A function is difined by the expression f(x,y)=4−(x−1)^2−(y−1)^2 calculate the coordinates of the Sfationary critical point of f. Classify this poinf using the second derivative test How can you arrive at this answer Without doing the math, 2
Answers
To find the coordinates of the stationary critical point of the function f(x, y) = 4 - (x - 1)^2 - (y - 1)^2, we can analyze the equation without performing the math.
The function represents a downward-opening paraboloid centered at the point (1, 1) with a maximum value of 4. The critical point occurs at the vertex of this paraboloid. Since the paraboloid opens downward, the maximum point at (1, 1) is the only stationary critical point.
To classify this critical point using the second derivative test, we would typically calculate the second partial derivatives and evaluate them at the critical point. However, in this case, we can observe that the function represents a maximum point, as the negative quadratic terms, -(x - 1)^2 and -(y - 1)^2, dominate the positive constant term 4. Thus, we can conclude that the critical point at (1, 1) is a maximum point without performing the calculations.
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Related Questions
What are the forms of protectionism in trade?
Answers
Answer:
Tariffs
Quotas
Export subsidies
Domestic subsidies
Import licensing
Exchange controls
Financial protectionism
Murky or hidden protectionism
Can someone pose help me with this?
Answers
What is the m (See image)
Answers
From the given figure, m∠AEB = (3x + 54)° and m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.
As given in the question,
For the given figure,
Two lines AC and BD intersect each other at point E.
Measure of angles in the form of x is given as :
m∠AEB = (3x + 54)°
m∠DEC = (7x -30)°
∠AEB and ∠DEC are vertically opposite angles.
⇒m∠AEB = m∠DEC
⇒ (3x + 54)°= (7x -30)°
⇒ 7x - 3x = ( 54 + 30 )°
⇒ 4x = 84°
⇒ x = 21°
Hence,
m∠AEB = (3x + 54)°
⇒m∠AEB = (3(21) + 54)°
⇒m∠AEB = 117°
Therefore, from the given figure m∠AEB = (3x + 54)° and
m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.
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The function f is defined below.
f(x)=−2x−3
Find f(1).
Answers
Answer:
\(f(1)=-5\)
Step-by-step explanation:
\(f(1)=-2(1)-3\\\\f(1)=-2-3\\\\f(1)=-5\)
f(1) means to substitute x with 1 or that x=1. So since x=1 you will substitute it in where x is and then solve like a regular equation which will give you -5.
The height of a cuboid whose volume is 275 cm3 and base area is 25 cm2 is:
Answers
Given:
The volume of a cuboid = 275 cm³
The base area of the cuboid = 25 cm²
To find:
The height of the cuboid.
Solution:
We know that, the volume of a cuboid is:
\(V=l\times b\times h\)
Where, l is length, b is breadth and h is the height.
It is also written as:
\(V=B\times h\) ...(i)
Where, B is the base area and h is the height of the cuboid.
Putting \(V=275, B=25\) in (i), we get
\(275=25\times h\)
\(275=25h\)
\(\dfrac{275}{25}=h\)
\(11=h\)
Therefore, the height of the cuboid is 11.
what is the perimeter of a square whose area is 9cm square
plz explain i will mark your answer bainliest
Answers
Answer:
perimeter=(lengths+breadth)×2
in this case its a square with 9 cm length
9+9×2
18×2
36 its ez
9000÷20=N ????? pls answer
Answers
To get the value of N let's do the division.
