Answer:
The points are "(2,2)".
Step-by-step explanation:
Given value:
[tex]f(x,y)=x^3-6xy+y^3+7[/tex]
Finding the first partial derivation which is equal to 0.
[tex]\to f_x(x,y)=3x^2-6y...............(a)\\\\ \to f_y(x,y)=-6x+3y^2...................(b)[/tex]
solve both the above equation by equal to 0.
For equation (a)
[tex]\to 3x^2-6y=0\\\\\to 3x^2=6y\\\\\to x^2=2y\\\\\to y=\frac{x^2}{2}\\\\[/tex]
For equation (b)
[tex]\to -6x+3y^2 =0 \\\\\to 3y^2 =6x\\\\\text{put the value of y in equation b}\\\\\to 3(\frac{x^2}{2})^2 -6x=0\\\\\to \frac{3}{4} x^4 -6x=0\\\\[/tex]
by solving the above value in the form of x we get:
[tex]\to x=0\\ \to x=2\\ \to x= -1 +\sqrt{3} i\\ \to x= -1 -\sqrt{3} i\\[/tex]
by solving the above value in the form of y we get:
[tex]\to y=0\\ \to y=2\\ \to y= -1 +\sqrt{3} i\\ \to y= -1 -\sqrt{3} i\\[/tex]
Solve the value by applying the second derivation method:
[tex]\to f_{xx}(x,y)=6x...............(a1)\\\\ \to f_{yy}(x,y)=6y...................(b2)\\\\\to f_{xy}(x,y)=-6...................(c2)[/tex]
calculating the value of discriminate:
[tex]d=f_{xx}(x,y) f_{yy}(x,y)-[f_{xy}(x,y)]^2[/tex]
The critical point of the given equation will be (2,2)
[tex]d=f_{xx}(2,2) f_{yy}(2,2)-[f_{xy}(2,2)]^2\\\\[/tex]
[tex]= (6 \times 2) (6 \times 2) -[(-6)^2]\\\\= (12) (12) -[36]\\\\= 144 -36\\\\= 108\\\\[/tex]
Answer:
[tex](2,2)[/tex] is a minimum point of the function [tex]f(x,y).[/tex]
Step-by-step explanation:
[tex]f(x,y)=x^3-6xy+y^3+7[/tex]
Find the partial differentiation w.r.t. [tex]x[/tex] and [tex]y[/tex].
[tex]\frac {\partial f}{\partial x}=3x^2-6y[/tex]
[tex]\frac {\partial f}{\partial y}=-6x+3y^2[/tex]
[tex]\frac {\partial^2 f}{\partial x^2}=6x[/tex]
[tex]\frac {\partial^2 f}{\partial y^2}=6y[/tex]
[tex]\frac{\partial f}{\partial xy}=-6[/tex]
Find the critical points.
[tex]\frac {\partial f}{\partial x}=\frac {\partial f}{\partial y}=0[/tex]
[tex]\Rightarrow 3x^2-6y=0 \;\text{and}\; -6x+3y^2=0[/tex]
[tex]\Rightarrow 6y=3x^2\Rightarrow y=\frac{x^2}2[/tex]
[tex]\Rightarrow -6x+\frac 34 x^4=0\Rightarrow \frac {x^3}4=2[/tex]
[tex]\Rightarrow x^3=8\Rightarrow x=2,y=2[/tex]
Therefore, [tex](2,2)[/tex] is a critical point.
Now, [tex]\frac {\partial^2 f}{\partial x^2}\frac {\partial^2 f}{\partial y^2}-{\frac {\partial f}{\partial xy}}^2[/tex]
[tex]=6x6y-36=36xy-36>0 \;\text{at critical point }\; (2,2)[/tex]
Thus, [tex](2,2)[/tex] is not a saddle point.
[tex]\because \frac{\partial^2 f}{\partial x^2}>0 \; \text{and}\; \frac {\partial^2 f}{\partial x^2}\frac {\partial^2 f}{\partial y^2}-{\frac {\partial f}{\partial xy}}^2>0 \;\text{at point}\; (2,2)[/tex]
Hence, [tex](2,2)[/tex] is a local minimum of a given function.
Demtermine the degree of the polynomial_57
Answer:
The degree of polynomial of 57 is 0.
Brainlist. Neeed this ASAP. please its on Simplify Expression and i put the picture below
Answer:
G
Step-by-step explanation:
the perimeter is the sum of all sides so we have
[tex]P=a^{2} -ab+a-2a+a^2+ab\\\\P=(a^2-2a^2+a^2)+(-ab+2b)+a\\\\P=(0a^2)+(ab)+a\\\\P=ab+a[/tex]
Answer:
G
Step-by-step explanation:
hope this helps!!!!!!!!!m:)
For the directed line segment whose endpoints are B(0, 0) and C(12, 24), find the point whose coordinates are 3/4 from B to C.
