Answer:
Step-by-step explanation:
Given that:
a)
[tex]f(x,y) = e^{3x} + y^3 - 3ye^x \\ \\ \implies \dfrac{\partial f}{\partial x} = 0 = 3e^{3x} -3y e^x = 0 \\ \\ e^{2x}= y \\ \\ \\ \implies \dfrac{\partial f}{\partial y } = 0 = 3y^2 -3e^x = 0 \\ \\ y^2 = e^x[/tex]
[tex]\text{Now; to determine the critical point:}[/tex]- [tex]f_x = 0 ; \ \ \ \ \ f_y =0[/tex]
[tex]\implies e^{2x} = y^4 = y \\ \\ \implies y = 0 \& y =1 \\ \\ since y \ne 0 , \ \ y = 1, \ \ x= 0\\\text{Hence, the only possible critical point= }(0,1)[/tex]
b)
[tex]\delta = f_xx, s = f_{xy}, t = f_{yy} \\ \\ . \ \ \ \ \ \ \ \ D = rt-s^2 \\ \\ i) Suppose D >0 ,\ \ \ r> 0 \ \text{then f is minima} \\ \\ ii) Suppose \ D >0 ,\ \ \ r< 0 \ \text{then f is mixima} \\ \\ iii) \text{Suppose D} < 0 \text{, then f is a saddle point} \\ \\ iv) Suppose \ D = 0 \ \ No \ conclusion[/tex]
[tex]Thus \ at (0,1) \\ \\ \delta = f_{xx} = ge^{3x}\implies \delta (0,1) = 6 \\ \\ S = f_{xy} = -3e^x \\ \\ \implies S_{(0,1)} = -3 \\ \\ t = f_{yy} = 6y \\ \\[/tex]
[tex]\implies t_{0,1} = 6[/tex]
[tex]Now; D = rt - s^2 \\ \\ = (6)(6) -(-3)^2[/tex]
[tex]= 36 - 9 \\ \\ = 27 > 0 \\ \\ r>0[/tex]
[tex]\text{Hence, the critical point} \ (0,1) \ \text{appears to be the local minima}[/tex]
c)
[tex]\text{Suppose we chose x = 0 and y = -3.4} \\ \\ \text{Then, we have:} \\ \\ f(0,-3.4) = 1+ (-3.4)^3 + 3(3.4) \\ \\ = -28.104 < -1[/tex]
[tex]\text{However, if f (0,1) = 1 +1 -3 = -1 \\ \\ f(0,-3.4) = -28.104} < -1} \\ \\ \text{This explains that} -1 \text{is not an absolute minimum value of f(x,y)}[/tex]
Please help me please help no links
A chocolate shop sells chocolates with a variety of different fillings.
hazelnut 68
caramel 8
orange 8
What is the probability that a randomly selected chocolate will have caramel filling?
Write your answer as a fraction or whole number.
Answer:
There is a [tex]\frac{2}{21}[/tex] chance of picking caramel-filled chocolate.
Step-by-step explanation:
To set this up, you need to make it a fraction. The denominator of the fraction is how many total chocolates you can pick from. You can figure this out by adding all of the chocolate choices together:
68 hazelnut + 8 caramel + 8 orange = 84 chocolates.
The numerator is defined by the number of caramel chocolates, in this case it is 8. That means the fraction will look like:
[tex]\frac{8}{84}[/tex]
Now that can be simplified down. I divided the top and bottom both by 4 to get [tex]\frac{2}{21}[/tex] and that is as far down as it can go. Therefore that is the probability you will get a caramel-filled chocolate.
Lena is saving money to buy a game. So far she has saved $12, which is three-fourths of the total cost of the game. How much does the game cost?
Answer:
12(3/4)=9
12/4=3
3•3=9
12. Draw an acute scalene triangle. Describe
the angles and sides of the triangle.
show
work.
Given the data set, calculate the median
{9, 3, 1, 8, 3, 6}
Answer:
4.5
Step-by-step explanation:
The median we know is the middle number of a set of numbers. Putting the set in least to great order, we have (1, 3, 3, 6, 8, 9). The middle number here is 3 and 6. We take the mean of 3 and 6, (3+6)/2 which gives us 4.5 and that is our answer.