The value of N is 450
Determine the derivative with quotient rule and find the equation of the tangent to f(x) at x=0
Answers
ANSWER
\(\text{ The derivative of the function is; }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ -2x}^2\text{ + 2}}{\text{ \lparen x}^2\text{ + 1\rparen}^2}\)EXPLANATION
Given that;
\(\text{ f\lparen x\rparen = }\frac{\text{ 2x}}{\text{ x}^2\text{ + 1}}\)Let U(x) = 2x and V(x) = x^2 + 1
Apply the quotient rule to find the derivative of f(x)
\(\text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ V}\frac{\text{ dU}}{\text{ dx}}\text{ - U }\frac{dv}{\text{ dx}}}{\text{ V}^2}\)Differentiate U and V with respect to x
\(\begin{gathered} \text{ U\lparen x\rparen = 2x} \\ \text{ }\frac{\text{ du}}{\text{ dx}}\text{ = 2} \\ \\ \\ \text{ V\lparen x\rparen= x}^2\text{ + 1} \\ \text{ }\frac{dv}{\text{ dx}}\text{ = 2x} \end{gathered}\)Hence, we have
\(\begin{gathered} \text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{(x^2\text{ + 1\rparen}\times2\text{ - 2x\lparen2x\rparen}}{(x^2\text{ + 1\rparen}^2} \\ \\ \text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ 2x}^2\text{ + 2 - 4x}^2}{(x^2\text{ + 1\rparen}^2} \\ \\ \text{ }\frac{\text{ dy}}{\text{ dx}}\text{ = }\frac{\text{ -2x}^2\text{ + 2}}{\text{ \lparen x}^2\text{ + 1\rparen}^2} \end{gathered}\)Indicate below whether the equation in the box is true or false 1/8 = to 2/4 true or false
Answers
Answer:
false
Step-by-step explanation:
1/8 = .125
2/4 = .5
therefore 1/8 does not = 2/4
When an alternating current of frequency f and peak current I_0 passes through a resistance R, then the power delivered to the resistance at time t seconds is P = I^2_0 R sin^2 2 pi ft. Write an expression for the power in terms of csc^2 2 pi ft. P = I^2_0 R/(csc^2 2 pi ft) P = I^2_0 R (csc^2 2 pi ft) P = I^2_0/(1 - csc^2 2 pi ft) P = I^2_0 R(1 - csc^2 2 pi ft)
Answers
The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).
According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.
To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).
Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.
Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).
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Evaluate the algebraic expression for the given values of x = 3 and y = 4. Tx - 2y - 1 = I
Answers
Answer:
7 or -9, dependent on if 2y is or is not negative
Step-by-step explanation:
If 2y is NOT negative
2(4)-1=i
8-1=i
i=7
If 2y IS negative
-2(4)-1=i
-8-1=i
i=-9
The point P = (-5/3 squared, y) lies on the unit circle shown below. What is the value of
y in simplest form?
Answers
The required value of y for the unit circle is: 2/3
How to find the point on the unit circle ?The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).
The equation of the circle is given by:
(x - h)² + (y - k)² = r²
where:
h, k is the coordinate of the center of the circle on coordinate plane.
r is the radius of the circle.
Here,
Equation of the unit circle is given as,
x² + y² = 1
Now substitute the given value in the equation,
5/9 + y² = 1
y² = 1 - 5/9
y² = 4/ 9
y = √(4/9)
y = 2/3
Thus, the required value of y for the unit circle is 2/3
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7. Luke, Evan, Sarah, and Skylar are equally sharing three pies: blueberry, apple, and cherry. What amount of pie will each person get? O 4/3 of a pie 3/4 of a pie O a 2/3 of a pie O 1/2 of a pie
Answers
There are 3 pies: blueberry, apple, and cherry
4 people are to share the pies
To get the amount each person will get, we can represent one person share with y
To obtain y, we will have to cross multiply
so that 4 x y = 3 x 1
4y = 3
Divide both sides by 4
y = 3/4
Answer = 3/4 of a pie
Three sons inherited 2,179 ducats from their father. The father bequeathed the older brother 2 times more money than the younger one. At the same time, the middle brother should receive more than the younger one, but less than the older one. How many ways are there to fulfill the will of the father, if each son must receive a whole number of ducats?
