Answer:
(0,0) is a saddle point
(-1,-3) is a local maximum
Step-by-step explanation:
Find critical points
[tex]f(x,y)=6x^3-y^2+6xy+2\\\\\frac{\partial f}{\partial x}=18x^2+6y\rightarrow18x^2+6y=0\\\\\frac{\partial f}{\partial y}=-2y+6x\rightarrow6x-2y=0[/tex]
[tex]6x-2y=0\\3x=y[/tex]
[tex]18x^2+6y=0\\18x^2+6(3x)=0\\18x^2+18x=0\\x^2+x=0\\x(x+1)=0\\x=0,-1[/tex]
Therefore, the critical points are [tex](0,0)[/tex] and [tex](-1,-3)[/tex].
Determine value of Hessian Matrix at critical points
[tex]H=\bigr(\frac{\partial^2 f}{\partial x^2}\bigr)\bigr(\frac{\partial^2 f}{\partial y^2}\bigr)-\bigr(\frac{\partial^2 f}{\partial x \partial y}\bigr)^2\\\\H=(36x)(-2)-6^2\\\\H=-72x-36[/tex]
For (0,0):
[tex]H=-72(0)-36=-36 < 0[/tex], so (0,0) is a saddle point
For (-1,-3):
[tex]H=-72(-1)-36=72-36=36 > 0[/tex], so (-1,-3) is either a local maximum or minimum. Since [tex]\frac{\partial^2 f}{\partial x^2}=36x=36(-1)=-36 < 0[/tex], then (-1,-3) is a local maximum.
Can someone please help me with math
Answer:
A. 20.2 ft
Step-by-step explanation:
use the pythagorean theorem to get your answer.
a^2+b^2=c^2
17^2+11^2=c^2
289+121=410
***IMPORTANT, remember to square root the answer. 410 isn't your final answer, it's still in c^2 form. 20.2 is the correct answer after square rooting it. don't forget that for future problems
Answer:
A. 20.2 ft
Step-by-step explanation:
Hope it helps..
Can someone help me with this. Will Mark brainliest. Need answer and explanation/work. Thank you.
Answer:
Parallel: y = -2x + 2 (Or any value that isn't 4), Perpendicular: 1/2x + (Anything),
Neither: y = 4x - 7 (Or any random equation that does not have the same, or opposite reciprocal slope)
Step-by-step explanation:
Tina drew a triangle with side lengths 6, 8, and 14. She claims it is a right triangle. Is she correct?
Answer:
No such a triangle can not exist.
find the value of x for both problems.
Answer:
Step-by-step explanation:
In Problem 6, 3/x = tan 30 degrees, or x/3 = 1 / (tan 30 degrees), or
x = 3 / (tan 30 degrees). Using a calculator: x = 3 / (0.449) = 6.68 units
In Problem 9, we begin by finding the length of the hypotenuse of the upper triangle: sin 60 degrees = 9√3 / hypotenuse, or
hypotenuse = 9√3/ (√3 / 2) = 9/2. Then the hypotenuse of the 45-45-90 triangle is 9/2. Thus, cos 45 degrees = x / (9/2), or
2x √3
---- = -------
9 2
9√3
Cross-multiplying, we get 4x = 9√3, so that x = -------------
4
What is the median of the data set? {5, 3, 4, 2, 6} Enter your answer in the box. Round to the nearest tenth.
The best answer will receive brainiest.
Answer:
4
Step-by-step explanation:
To find median, arrange the data set in ascending order. Then the middle term is the median
2 , 3 , 4 , 5 , 6
Median = 3rd term = 4
Answer:
4 is the median
Step-by-step explanation:
From least to greatest:
2,3,4,5,6
Since the total values is odd, the middle number is the median
4 is the median
What is the probability of 4 consecutive 2-sided coin tosses all coming up heads?
The probability of getting four consecutive heads in four 2-sided coin tosses is 1/16 or 0.0625 or 6.25%.
The Probability is defined as a measure of the likelihood or chance that an event will occur, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.
To calculate the probability of getting four consecutive heads in a row, we multiply the probabilities of each individual toss.