Answer:
(9, 18)
Step-by-step explanation:
If point P is 3/4 of the distance from B to C, it means that ...
BP/BC = 3/4
(P - B) = 3/4(C - B) . . . . . . multiply by BC = (C-B)
P = B + 3/4C -3/4B . . . . . add B
P = (1/4)B +(3/4)C = (B +3C)/4
P = ((0, 0) +3(12, 24))/4 = (36, 72)/4 = (9, 18)
The desired point is (9, 18).
__
As we showed, since B = (0, 0), the point is 3/4 of the coordinates of C.
Hamilton High School has 900 students in school. There are 60 more girls than boys.
How many boys and how many girls are there?
I have 30 ones, 2 thousands, 4 hundred thousands,60 tens and 100 hundreds. What number am I?
2.) You can run 1/5 of a mile in 5 minutes. What is your rate per hour?
Find a conversion factor between cubic meters and cubic
centimeters. Write it in three forms.
I need help please someone let me know!!
Answer:
[tex]1\,\,m^3\,=\,10^6\,\,cm^3[/tex]
Step-by-step explanation:
To find: conversion factor between cubic meters and cubic centimeters
Solution:
One meter is 100 times greater than one centimeter .
1 meter = 100 centimeter
That is [tex]1\,\,m\,=\,100\,\,cm[/tex]
So,
[tex]1\,m^3\,=\,1000000\,cm^3[/tex]
or
[tex]1\,m^3\,=10^6\,cm^3[/tex]
or
[tex]1\,cm^3\,=\,\frac{1}{10^6}\,m^3[/tex]
Which of the following is true?a. The Z score for the median of a left skewed distribution is negative.b. Z scores are defined for observations from distributions of any shape and skew.c. The Z score for the median of a symmetric distribution is approximately 0.d. Calculating percentiles based on the Z table is only appropriate for observations that come from a nearly normal distribution.
Answer: b,c and d.
Step-by-step explanation:
The options that are true are:
b. Z scores are defined for observations from distributions of any shape and skew.
c. The Z score for the median of a symmetric distribution is approximately 0.
d. Calculating percentiles based on the Z table is only appropriate for observations that come from a nearly normal distribution.
It should be noted that option A"The Z score for the median of a left skewed distribution is negative" is false.
For a left skewed distribution, it should be noted that the mean is less than the median which in turn is less than the mode and this will bring about a positive outcome, therefore the corresponding z-score for the median will also be positive and bit negative.
Therefore, b, c and d are true.
If the z-score for the median of the left-skewed distribution is negative then A is false. Then the correct option is B, C, and D.
What is a z-score?The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
It should be noted that in option A, the z-score for the median of the left-skewed distribution is negative.
A. The Z-score for the median of a left-skewed distribution is negative. This is false.
B. Z-scores are defined for observations from distributions of any shape and skew. This is true.
C. The Z-score for the median of a symmetric distribution is approximately 0. This is true.
D. Calculating percentiles based on the Z-table is only appropriate for observations that come from a nearly normal distribution. This is true.
More about the z-score link is given below.
https://brainly.com/question/13299273
What expression can be modeled using the number line?
Answer:
B?
Step-by-step explanation:
On this number line there is no seven, but there is everything from 1 to 0.
Answer:
B. ( 7/10) / ( 1/10)
Step-by-step explanation:
|
|
V
The Schmidts brought a house 10 years ago and took out a mortgage. They are considering selling and want to know how much they still owe. They know their monthly payment and interest rate. Which of the following methods and correctly allow them to find the amount still owed?
Answer: a. They can find the present value of the remaining 20 years worth of payments.
Step-by-step explanation:
The present value of the payments for the servicing of the loan is the amount of the loan that is still owed because the payments include both the interest and the principal repayments.
The Schmidts can therefore find out the amount they still owe by checking the present value of the remaining 20 years worth of payments.
As the payments are usually constant they can be treated as an annuity so using the monthly payment as the annuity, the interest rate as the discount rate and the 20 years ( 240 months) as the period, they should be able to find the present value of the loan.
Solve each proportion. 2/3=x/15
Hey there! ☺
[tex]Answer:\boxed{x=10}[/tex]
[tex]Explanation:[/tex]
2/3 = x/15
(2) * (15) = x * (3) Cross Multiply
30 = 3x
3x = 30 Flip up the equation
3x/3 = 30/3
30/3 = 10 Simplify 30/3
x=10
Hope this helps!
