Answer:
In a function of two variables, the critical points are these in which both derivatives are 0, and if:
[tex]\frac{d^2f}{dx^2}*\frac{d^2f}{dy^2} - [ \frac{d^2f}{dxdy} ]^2 < 0[/tex]
the point is a saddle point.
If the above equation is larger than zero, the critical points can be either a local maximum or a local minimum.
If it is equal to zero, no conclusions can be made.
First, let's find all these derivatives.
df/dx = 4*(x^3)*(y^2)
This is zero when x or y are equal to zero.
df/dy = 2*(x^4)*(y)
This is equal to zero when either x or y are equal to zero.
So in both cases, the points of the form:
(x, 0) and (0, y) are zeros of the first derivative, so these are the critical points.
Now let's look at the second derivatives:
[tex]\frac{d^2f}{dx} = 4*3*x^2*y^2 = 12*x^2*y^2[/tex]
[tex]\frac{d^2f}{dy^2} = 2*x^4[/tex]
[tex][\frac{d^2f}{dxdy} ]^2 = (4*x^3*2*y)^2 = 64*x^6*y^2[/tex]
Then, the equation to see if the points are saddle points or not are:
[tex](12*x^2*y^2)*(2*x^4) - 64*x^6*y^2 < 0[/tex]
In any of the previous found points (the ones of the form (x, 0) and (0, y)) the above equation will be equal to zero, then none of these points is a saddle point. More than that, in the particular case where the above equation is equal to zero, the critical points can be either: A relative minimum, a relative maximum, or a saddle point (so we need more analysis to find it out)
But in this case is ratter simple, because both powers in f(x, y) are even, we can conclude that the function is even and symmetric about x= 0 and y = 0, and the function is also positive, so all the points:
(0, y) and (x, 0) are the minimum values that f(x, y) can take.
Then the critical points are relative minimums.
consider the following exam scores from a class of 8 students
55,65,77,79,84,89.91,99
What is the rank of the student that scored a 77 on the exam?
Answer:
rank 6
Step-by-step explanation:
Some1 hurry need help
Answer:
Y=x/3 is the answer
Step-by-step explanation:
Hope this helps!!
WILL
GIVE BRAINLIST
ANSWER
MATH
Answer:
Mean = 4.7
Mode = 5
Median = 5
Step-by-step explanation:
Mean = Σfx / Σf
Σfx = (3*4) + (4*5) + (5*7) + (6*2) + (7*2) = 93
Σf = (4+5+7+2+2) = 20
Mean = 93 / 20
= 4.65
= 4.7
Mode = highest occurring = vlaue with highest frequency = 5
Median :
20 / 2 = 10
Value corresponding to the 10th term = 5
A random sample of 300 balls hit into play in college baseball games is taken. For each ball hit into play, it is recorded whether the ball was hit to the left, center, or right of the field, and whether the ball resulted in a hit or an out. Which of the following is the appropriate null hypothesis to test if there is a relationship between the direction of the ball and if it resulted in a hit or an out?
(A) H_0H0: The proportion of balls hit to the left, right, and center is the same.
(B) H_0H0: The proportion of balls that result in hits and outs is the same.
(C) H_0H0: The distribution of the direction of the ball is the same for the population of hits and the population of outs.
(D) H_0H0: The direction of the ball and whether it results in a hit or an out are independent.
(E) H_0H0: There is an association between the direction of the ball and whether it results in a hit or an out.
Answer:
(D) H_0H0: The direction of the ball and whether it results in a hit or an out are independent.
Step-by-step explanation:
Given that
There is 300 balls random sample is taken
We need to find out the appropriate null hypothesis that lies between the ball direction and lead to a hit or an out
So
Based on the given options, the option d is correct as the ball direction and its results either be hit or on out would represent that they are independent
Therefore the option d is correct
please help my teacher wont help
Answer: Choice B
They traveled 250 miles in 4 hours. Their speed was 62.5 mph.
=============================================================
Explanation:
Start at point X. Draw a horizontal line straight across until you reach the y axis. You should arrive at y = 250. This tells us that they traveled 250 miles.
Go back to point X. Draw a vertical line until you reach the x axis. You should reach x = 4. This indicates 4 hours.
Pairing up the two values together means they traveled 250 miles in 4 hours. Divide the distance over time to get the speed
speed = distance/time = 250/4 = 62.5 miles per hour
--------
Side note: unfortunately your teacher chose the label uppercase X for the point, which may be a bit confusing since it could clash with the lowercase x along the horizontal axis.