The Probability of heads (H) is = 1/2,
So, The Probability of four consecutive heads (HHHH) is :
= (1/2) × (1/2) × (1/2) × (1/2) = (1/2)⁴ = 1/16,
Therefore, the required probability is 1/16 or 6.25%.
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Write an expression in factored form to represent the area of each shaded region. Include the area formula and full steps and write your answer in simplified form. 3x a) (3 marks) 3x + y 2x +y 3x b) 3y (3 marks) B 2x 2x
a. The area of the shaded region = (3x)(5x + 2y).
b. The area of shaded region = 2x(2xπ - 3x).
Given that,
We have to write an expression in factored form to represent the area of each shaded region.
We know that,
a. In the picture we can see that the shaded region.
The area of the shaded region is area of rectangle with vertical + area of rectangle Horizontal
The area of rectangle is length × width.
The area of the shaded region = (3x)(3x + y) + (2x + y)(3x)
The area of the shaded region = (3x)(3x + y + 2x + y)
The area of the shaded region = (3x)(5x + 2y)
Therefore, The area of the shaded region = (3x)(5x + 2y)
b. In the picture we can see that circle with shaded region,
The area of shaded region is area of the circle - area of the rectangle
The area of the circle is πr² and area of rectangle is length × width.
The area of shaded region = πr² - (l×w)
The area of shaded region = π(2x)² - (2x × 3x)
The area of shaded region = 4x²π - 6x²
The area of shaded region = 2x(2xπ - 3x)
Therefore, The area of shaded region = 2x(2xπ - 3x).
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Use the following diagram to answer question 4 and 5
Exterior Angle Theorem
8.6 points
The measure of ZA is
Given the following diagram, find the measures of
LA and ZB
Type your answer...
B (2x + 4)
5
8.6 points
The measure of ZB is
Type your answer...
(3x - 13)
116°
А
Answer:
3x-13+2x+4=116( the sum of two interior angle is epual to the sum of exterior angle )
5x =116-9
5x=107
x=21.4 degree
then
angle a= 3*21.4-13
a=51.2degree
angle b=2*21.4+2
b =44.8degree
Step-by-step explanation:
plz make me brainliest
Simplify this expression
A password is required to log into a system that only recognizes numbers and letters of the alphabet (not case sensitive). You want to create a password using 5 numbers or letters, but cannot reuse any of them. How many different passwords are possible?
There are 60,466,176 possible passwords for a system that acknowledges both digits and letters of the alphabet (and does not differentiate between uppercase and lowercase letters) and requires a 5-character password with no repeated characters.
For the purpose of computing the total number of possible passwords, it is necessary to take into account the number of options available for each character position. Within the constraints of the system, there are 10 different options for each number (0-9) and 26 different options for each letter (A-Z).
There are a total of 36 options available to us when it comes to the first character position (26 letters and 10 numerals). We are left with 35 options for the second place because we are unable to recycle any of the characters (36 options, minus the one that has already been used). In a similar fashion, we have 34 options for the third position, 33 options for the fourth position, and 32 options for the fifth position.
To calculate the total number of possible passwords, we multiply the number of choices for each position together: 36 * 35 * 34 * 33 * 32 = 60,466,176. Given the parameters of this system, there are consequently sixty-four million, four hundred sixty-six thousand, one hundred seventy-seven different passwords that might be used.
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Mario tiene 4 pantalones de diferente color (azul, café, negro y blanco) y 6 camisas también de diferente color (blanca, negra, azul, café, gris y verde). Si Mario escoge una combinación al azar, ¿cuál es la probabilidad de que se vista con pantalón azul y camisa blanca?
Find the basis for the kernel and imagine of this transformation. Let T : P₂ → R where T(p(x)) = p(1). Find a or the kernel and image of this transformation.
The basis for Ker(T) is {}, and the basis for Im(T) is {1}.
Since, The kernel of T, denoted Ker(T), is the set of all elements in P₂ that are mapped to zero in R by T.