Answers
Three sons inherited 2,179 ducats from their father. The number of ways the father can bequeath the resources is
108 waysHow to find the number of ways of fulfilling the fathers wishInformation from the problem helped in generating the following equations
The father bequeathed the older brother 2 times more money than the younger one
let the youngest receive an amount equivalent to y
then the eldest will receive 2y
let the middle receive x
Using the sharing formula described we have
y + 2y + x = 2179
3y + x = 2179
the middle brother should receive more than the younger one, but less than the older one
x > y
x < 2y
plotting the equations on a graphing calculator and getting the solutions we have
(544.75, 544.75) and (871.6, 435.8)
y ranges from 435.8 to 544.75 using whole numbers
436 to 544
The number of ways
= 544 - 436
= 108 ways
the number of ways of sharing according to fathers will is 108
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Evaluate 7.6 x 103 +5.2 x 103 and write its solution in scientific notation.
Answers
j divided by 9 is 5 , write an equation to represent the following statement
Answers
Answer:
The first answer is incorrect
Step-by-step explanation:
45 divided by 9 is 5 not 40
The equation that represents the statement is j / 9 = 5.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
The statement j divided by 9 is 5 can be written in equation form as follows:
j / 9 = 5
j = 45
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What is 2- 1/4
Write your answer as a fraction
Meh will mark you
Answers
Answer:
1 3/4
Step-by-step explanation:
Answer:
7/4
Step-by-step explanation:
We have the equation 2 - 1/4. The question is asking us to solve and turn the answer into a fraction.
So let's solve it first.
To make this easier, we must turn 1/4 into a decimal, which would be 0.25.
2 - 0.25
1.75
Now that we have the answer, we must change it into a fraction, so :
1.75 = 7/4
Therefore, 7/4 is the answer.
At the beginning of the year, Skylar had $30 in savings and saved an additional $16 each week thereafter. Faith started the year with $100 and saved $6 every week. Let SS represent the amount of money Skylar has saved tt weeks after the beginning of the year and let FF represent the amount of money Faith has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the amount of money Skylar and Faith have saved in the week that they have the same amount of money saved.
Answers
The linear equations for each situation would be: F = 6t + 100 and S = 16t + 30.
The amount of money Skylar and Faith would have saved in the week that they both have the same amount of money saved is: $142.
How to Write a Linear Equation of a Situation?A linear equation that models a situation can be expressed as y = mx + b, where the unit rate or slope value is represented as m, and the y-intercept or initial value (starting value) is the value of b.
Equation that represents the savings made by Skylar:
Unit rate (m) = $16 per week
Starting value/y-intercept (b) = $30
S = y
t = x
The equation for Skylar would be written by substituting m = 16 and b = 30 into S = mt + b:
S = 16t + 30.
Equation that represents the savings made by Faith:
Unit rate (m) = $6 per week
Starting value/y-intercept (b) = $100
F = y
t = x
The equation for Skylar would be written by substituting m = 6 and b = 100 into F = mt + b:
F = 6t + 100.
They will both saved the same amount of money, when F = S. Therefore:
16t + 30 = 6t + 100
Solve for t
16t - 6t = -30 + 100
10t = 70
t = 7
Substitute t = 7 into any of the equations:
6t + 100 = 6(7) + 100
= 142.
Therefore, they would both save $142.
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A ribbon 9 feet long is cut into two pieces. One piece is 1 foot longer than the other.
What are the lengths of the two pieces?
Answers
choose the random variables from this set that are discrete. select all that apply. multiple select question. the weight of a bag of a dozen apples. the travel time of an airline flight. the number of dots uppermost of rolling a pair of dice. number of drive-thru customers to the bank on a given day.
Answers
Examples of random variables are option A: the weight of a bag of a dozen apples, and option C: the number of dots uppermost of rolling a pair of dice.
Because they can only have a finite number of values, discrete random variables include things like the weight of a bag of twelve apples and the number of dots that appear on top of a pair of dice.
Examples of continuous random variables are the length of an airline flight and the quantity of drive-through clients at a bank on a particular day since they might have any value within a specified range.
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Correct question:
Choose the random variables from this set that are discrete. select all that apply. multiple select question.
the weight of a bag of a dozen apples.
the travel time of an airline flight.
the number of dots uppermost of rolling a pair of dice.
number of drive-thru customers to the bank on a given day.
