Answer:
44
Step-by-step explanation:
Local versus absolute extrema. If you recall from single-variable calculus (calculus I), if a function has only one critical point, and that critical point is a local maximum (or say local minimum), then that critical point is the global/absolute maximum (or say global/absolute minnimum). This fails spectacularly in higher dimensions (and thereís a famous example of a mistake in a mathematical physics paper because this fact was not properly appreciated.) You will compute a simple example in this problem. Let f(x; y) = e 3x + y 3 3yex . (a) Find all critical points for this function; in so doing you will see there is only one. (b) Verify this critical point is a local minimum. (c) Show this is not the absolute minimum by Önding values of f(x; y) that are lower than the value at this critical point. We suggest looking at values f(0; y) for suitably chosen y
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]
Help please question in the picture
Answer:
17.5
Step-by-step explanation:
The area of a triangle is (height*base)divided by two
(the eight is really unnecessary)
so 7=base
8=height
7*5=35
35/2=17.5
John buys an item that costs $50.00 is marked 20% off. Sales tax for the item is 8%. What is the final price that John pays, including tax?
Answer:
$43.20
Step-by-step explanation:
20% of $50.00 is $10.00. $50 - $10 is $40. 8% of $40 is $3.20. Since this is tax, you must add it. $40+$3.20 = $43.20
2^3=4^p find the value of p
Answer:
Exact form: p= 3/2
Decimal form: p= 1.5
Mixed Number: p=1 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
one of the fastest times for 1,500-meter race is 3 minutes and 34 seconds. How many seconds is this time?
Answer:
214 seconds
Step-by-step explanation:
3 times 60 is 180. 180 plus 34 is 214.
surface area of a pyramid
WILL GIVE BRAINLIEST TO FIRST TO ANSWER CORRECTLY
Find the surface area of the pyramid. Round to the nearest tenth if necessary.
12.25 in.
15.75 in.
15.75 in.
in^2 = ?
Answer:
633.9 in.²
Step-by-step explanation:
Surface Area = Base Area + ½(Perimeter of Base)(slant height)
Base area = s² = 15.75² = 248.0625 in.²
Perimeter = 4(15.75) = 63 in.
Slant height = 12.25 in.
Surface area = 248.0625 + ½(63)(12.25)
= 633.9375 ≈ 633.9 in.² (nearest tenth)
giving brainliest!! easy*
Answer:
1584mm^2
Step-by-step explanation:
20 x20 = 400 and there are 3 of them
400+400+400 = 1200
1/2(16x24 ) =192 and there are 2 of them
192+192 = 384
1200+384
Answer:
1408
Step-by-step explanation:
20·16+24·16+20·16+12·﹣204+2·(20·24)2+2·(20·20)2﹣244+2·(24·20)2﹣204=1408
if i did something wrong please let me know
(i might have done it wrong, please use the answer above which would be 1584mm^2)
Point M is on line segment LN. Given LN=4x, MN= x, and LM=3, determine the numerical length of LN.
Answer:
LN = 4 units
Step-by-step explanation:
Since M is on LN , then
LN = LM + MN , that is
4x = 3 + x ( subtract x from both sides )
3x = 3 ( divide both sides by 3 )
x = 1
Then
LN = 3 + x = 3 + 1 = 4
The required length of the line LN = 4.
Given that,
Point M is on the line segment LN. Given LN=4x, MN= x, and LM=3, to determine the numerical length of LN.
The line is a curve showing the shortest distance between 2 points.
LN = LM + MN
4x = 3 + x
4x - x = 3
3x = 3
x = 3 / 3
x = 1
Length of LN
LN = 4x
= 4 * (1)
= 4
Thus the required length of the line LN = 4.
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PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
697.5 ft squared
Step-by-step explanation:
Divide into top two squares and rectangle on bottom so...
(10×7.5)+(8×7.5)×(12.5×45)=area
75+60+562.5=697.5 ft squared
Select the option that best describes the relationship
between the variables on the scatter plot.
35
positive, linear association
30
25
no association
20
15
positive, non-linear association
10
5
negative, linear association
10
12
Activate Windows
Answer:
4th one its negative,linear association
Step-by-step explanation:
The option that best describes the relationship between the variables on the scatter plot is negative, linear association.