Answer:
4.5
Step-by-step explanation:
i took the test
The function m is given in three equivalent forms.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
B
m(x) = -2x² +24x54
-
m(x) = -2(x - 6)² + 18
m(x) = -2(x - 3)(x-9)
Write one of the zeros.
Answer:
m(x) = -2(x - 3)(x - 9)
One of the zeros of the function is x = 3
Step-by-step explanation:
The form that most quickly reveals the zeros (or "roots") of the function is:
m(x) = -2(x - 3)(x - 9)
To find the zeros of the function, we set m(x) equal to zero:
-2(x - 3)(x - 9) = 0
From this equation, we can see that the zeros (roots) of the function occur when either (x - 3) equals zero or (x - 9) equals zero. Solving these equations gives us the zeros:
x - 3 = 0
x = 3
x - 9 = 0
x = 9
Therefore, one of the zeros of the function is x = 3.
Hope this helps!
Dory can run 3.25 miles every hour. How long will it take her to run a race that is
16 1/4 miles long?
Answer:
it would take her 5 hours
Step-by-step explanation:
16 1/2 divided by 3.25 is 5
Brainliest plz
Will give brainliest
Find the area of the following
triangle:
5 cm
10 cm
A= [?] cm2
Enter the exact answer as a decimal.
Answer:
25
Step-by-step explanation:
a=1/2bh
a=1/2(5)(10)
a=1/2(50)
a=25
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
will mark brianliest please help
Answer:
See below.
Step-by-step explanation:
7x^2 = 343 Divide both sides by 7
7x^2/7 = 343/7
x^2 = 49 Take the square root of both sides.
sqrt(x^2) = sqrt(49)
x = +/- 7
Answers
7- 7sqrt(49)- sqrt(49)I think the last two are kind of iffy. I'm not sure you can call them solutions, but the question probably assumes they are. If you use all four answers and get it wrong, them submit +7 and - 7.
In a middle school of 80 students, 42 girls and 38 boys. What is the probability
that if two students were randomly chosen, the first is a boy and then a girl
sequentially?
Answer:
dont have idea
Step-by-step explanation:
have not studied that topic
Jaelyn uses 3 3/4 cups of flour to make 5 batches of pancakes. How many cups of flour she need to make 1 batch?
NO ANSWERS IN UNKNOWN SITES PLEASE OR I'LL REPORT IT!!!
Answer:
3/4
Step-by-step explanation:
Divide 3 3/4 by 5. 3 3/4 as an improper fraction is 15/4. 15/4 * 1/5 (divided by 5) is 3/4. :D dont report me
3 Select the correct answer. 52 + 51 + 6 For the rational equation, 1 + 3 = 1 what is a valid value of x? ОА. B. -1 O C. 2 O D. 3 Reset Next
9514 1404 393
Answer:
B. -1
Step-by-step explanation:
[tex]\dfrac{x^2 +5x +6}{x+3}=1\qquad\text{given}\\\\\dfrac{(x+2)(x+3)}{x+3}=1\qquad\text{factor}\\\\x+2=1\qquad x\ne-3\qquad\text{cancel factors}\\\\x=-1\qquad\text{add $-2$}[/tex]
The only valid value of x is -1.
What is the slope of a line that is perpendicular to the line whose equation is y=45x−3
y
=
4
5
x
−
3
?
56 + 72 = ( + )
help plz
Answer:
128 = +
Step-by-step explanation:
56 + 72 = 128 (+)
Andrew is shooting arrows at a target.
The experimental probability that one will hit a bulls eye is 1/4. If he shoots 60 arrows, how many times can he expect to hit a bulls eye?
Answer:
15
Step-by-step explanation:
60/4 = 15
So, Andrew would probably hit a bullseye 15 times.
What is the solution for this equation?