Help please! I don't understand
Answer:
the 3rd triangle
Step-by-step explanation:
they are congruent
sub to pewdiepie
Suppose one person used 2 parts blue paint to 3 parts yellow paint. Another person used 4 parts blue paint to 6 parts yellow paint. Do the ratios of blue paint to yellow paint form a proportional relationship? Explain!
Answer:
Yes, ratios of blue paint to yellow paint form a proportional relationship
Step-by-step explanation:
In case of the first person:
Number of blue parts = 2
Number of yellow parts [tex]=3[/tex]
In case of another person:
Number of blue parts [tex]=4[/tex]
Number of yellow parts [tex]=6[/tex]
Ratio of blue parts [tex]=2:4=1:2[/tex]
Ratio of yellow parts [tex]=3:6=1:2[/tex]
As ration of blue parts is equal to the ratio of yellow parts, ratios of blue paint to yellow paint form a proportional relationship
3m-n=km-8, solve for m
Add n on both sides:
3m = km - 8 + n
Subtract km on both sides:
3m - km = n - 8
Factor the Left-Hand Side:
m(3 - k) = n - 8
Divide both sides by (3 - k):
m = (n - 8) / (3 - k)
Answer:
(8-n)/(k-3) =m
Step-by-step explanation:
3m-n=km-8
Subtract 3m from each side
3m -3m-n=km -3m-8
-n =km -3m-8
Add 8 to each side
8-n =km -3m-8+8
8-n =km -3m
Factor out m
8-n =m(k -3)
Divide by (k-3)
(8-n)/(k-3) =m(k -3)/( k-3)
(8-n)/(k-3) =m
6 = (1 - 9) = (6 - 1) = 9
A. True
B. False
Answer:
False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
[tex]6=(1-9)=(6-1)=9\\\\6=-8=5=9\\\\\boxed{6\neq-8\neq5\neq9}[/tex]
Hope this helps.
Simon is trying to figure out how much it will cost to buy 30 cases of water for a school picnic. How much will Simon pay for 30 cases of water?
Water Prices by the Case
Number of cases
Price in dollars
15 66.00
20 88.00
35 154.00
1. $99.00
2. $119.00
3. $121.00
4. $132.00
which one is right
PS this is for my little sis
Answer:
D;132.00
Please Mark me the Brainleist.
Find the sum of the positive integers less than 200 which are not multiples of 4 and 7
Answer:
[tex]12942[/tex] is the sum of positive integers between [tex]1[/tex] (inclusive) and [tex]199[/tex] (inclusive) that are not multiples of [tex]4[/tex] and not multiples [tex]7[/tex].
Step-by-step explanation:
For an arithmetic series with:
[tex]a_1[/tex] as the first term, [tex]a_n[/tex] as the last term, and[tex]d[/tex] as the common difference,there would be [tex]\displaystyle \left(\frac{a_n - a_1}{d} + 1\right)[/tex] terms, where as the sum would be [tex]\displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n)[/tex].
Positive integers between [tex]1[/tex] (inclusive) and [tex]199[/tex] (inclusive) include:
[tex]1,\, 2,\, \dots,\, 199[/tex].
The common difference of this arithmetic series is [tex]1[/tex]. There would be [tex](199 - 1) + 1 = 199[/tex] terms. The sum of these integers would thus be:
[tex]\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}[/tex].
Similarly, positive integers between [tex]1[/tex] (inclusive) and [tex]199[/tex] (inclusive) that are multiples of [tex]4[/tex] include:
[tex]4,\, 8,\, \dots,\, 196[/tex].
The common difference of this arithmetic series is [tex]4[/tex]. There would be [tex](196 - 4) / 4 + 1 = 49[/tex] terms. The sum of these integers would thus be:
[tex]\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}[/tex]
Positive integers between [tex]1[/tex] (inclusive) and [tex]199[/tex] (inclusive) that are multiples of [tex]7[/tex] include:
[tex]7,\, 14,\, \dots,\, 196[/tex].
The common difference of this arithmetic series is [tex]7[/tex]. There would be [tex](196 - 7) / 7 + 1 = 28[/tex] terms. The sum of these integers would thus be:
[tex]\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}[/tex]
Positive integers between [tex]1[/tex] (inclusive) and [tex]199[/tex] (inclusive) that are multiples of [tex]28[/tex] (integers that are both multiples of [tex]4[/tex] and multiples of [tex]7[/tex]) include:
[tex]28,\, 56,\, \dots,\, 196[/tex].