In other words, Ker(T) is the set of all polynomials in P₂ such that
T(p(x)) = p(1) = 0.
Hence, To find the kernel, we need to solve the equation p(1) = 0.
Since, The only polynomial that satisfies this condition is p(x) = 0.
Therefore, Ker(T) = {0}.
Now, the image of T.
The image of T is the set of all elements in R that are mapped to by some element in P₂ under T.
In other words, Im(T) is the set of all possible values of p(1) for all polynomials p(x) in P₂.
Some example: - If p(x) = 1 + 2x + x², then p(1) = 1 + 2 + 1 = 4.
So, we can see that Im(T) is the set of all real numbers.
Hence, the basis for the kernel and image of T.
Since Ker(T) = {0}, the basis for the kernel is the empty set, denoted by {}.
Since Im(T) is the set of all real numbers, any non-zero real number can be expressed as a scalar multiple of any other non-zero real number.
Therefore, the basis for Ker(T) is {}, and the basis for Im(T) is {1}.
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How many real solutions exist for this system of equations? Y = -x + 1 y = -x2 + 4x − 2 A. Zero B. One C. Two D. Infinite
Answer:
Two solutions
Step-by-step explanation:
Given the functions Y = -x + 1 y = -x² + 4x − 2
Since they are both y values, we will equate them to have:
-x+1 = -x² + 4x − 2
Equate to zero
x²-x-4x+1+2=0
x²-5x+3 = 0
Since the resulting equation is quadratic (highest degree being 2), hence there will be two solutions to the equation
find the area of this polygon
Answer:
answer is 65 in²
hope this helps
Make r the subject of x=e+r/d
Answer:
r = dx - de
Step-by-step explanation:
x = e + r/d
x - e = r/d
d (x - e) = r
dx- de = r
r = dx - de
We know the following about the transformation A:
A ï1 0 ò=ï2 0 ò
and A ï0 1 ò=ï1 1 ò
73.1 Draw C2 and A(C2), the image of the unit square under A.
73.2 Compute the area of A(C2).
73.3 Compute det(A).
73.1 A(C2) is a quadrilateral with vertices (0, 0), (1, 0), (1, 2), and (0, 2).
73.2 The area of A(C2) is 2.
73.3 The determinant of A is 0
To draw C2 and A(C2), to understand the transformation A and to the unit square.
Given the information:
A:
| 1 0 |
| 2 0 |
A maps the vector [1, 0] to [2, 0], and it maps the vector [0, 1] to [1, 1]. This provides us with the information to draw C2 and A(C2).
73.1 Draw C2 and A(C2):
C2 represents the unit square with vertices (0, 0), (1, 0), (1, 1), and (0, 1).
To draw A(C2), the transformation A to each vertex of C2 and connect the transformed vertices to form the image of C2 under A.
Applying A to the vertices of C2:
A(0, 0) = (1 × 0, 2 × 0) = (0, 0)
A(1, 0) = (1 × 1, 2 × 0) = (1, 0)
A(1, 1) = (1 × 1, 2 × 1) = (1, 2)
A(0, 1) = (1 × 0, 2 × 1) = (0, 2)
Connecting the transformed vertices, we get the image of C2 under A:
73.2 Compute the area of A(C2):
To compute the area of A(C2), divide it into two triangles and calculate their areas separately.
Triangle 1: (0, 0), (1, 0), (1, 2)
Base of Triangle 1 = 1 - 0 = 1
Height of Triangle 1 = 2 - 0 = 2
Area of Triangle 1 = (1/2) × Base × Height = (1/2) × 1× 2 = 1
Triangle 2: (0, 0), (0, 2), (1, 2)
Base of Triangle 2 = 1 - 0 = 1
Height of Triangle 2 = 2 - 0 = 2
Area of Triangle 2 = (1/2) × Base × Height = (1/2) × 1 × 2 = 1
Total Area of A(C2) = Area of Triangle 1 + Area of Triangle 2 = 1 + 1 = 2
73.3 Compute det(A):
To compute the determinant of A (denoted as det(A)), use the formula for a 2x2 matrix.