Another note: the speed represents the slope of the line
In a lab experiment, 300 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 18 hours. How many bacteria would there be after 3 hours, to the nearest whole number?
Answer:
337
Step-by-step explanation:
300(2)^(3/18)
= 300(2)^1/6
= 337.
Find the value of x.
Answer:
x = 14
Step-by-step explanation:
Hope that will help you
The radius of a cylinder is 5 cm and the height is 7 cm.
Find the Lateral Area for the cylinder.
8011
A7011
12011
17511
Answer:
70 πStep-by-step explanation:
Lateral Area of a Cylinder is A = 2πrh
Substitue the values in the above equation to get:
A = 2(π) * 5 * 7
A = 70 π
solve for x 5x 2^3x = 21
Answer:
0.69
Step-by-step explanation:
someone please help me
Answer:
the answer is 35 mi
Step-by-step explanation:
28 squared = 784
21 squared = 441
784+441 = 1225
Square root of 1225 is 35
Carson = C
Hanford = H
Ridgewood = R
CR²=CH²+HR² <=>
<=> CR²=28²+21²=1225 <=> CR=√1225=35
Jennifer has 84.5 yards of fabric to make curtains for her new house. She made
identical curtains and has 19.7 yards of fabric left over.
How many yards of fabric does Jennifer use for each curtain?
Answer:
64.8
Step-by-step explanation:
84.5 - 19.7 = 64.8
Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio.
A (8,6), B(-2,-9); 3 to 2
The coordinates of point P are
Answer:
[tex]P = (2,-3)[/tex]
Step-by-step explanation:
Given
[tex]m : n = 3 : 2[/tex]
[tex]A = (8,6)[/tex]
[tex]B = (-2,-9)[/tex]
Required
The coordinate of {
This is calculated as:
[tex]P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
So, we have:
[tex]P = (\frac{3*-2 + 2*8}{3 + 2},\frac{3*-9 + 2*6}{3 + 2})[/tex]
[tex]P = (\frac{10}{5},\frac{-15}{5})[/tex]
[tex]P = (2,-3)[/tex]
HELP ME AND GIVE ME THE ANSWER I DONT NEED U TO EXPLAIN ANYTHING JUST HURRY UP
Answer:
x = 9.1
Step-by-step explanation:
What is 34×67 what is it
Answer:
2278
Step-by-step explanation:
What is the z score associated with sleeping 503 minutes per night
Answer:
you need to mutiply zero meana503 neary by 500
In a psychology class, 60 students have a mean score of 96.9 on a test. Then 19 more students take the test and their mean score is 71.3.
What is the mean score of all of these students together? Round to one decimal place.
Help please, and thank you! C:
Answer:83.3
Step-by-step explanation:
plz i need help asappppppppp
i think the answer is -5???
Answer:
-10
Step-by-step explanation:
a bag contains 48 balls
the ratio of red to blue balls is 3:5 find how many red and blue balls there are.
please help
Answer:
25 Balls
Step-by-step explanation:
Does the quadratic function
y = 3x2 + 7x - 8
have one, two or no real zeros?
Utilize the quadratic formula to
determine the answer.
[?] real zeros
Answer:
Two real roots
Step-by-step explanation:
The portion of the quadratic formula that determines the number of roots is
b² - 4ac
If it's positve there are two real roots
If it's zero there is one real root
If it's negative there are no real roots
------------------------------
b² - 4ac = 7² - 4(3)(-8)
b² - 4ac = 49 + 96
b² - 4ac = 145
Two real roots since 145 is positive
The quadratic equation has two real zeroes
What is quadratic equations?
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfill the equation (, ).
It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
What is quadratic formlua?
D=b²-4ac
x=(-b±√(b²-4ac))/2a
y = 3x² + 7x - 8
On comparing with ax²+bx+c, we get
a=3, b=7 and c=-8
Using Quadratic formula
D=b²-4ac
=7²+4x3x8
=49+96
=145>0
Hence it has real zeroes
Learn more about Quadratic equation,
https://brainly.com/question/776122
#SPJ2
Find the volume of the square pyramid shown (please help)
Answer:
Given:
b = 8 cm
h = 3 cm
Find : Volume
Formula: V = [tex]a^{2}[/tex]h/3
Solution: V = (8 cm)2 ( 3 cm)/ 3
V = (64 cm2)(3 cm)/3
V = 192 cm3/3
V = 64 cubic cm
Rocco has a garden and an oak tree. The oak tree is 11 times as old as the garden. The sum of their ages is 108 years. How old is each the garden and tree?