The common difference of this arithmetic series is [tex]28[/tex]. There would be [tex](196 - 28) / 28 + 1 = 7[/tex] terms. The sum of these integers would thus be:
[tex]\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}[/tex].
The requested sum will be equal to:
the sum of all integers from [tex]1[/tex] to [tex]199[/tex], minus the sum of all integer multiples of [tex]4[/tex] between [tex]1\![/tex] and [tex]199\![/tex], and the sum integer multiples of [tex]7[/tex] between [tex]1[/tex] and [tex]199[/tex], plus the sum of all integer multiples of [tex]28[/tex] between [tex]1[/tex] and [tex]199[/tex]- these numbers were subtracted twice in the previous step and should be added back to the sum once.That is:
[tex]19900 - 4900 - 2842 + 784 = 12942[/tex].
Standing from the top of a platform. Frank
shot an arrow vertically into the air at an
initial velocity of 118 ft/s. The height of the
arrow, h, at t seconds is modeled by the equation h = -16t^2 + 118t + 15. How many seconds will take the arrow to reach the
ground?
Answer:
7.5 seconds.
Step-by-step explanation:
The height of the arrow as a function of time t is given by :
[tex]h = -16t^2 + 118t + 15[/tex]
Here, 118 ft/s is the initial velocity and 15 feet is the height of the platform. We need to find How many seconds will take the arrow to reach the ground. When it reaches the ground, h(t) = 0
[tex]-16t^2 + 118t + 15=0[/tex]
The above is a quadratic equation. The solution of the above equation is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Here, b = 118, a = -16 and c = 15
So,
[tex]t=\dfrac{-118\pm \sqrt{(118)^2-4(-16)(15)} }{2\times (-16)}\\\\t=-0.125\ \text{and}\ 7.5\ s[/tex]
Time can't be negative.
So, it will take 7.5 seconds to reach the ground.
Put these numbers in order from least to greatest.
-22/40, 8, 18/24
Answer:
-22/40, 18/24, 8
Step-by-step explanation:
Consider the expression 63+81. How can you use the distributive property and the GCF to find an equivalent expression? Explain how you can check your answer.
Answer:
9(7+9)
Step-by-step explanation:
The greatest common factor in this situation is 9 so you could factor out 9 and get 9(7+9) you can check this answer by multiplying both numbers by the number on the outside of the parenthesis.
hope this helps mark brainliest please
Answer:
The greatest common factor is 9 you could change it to 9(7+9) you can make sure this answer is correct by multiplying both numbers by the number in the parentheses.
Step-by-step explanation:
What do we call the characteristics of the individual to be measured or observed
Answer:
variable
Step-by-step explanation:
lndividuals are the people or objects included in the study. A variable is the characteristic of the individual to be measured or observed. For example, if we want to do a study about the people who have climbed Mt.
Answer:
variable is the characteristics of an individual to be observed or measured.
please follow me
One angle of an octagon is 65º. The
others are equal to each other. Find them.
x = 145°
Step-by-step explanation:the sum of interior angles of octagon formula
S = (n - 2)×180°
n = 8
S = (8 - 2)×180°
S = 6×180°
S = 1080°
we have 1 angle = 65° & others are equal to each other
1080° - 65° = 7x
7x = 1015°
x = 1015° : 7
x = 145°
Consider f (x) = StartRoot x squared minus 1 EndRoot and g (x) = StartRoot x squared + 1 EndRoot. What value(s) of x would make f(g(x)) and g(f(x)) commutative? x greater-than-or-equal-to 1 or x less-than-or-equal-to negative 1 Negative 1 less-than-or-equal-to x less-than-or-equal-to 1 any value of x no value of x
Answer:
Any value of x
Step-by-step explanation:
Given
[tex]f(x) = \sqrt{x^2 - 1}[/tex]
[tex]g(x) = \sqrt{x^2 + 1}[/tex]
Required
What value of x is [tex]f(g(x)) = g(f(x))[/tex]
Solving for f(g(x))
[tex]f(x) = \sqrt{x^2 - 1}[/tex]
[tex]f(g(x)) = \sqrt{(\sqrt{x^2 + 1})^2 - 1}[/tex]
Solve the inner square
[tex]f(g(x)) = \sqrt{(x^2 + 1 - 1}[/tex]
[tex]f(g(x)) = \sqrt{x^2 } }[/tex]
[tex]f(g(x)) = x[/tex]
Solving g(f(x))
[tex]g(x) = \sqrt{x^2 + 1}[/tex]
[tex]g(f(x)) = \sqrt{(\sqrt{x^2 - 1})^2 + 1}[/tex]
[tex]g(f(x)) = \sqrt{x^2 - 1 + 1}[/tex]
[tex]g(f(x)) = \sqrt{x^2 }[/tex]
[tex]g(f(x)) = x[/tex]
Equate f(g(x)) and g(f(x))
[tex]f(g(x)) = g(f(x))[/tex]
[tex]x = x[/tex]
This implies that [tex]f(g(x)) = g(f(x))[/tex] at any value of x
Answer:
C, any value of x
Step-by-step explanation:
EDGE
The length of a rectangle is 3 units greater than its width. If the width is w, what expression gives the perimeter of the rectangle in terms of its width?