A:
| 1 0 |
| 2 0 |
det(A) = (1 ×0) - (0 × 2) = 0 - 0 = 0
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Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be . Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.
The question is incomplete. The compete question is :
Saul decides to use the IQR to measure the spread of data. Saul calculates the IQR of the data set to be 27. Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine. 25, 30, 50, 50, 50, 50, 56, n, 250. What is the value of n that will make the IQR of the data set equal to 27?
Solution :
The inter quartile range is being measured as : 3rd quartile - 1st quartile
The 1st quartile = 25% mark
The 3rd quartile = 75% mark
The data set as given in the question is :
25, 30, 50, 50, 50, 50, 56, n, 250
Therefore, the total number of the sample = 9
And the median is = 50
The median separates the given data sets into two equal halves-- that is the upper half and the lower half.
Let the middle of a lower half is the 1st quartile be [tex]$Q_1$[/tex]
And the middle of a 2nd half is the 3rd quartile be [tex]$Q_3$[/tex]
∴ [tex]$Q_1=\frac{30+50}{2}$[/tex]
[tex]$=40$[/tex]
[tex]$Q_3=\frac{56+n}{2}$[/tex]
Now for the IQR of the data set to be equal to [tex]$27$[/tex],
[tex]$\frac{56+n}{2}-40=27$[/tex]
[tex]$\frac{56+n}{2}=27+40$[/tex]
[tex]$\frac{56+n}{2}=67$[/tex]
[tex]$56 +n=134$[/tex]
[tex]$n=134-56$[/tex]
[tex]$n=78$[/tex]
CORRECT ANSWER GETS BRAINLIEST
Explain how you would apply exponent rules to evaluate for the value of (x³/x)² if x =1/2?
Answer:
1/16
Step-by-step explanation:
Picture is attached. The quickest way is to simplify BEFORE plugging in x = 1/2
Im giving brainliest
Answer:
√17 - 3 > -2 + √5How many days in April
Answer:
There are 30 days according to the Georgian calender of the month of april.
Step-by-step explanation:
In desperate need of help. If anyone could help it would be greatly appreciate. Will rate brainliest!
Answer:
7 people
Step-by-step explanation:
Chocolate: 350 / 100 = 3.5 x 2 = 7
Butter: 45 / 10 = 4.5 x 2 = 9
Eggs: 8 / 2 = 4 x 2 = 8
The amount of chocolate is the limiting factor as you have enough eggs for 8 people and enough butter for 9 people, but only enough chocolate for 7 people
encontre as raízes quadradas dos números:
a)²√625
25
porque al multiplicar 25×25 nos da 625
Answer:
25
Step-by-step explanation:
25x25=625
¿Cuáles son los números primos entre 2 y 20?
Answer:
2 3 5 7
Step-by-step explanation:
A rectangular prism has a base perimeter of 28 inches and a height of 6 inches. What is the lateral surface area of the prism?
Answer:
uhuhuhuhuhuhuhuhuhuhuh oh yeah
Step-by-step explanation:
What’s the opposite of -5/8
what is the volume of a right triangular prism whose height is 20 units and whose base is a right triangle with side lengths of 3,4, and 5?
Help pls I’m on a time limit. Please and thank you <33
Answer: the answer is 3/10
Step-by-step explanation: because its 3/10
Answer:
es
3/ 10
Step-by-st
PLSSSS HELPPPP PLSSSS PLS HELPPPPP!!!!!!
Answer:
B -- (5 smoothings)(price of 1 smoothie) + tip = $23
Step-by-step explanation:
5 smoothies(price of 1 smoothie)+tip=23
Use the box method to distribute and simplify (2 + 1)(2x - 3). Drag and drop the
terms to the correct locations of the table.
Answer:
2x^2-x-3
(2x)(-3)
(x)
(1)
Step-by-step explanation:
Distribute
(2x^2) (-3x)
(2x) (-3)
Please help me, GodBless.
Answer:
Rate of change is 1
Step-by-step explanation:
Well rate of change in a function is basically slope
theres 1 rise and.1 run
1/1=1
So rate of change is 1