A coordinate plane. Use the coordinate plane to plot the points (6, 0) and (0, 5). Which statement is true? (0, 5) is located on the x-axis. (0, 5) is located at the origin. (6, 0) is located on the x-axis. (6, 0) is located at the origin.
Answers
Hi!
Answer:
C, (6,0) is located on the x-axis.
Step-by-step explanation:
A. is wrong because (0,5) is located on the y-axis because it is going 5 points up, not right
B. and D. are wrong because none of them are located on the origin
That leaves C. and it is right because (6,0) is located on the x-axis
Want proof?
I have some:
Hope this helps anybody!
Answer:
c
Step-by-step explanation:
Bill needs to edge his yard with the dimensions in the shape below. What distance will he have walked after completing his edging? Round your answer to one decimal place. Do not include units in your answer.
Answers
Answer:
37.8 m
Step-by-step explanation:
The computation of the distance is shown below:
In triangle ADE
\(AD^2 = AE^2 + DE^2 \\\\ AD^2 = 5^2 + 3^2 \\\\ AD^2 = 34\)
AD = 5.8
Now the distance walked after completing his edging is
Distance = AD + AB + BC + CD
= 5.8 + 12 + 5 + 15
= 37.8 m
We simply added these four sides so that the correct distance could arrive
Hence, the distance walked after completing his edging is 37.7
please help me I have to submit it tomorrow and please while sending solution write it and send a pic please because I don't understand when someone explains it in the answer
Answers
Answer:
A
Step-by-step explanation:
I think
The population of a state was estimated to be
about 38,332,521 people. Write the estimated
population as a single digit times a power of 10.
Answers
The state population as a single-digit time power of 10 is approximately 4 × 10⁷.
What is estimation?Calculations are made easier and more realistic when a number is estimated, which is a plausible estimation of its true value.
To estimate something is to approximate it as accurately as possible.
To acquire a quick and approximate response is obtained by rounding down the values used in the computation.
Given the state estimated population = 38,332,521
Divide and multiply by 10
So,
= 3,833,252.1 × 10¹
= 383,325.21 × 10²
So, similarly, we can write
= 3.8332521 × 10⁷
So, we can write the state population as approximately 4 × 10⁷
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Write the standard form of the equation where p=5 and theta = 90
Answers
m
=
y
2
−
y
1
x
2
−
x
1
Where
m
is the slope and (
x
1
,
y
1
) and (
x
2
,
y
2
) are the two points on the line.
Substituting the values from the points in the problem gives:
m
=
−
3
−
5
−
3
−
5
=
−
8
−
8
=
1
Next, we can use the point-slope formula to get an equation for the line. The point-slope formula states:
(
y
−
y
1
)
=
m
(
x
−
x
1
)
Where
m
is the slope and
(
x
1
y
1
)
is a point the line passes through.
Substituting the slope we calculated and the first point from the problem gives:
(
y
−
5
)
=
1
(
x
−
5
)
The standard form of a linear equation is:
A
x
+
B
y
=
C
Where, if at all possible,
A
,
B
, and
C
are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
We can now transform the equation we wrote to standard form as follows:
y
−
5
=
x
−
5
−
x
+
y
−
5
+
5
=
−
x
+
x
−
5
+
5
−
x
+
y
−
0
=
0
−
0
−
x
+
y
=
0
−
1
(
−
x
+
y
)
=
−
1
⋅
0
x
−
y
=
0
1
x
+
−
1
y
=
0
Can someone please help me with #5. Substitution method
Answers
\(x-y=1\\x=1+y........(3) equation\)
5.I derived the third equation from the second equation therefore I will substitute the above equation x=1+y in the first equation .Mind you to derive the third equation I made x the subject of the equation in the second equation. You can use any equation to derive the third equation. I chose to use the second equation because the variable have the coefficient of 1 so it will be very easier foe me without any divisions to leave the variable independent.