A.X=2
B. X = 4
C. X=8
D. x = 12
The right side equals 12 so the left side needs to equal 12
Subtract the 4 circles:
12-4 = 8
There are 2 x’s so 8/2 = 4
X = 4
The answer is B. X = 4
What is the value of the expression: x2 + y2 + x - y
when x = -1 and y = 3
Question 1 options:
6
8
12
16
Answer: 6
Step-by-step explanation:
x^2+y^2+x-y
Put x=-1 and y=1
(-1)^2+(3)^2+(-1)-(3)
1+9-1-3
10-4
6
Can someone help with number 1 please?
Find the product of (x + 3)(x − 3).
x2 − 6x + 9
x2 + 6x + 9
x2 + 9
x2 − 9
Step-by-step explanation:
[tex](x + 3)(x - 3) \\ = {x}^{2} - 3x + 3x - 9 \\ = {x}^{2} - 9[/tex]
#CMIIWThis test will not impact your grade.
Exam
5
Shot
1.38
Find the missing side. Round
to the nearest tenth.
S
02
17
у
SC
440
Х
x= [?]
Enter
Answer:
if i am not wrong is 119
Step-by-step explanation:
I did it like this:
I took 44 + 17= 61
And then I took 180-61= 119
Which of the following exam scores should lead to the better grade? Explain your answer. (4 points)
A score of X = 55 on an exam that has a mean of 60 and a standard deviation of 5.
B. A score of X = 40 on an exam that has a mean of 50 and a standard deviation of 20.
Based on the z-score calculations, score A with a score of X = 55 should lead to the better grade.(option-a)
For score A with X = 55, the z-score can be calculated as:
z = (X - mean) / SD = (55 - 60) / 5 = -1
For score B with X = 40, the z-score can be calculated as:
z = (X - mean) / SD = (40 - 50) / 20 = -0.5
The z-score represents the number of standard deviations that a score is above or below the mean. A negative z-score means that the score is below the mean.
Since a z-score of -1 is greater than a z-score of -0.5, score A with X = 55 would be the better score. This is because score A is closer to the mean (60) than score B (50), and it has a smaller standard deviation (5) than score B (20). The lower standard deviation means that scores are more tightly clustered around the mean, making it more difficult to obtain a score that is much higher or lower than the mean.(option-a)
For such more questions on calculation
https://brainly.com/question/17145398
#SPJ8
What is the vertex of the parabola
Answer:
lallalalaal hiiiiii
Step-by-step explanation:
The standard form is written as y = ax ^2 + b + c
Using the given equation:
A = -5, b = 30 and c = 7
The x value of the vertex = -b/ 2/a = -30/2(-5) = -30/-10 = 3
To find the y value replace x with the x value and solve for y:
Y = -5(3)^2 + 30(3) + 7
Y = -45 + 90 + 7
Y = 52
The vertex is (3,52)
The answer is G
Need to know angle 1, angle 2, angle 3
Answer: Step-by-step explanation:
angle 1=41°
angle 2=angle 1=41°
angle 3=180-2×41=98
how long will it take with 0.5kW power rating to do 1500J of work?
3 seconds
3 microseconds
3 minutes
0.3 seconds
id- 5121786233 p/w- tepQ3w
Answer:
ok
Step-by-step explanation:
When two 6-sided dice are rolled, there are 36 possible outcomes. Find the probability that the sum is 8
Answer:
5/36
Step-by-step explanation:
Probability is the outcome that a event will occur
Probability = Expected outcome/Total outcome
Since two sided dice are rolled, the total outcome will be expressed as;
Total outcome = 36
Since we are to find the probability that the sum is 8, the values that gives a sum of 8a re;
(2,6)(6,2), (5, 3), (3,5), (4, 4)
The expected outcome = 5
Probability = 5/36
Hence the probability that the sum is 8 is 5/36
whoever gets this correct first gets brainlest!!
D. f(x)=4 (5/2)^x
Are really good tool for graphing problems is Demos.com
what's the x-intercept
Answer:
perhaps around 7.5?
Step-by-step explanation:
hope this is right :)
Please please please help no link no links no links
Answer:
400
Step-by-step explanation:
V = a² * h/3
Plug in your values:
V = 10² * 12/3
Then solve:
100 * 4 = 400