Answer:
GARDEN = 9 years
TREE = 99 years
Step-by-step explanation:
the following equation can be derived from the question
age of oak tree = 11x
age of garden = x
11x + x = 108
12x = 108
x = 9
oak tree = 11 x 9 = 99
In the figure below, points A, B, and C are ______ points because they lie on the same line.
Answer:
A, B, C are Collinear points
Step-by-step explanation:
Find tano, where is the angle shown.
Give an exact value, not a decimal approximation.
17
ө
8
Answer:
Step-by-step explanation:
cos θ=8/17
sec θ=17/8
sec² θ-tan²θ=1
tan θ=√(sec²θ-1)=√((17/8)²-1)=√((289-64)/64)=√(225/64)=15/8
A used bookstore is having a sale. All paperback books
are $0.75 and all hardcover books are $3. Ginny has $10.
She wants to buy one hardcover book and as many
paperback books as she can. Which inequality represents
this situation, where p represents the number of paperback
books Ginny can buy?
Answer:
Ha ha ha ha ha
Yo, I'll tell you what I want, what I really, really want
So tell me what you want, what you really, really want
I'll tell you what I want, what I really, really want
So tell me what you want, what you really, really want
I wanna, (ha) I wanna, (ha) I wanna, (ha) I wanna, (ha)
I wanna really, really, really wanna zigazig ah
If you want my future, forget my past
If you wanna get with me, better make it fast
Now don't go wasting my precious time
Get your act together we could be just fine
I'll tell you what I want, what I really, really want
So tell me what you want, what you really, really want
I wanna, (ha) I wanna, (ha) I wanna, (ha) I wanna, (ha)
I wanna really, really, really wanna zigazig ah
If you wanna be my lover, you gotta get with my friends
(Gotta get with my friends)
Make it last forever, friendship never ends
If you wanna be my lover, you have got to give
Taking is too easy, but that's the way it is
Oh, what do you think about that
Now you know how I feel
Say, you can handle my love, are you for real
(Are you for real)
I won't be hasty, I'll give you a try
If you really bug me then I'll say goodbye
Yo I'll tell you what I want, what I really, really want
So tell me what you want, what you really, really want
I wanna, (ha) I wanna, (ha) I wanna, (ha) I wanna, (ha)
I wanna really, really, really wanna zigazig ah
If you wanna be my lover, you gotta get with my friends
(Gotta get with my friends)
Make it last forever, friendship never ends
If you wanna be my lover, you have got to give
(You've got to give)
Taking is too easy, but that's the way it is
So, here's a story from A to Z
You wanna get with me, you gotta listen carefully
We got Em in the place who likes it in your face
You got G like MC who likes it on a
Easy V doesn't come for free, she's a real lady
And as for me, ha you'll see
Slam your body down and wind it all around
Slam your body down and wind it all around
If you wanna be my lover, you gotta get with my friends
(Gotta get with my friends)
Make it last forever, friendship never ends
If you wanna be my lover, you have got to give
(You've got to give)
Taking is too easy, but that's the way it is
If you wanna be my lover
You gotta, you gotta, you gotta, you gotta, you gotta
Slam, slam, slam, slam (make it last forever)
Slam your body down and wind it all around
Slam your body down and wind it all around
Ha, ha, ha, ha, ha
Slam your body down and wind it all around
Slam your body down and zigazig ah
If you wanna be my lover
Step-by-step explanation:
Need help asap please
Answer:
58
Step-by-step explanation:
50 POINTS !!
PLEASE HELP
EXPLAIN HOW YOU GOT IT !!!!
ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
Step-by-step explanation:
Hope this helps u!!
Which Number has the highest value?
-25
16
-32
34
Answer:
34
Step-by-step explanation:
Answer:
34
Step-by-step explanation:
its the largest, positive number
Find the total cost of $16 IMax movie with you have a 15% student
discount. *
Answer:
$13.60
Step-by-step explanation:
16.00 x .85 = 13.60$
-- Gage Millar, Algebra 2 Tutor
Answer:
$18.40 is the final cost
Explanation:
Multiply 15% and 16 and add the product with 16.
Someone said the answer is -5 but can you explain how?
Answer:
-5
Step-by-step explanation:
add 5 and 10 makes 14
minus 5 from 15
multiply 10 and 4 and add to 15 to get 40
subtract 45 from 40 and get -5
m and n are parallel lines cut by a transversal.
What is the value of x + y?
Answer:
180°
Step-by-step explanation:
It will be answer ...............