Step-by-step explanation:
let width be "w"
given,length of rectangle is 3 units greater than its width
length= w+ 3
perimeter of rectangle= 2( l+ b)
= 2[( w+3)+ w]
= 2(w to the power of 2 + 3w)
= 2w to the power of 2 + 6w
is the answer
The perimeter of the rectangle is 4w+6 units
What is the perimeter of rectangle?The perimeter of a rectangle is the sum of its four sides. Perimeter of Rectangle = 2 (Length + Width) units.
According to the question
Width of rectangle = w
Length of rectangle = w+3
Perimeter of Rectangle = 2 (Length + Width)
= 2( w+3 +w)
= 2(2w+3)
= 4w+6 units
Hence, The perimeter of the rectangle is 4w+6 units .
To know more about Perimeter of Rectangle here :
https://brainly.com/question/4074407
# SPJ2
Express the interval using inequality notation.
-3,8
Answer:
- 3 ≤ n ≤ 8
Step-by-step explanation:
Express the interval using inequality notation: -3,8
Interval between - 3 and 8, assumed both included, expressed as:
- 3 ≤ n ≤ 8the scale from a square exercise mat in a gymnastic arena to a scale copy of the exercise mat is 8 m for every 2 in. The actual area of the exercise mat is 144m2. What are the dimensions of the mat on the scale copy?
Answer: 18 and 36
Step-by-step explanation:
The scale is 8m for every 2 in and the actual area is 144m2 so we need to covert that into inches. You divide 144 by 8 which = 18 and then multiply 18 x 2 which is equal to 36.
Maya is saving up to buy a new jacket. She already has $30 and can save an additional $10 per week using money from her after school job. How much total money would Maya have after 6 weeks of saving? Also, write an expression that represents the amount of money Maya would have saved in w w weeks.
Answer:
x = 6 weeks
Step-by-step explanation:
We'll let x represent the number of weeks it will take to save enough money. If she saves $11 each week, then in x weeks she will save 11x dollars.
Add this to the 107 she has already saved, and at the end of 11 weeks she will have 11x + 107 dollars.
We want the amount saved to be equal to the price of the bike, so our equation is
11x + 107 = 173
In a word problem, writing the equation is usually the hardest part. Now we solve the equation.
Subtract 107 from both sides to get
11x = 66
Divide both sides by 11 to get
x = 6 weeks
The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. draw another scale drawing of the pool using the scale 25 m to 2 cm. Explain why your drawing is accurate.
Answer:
Step-by-step explanation:
From the given rectangle,
Length of the rectangle = 5 cm
Width of the rectangle = 10 cm
Ratio of length : width = 1 : 2
Perimeter of the rectangle = 2(l + b)= 150 cm
l + b = 75 -----(1)
Since, l : b = 1 : 2
[tex]\frac{l}{b}= \frac{1}{2}[/tex]
b = 2l ------(2)
From equations (1) and (2),
l + 2l = 75
3l = 75
l = 25 m
Width 'b' = 2(25) = 50 m
Now we have to draw a rectangle with a scale = 25 : 2
Therefore, Scale factor = [tex]\frac{25}{l}=\frac{25}{2}[/tex]
l = 2 cm
Similarly,
[tex]\frac{50}{w}=\frac{25}{2}[/tex]
w = 4 cm
Now we can draw a rectangle with length = 2 cm and width = 4 cm.
Solve the equation. Enter the answer as an equation showing the value of the
variable (like s=-6, or w=1/2). Use a slash mark (/) as the fraction bar if
necessary
6x= 18
Answer:
x = 3
Step-by-step explanation:
We divide 6 on both sides
Answer:
3
Step-by-step explanation:
On Monday Tino, explored a cave that was 127 feet below sea level, and on Tuesday he explored a cave that was 203 above sea level. What is the difference in the sea level of the two caves?
