.5 meters, the force (F) is approximately 0.0827 Newtons (rounded to 2 decimal places).
According to the given information, the force (F) between two objects is inversely proportional to the square of the distance (d) between them. Mathematically, this can be represented as \(F = k/d^2,\)
where k is the constant of proportionality.
To find the value of k, we can use the given data point where the force is 0.07 Newtons when the distance is 6 meters. Plugging these values into the equation, we get:
\(0.07 = k/6^2\)
Simplifying, we have:
0.07 = k/36
To solve for k, we can multiply both sides of the equation by 36:
\(k = 0.07 \times 36\)
k = 2.52
Now that we have the value of k, we can calculate the force (F) when the distance (d) is 5.5 meters:
\(F = 2.52 / 5.5^2\)
F ≈ 0.0827
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The angles of elevation to an airplane from two points A and B on level ground are 58° and 76°, respectively. The points A and B are 2.1 miles apart, and the airplane is east of both points in the same vertical plane. Find the altitude of the plane. (Round your answer to two decimal places.)
Answer:
90
Step-by-step explanation:
45x2=90
SET of 3! Please help
Answer:
1. 24/40, 32/40, 24/32 (This is in order from top to bottom)
2. 21.1
3. 4.1
Step-by-step explanation:
1. Here, we only have to focus on Angle X.
Let's label in the sides:
Opposite = YZ = 24
Adjacent = XY = 32
Hypotenuse = XZ = 40
SOHCAHTOA simply means: You can memorise this through the acrostic poem of - Slap On Head Causes A Headache Take One Aspirin, but I remember it by Suck A Toe because that's what it sounds like.
Sin(x) = Opposite/Hypotenuse
Cos(x) = Adjacent/Hypotenuse
Tan(x) = Opposite/Adjacent
Sin(X) = 24/40
Cos(X) = 32/40
Tan(X) = 24/32
The question only asks to give the ratios by using / for a fraction, so we don't simplify it.
2. We are given the angle of 64°, the opposite length 19 and we have to work out x, which is the hypotenuse. We can use the sin function as we have our opposite length and we have to work out the hypotenuse.
Sin(64) = 19/x
xSin(64) = 19
x = 19/Sin(64)
x = 21.13943687
x = 21.1
3. We are given the angle of 70°, the hypotenuse 12 and we have to work out x, which is the adjacent side. We can use the cos function as we have to work out the adjacent side and we have our hypotenuse given to us.
Cos(70) = x/12
12Cos(70) = x All we have to do here is multiply by 12!
x = 4.10424172
x = 4.1
Find the critical points of the given function. Then use the second derivative test to determine if the critical points correspond to local maxima, local minima, or saddle points of the graph of the function or if the test is inconclusive.f(x,y)=x3+y3−3xy
For the given function, the critical point (0,0) corresponds to a saddle point, the critical point (1,1) corresponds to a local minimum, and the critical point (-1,-1) corresponds to a saddle point.
In this case, we are given a function of two variables, f(x,y) = x^3 + y^3 - 3xy. To find the critical points of this function, we need to find where the partial derivatives with respect to x and y are equal to zero. Taking the partial derivative with respect to x, we get:
fx = 3x² - 3y
Taking the partial derivative with respect to y, we get:
fy = 3y² - 3x
Setting both of these partial derivatives equal to zero and solving for x and y, we get:
x = y and x = -y
Substituting either of these into the original function, we get:
f(x,y) = 2x^3 - 3x(x) = -x³
or
f(x,y) = 2y^3 - 3y(-y) = 4y³
So the critical points of the function are (0,0) and (1,1) or (-1,-1).
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A parallelogram-shaped window is divided into two sections by a rectangular piece of wood. Find the total of the area of the surface.
The total area of the glass surface is _ square inches
Charlie and Leo were playing with toy cars. Charlie said to Leo that if you give me one car, then i will have twice as many cars as you have. Leo said if charlie gives him a car, they will be equal. How many cars does each boy have? HELP IN PLAYING A BATTLESHIP GAME
Step-by-step explanation:
C + 1 = 2(L-1)
C +1= 2L -2
C- 2L = -3 ......(eq.1)
L+1 = C-1
C- L = 2 .....(eq.2)
by elimination :
C - 2L = -3
C - L = 2
________-
- L = -5
L = 5
C = 2+5 = 7
so, Leo has 5 cars and Charlie has 7 cars
Answer:
Charlie=7, Leo=5
Step-by-step explanation:
cant explain