I will substitute the equation x=1+y in the equation -3x+3y=3.
If you derived the third equation from the second equation DO NOT substitute in the equation you derived the new equation from.
\(-3(1+y)+3y=3\\-3-3y+3y=3\\-3\neq 3\)
as far as I went you can see that there is no solution for the first problem
No solution
6. Substitute y=-x+4 in the equation 2x-3y=3. In the place of y plug in-x+4
\(2x-3(-x+4)=3\\\\2x+3x-12=3\\5x=3+12\\5x=15\\\)
\(\frac{5x}{5} =\frac{15}{5} \\x=3\\\\y=-(3)+4\\y=1\)
Hope this helps
Answer: the system of equations has no solution
Step-by-step explanation:
\(\displaystyle\\\left \{ {{-3x+3y=3} \atop {x-y=1}} \right. \ \ \ \ \Rightarrow\ \ \ \ \ \left \{ {{-3x+3y=3} \atop {x-y+y=1+y}} \right. \ \ \ \ \ \left \{ {{-3x+3y=3} \atop {x=1+y}} \right.\ \ \ \ \ \Rightarrow \\\\\\\left \{ {{-3x+3y=3} \atop {x-1=1+y-1}} \right.\ \ \ \ \ \Rightarrow\ \ \ \ \ \left \{ {{-3x+3y=3\ \ \ \ (1)} \atop {x-1=y\ \ \ \ (2)}} \right. \\\)
Divide equation (1) by 3:
\(\displaystyle\\\left \{ {{-x+y=1\ \ \ \ \ (3)} \atop {y=x-1\ \ \ \ \ (4)}} \right.\)
Substitute equation (4) into equation (3):
\(-x+x-1=1\\\\-1\neq 1\)
Hence, the system of equations has no solution
Armando has $25 to spend. he wants to buy 2 pounds of hamburgers at $3 per pound, a bag of buns for $2, and 5 bags of chips for $4 each. Sort each statement into True or False.
Answers
Answer:
True- She needs $3 more. She will not have enough money to buy everything. The cost is $28.
False- She has $3 left over.
Step-by-step explanation:
2 pounds of burgers for $3 each is $6
1 bag o bun equals $2
5 bags of chips for $4 each is $20
$20 + $6 +$2 = $28
She only had $25 to spent, so she doesn't have enough money and needs to 3 more dollars.
A quadrilateral has 2 pairs of parallel sides and no right angles.
What shape could it be?
please help me I'm kinda in a life or death situation here....
Answers
Answer:
A parallelogram
Step-by-step explanation:
Answer:
Parallelogram and rhombus.
b) James went to Black Rock coffee shop and ordered
2 coffees and 5 bagels for which he paid $24. The next
morning he returned to buy 3 coffees and 4 bagels for
$22. Based on this information, determine how much
each item costs.
Answers
Answer:
Coffees cost $2 each and bagels cost $4 each
Step-by-step explanation:
Let
Coffee=c
Bagels= b
2 coffees and 5 bagels for which he paid $24
2c + 5b= 24 (1)
he returned to buy 3 coffees and 4 bagels for
$22
3c + 4b = 22 (2)
2c + 5b= 24 (1)
3c + 4b = 22 (2)
Multiply (1) by 3 and (2) by 2
6c + 15b = 72 (3)
6c + 8b = 44 (4)
Subtract (4) from (3)
15b - 8b = 72 - 44
7b = 28
Divide both sides by 7
b= 28 / 7
= 4
b= $4
Substitute b=4 into (1)
2c + 5b= 24
2c + 5(4) = 24
2c + 20 = 24
2c = 24 - 20
2c = 4
Divide both sides by 2
c= 4 / 2
c= $2
Therefore,
Coffees cost $2 each and bagels cost $4 each
Find the slope of the line that passes through the pair of points.
(3, 1), (9, 1)
Answers
Answer:
gradient:
y2-y1/x2-x1
1-1/9-3
0/-6
= 0