What is a negative linear association?Variables have a negative association when the line of best fit is downward sloping. Variables have a linear association when the line of best fit is a straight line. Variables have a positive association when the line of best fit is upward sloping.
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85.82 rounded to the hundredths place
Answer:
85.80
Step-by-step explanation:
85.82 is closet to 85.80 snice 2 is a low number
John used AABC to write a proof of the Centroid Theorem. He began by drawing medians AK and CL,
intersecting at Z. Next he drew midsegments LM and NP, both parallel to median AK.
Given: AABC with medians AK and CL, and midsegments LM and NP.
2
Prove: Z is located of the distance from each vertex of AABC to the midpoint of the opposite side.
3
Answer:
Hello your question is poorly written attached below is the complete question
answer : attached below
Step-by-step explanation:
To Prove: Z is located 2/3 of the distance from each vertex of ΔABC to the midpoint of the opposite side. we will apply ; property of bisecting a line , equality theorem , transitive property and similarity theorem
Attached below is the proof
ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !
Answer:
24 square kilometers
Step-by-step explanation:
Well, this is a trapezoid. The formula for the area of a trapezoid is 1/2 the height times base one plus base two. In other words, 1/2 h x (base 1 + base 2)
So in this case, the two bases are 4 and 12. So we would add the two bases to get 16. Now, we have to half the height. 3 divided by 1/2 is 1.5. So we then do the last step which is multiplying the height by the two bases. So in other words, 1.5 times 16. And 1.5 times 16 is 24. Therefore, the answer is 24 sqaure kilometers.
Answer:
Step-by-step explanation:
Josiah earns $8.00 per hour at his job.
Write and solve an inequality that represents how many hours it will take him to earn at least $120.
Answer:
15 hours
so, 8 x y = 120
Step-by-step explanation:
[tex]8\sqrt{120} =[/tex] 15
Is the following relation a function? *
{(-3, 2), (1, 8), (-1, 5), (3, 11)}
Yes
No
Why or why not?
Answer:
No.
Step-by-step explanation:
Well at first glance it might seem so but there are two points particularly that can tell you that these points cannot be within a function.
The points (3,2) and (3,-2) will yield an undefined slope (a straight vertical line). There is no possibility that the other points can be in this line (as their y - values are different) and there is no possibilty that this is a function at all according to the vertical line test (the test is that if you draw a vertical line that there shouldn't be more than one point on it).
A roadside assistance company gets millions of requests per year, with about a quarter of the requests in
summer and a quarter in winter. Suppose that 12% of all of the summer requests and 15% of the winter
requests are for help with a lockout. A data analyst pulls separate random samples of 200 summer and winter
requests and will look at the difference (summer winter) between the proportion of requests for help with
a lockout in each sample.
What are the mean and standard deviation of the sampling distribution of the difference in sample
proportions?
Answer: -0.03
sqrt ((0.12 (0.88) / 200) + (0.15)(0.85)/200)
Step-by-step explanation:
The mean of the sampling distribution of the difference in sample proportions is -0.03, and the standard deviation is 0.0321.
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
The proportion of lockout help requests in the summer population is 12% or 0.12, and the proportion in the winter population is 15% or 0.15. The sample sizes are both 200.
Using these values, we can calculate the mean and standard deviation of the sampling distribution of the difference in sample proportions:
Mean = p₁ - p₂ = 0.12 - 0.15 = -0.03
Standard deviation = √[ (p₁ (1 - p₁) / n₁) + (p₂ (1 - p₂) / n₂) ]
= √[ (0.12 (1 - 0.12) / 200) + (0.15 (1 - 0.15) / 200) ]
= √[ (0.000504) + (0.000525) ]
= √[ 0.001029 ]
= 0.0321
Therefore, the mean of the sampling distribution of the difference in sample proportions is -0.03, and the standard deviation is 0.0321.
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The following data show the average retirement ages for a random sample of workers in the United States and a random sample of workers in Japan. Perform a hypothesis test using α = 0.05 to determine if the average retirement age in Japan is different from the United States. Calculate the test-statistics (round to 3 decimals - report the absolute value).
Answer:
[tex]t \approx 2.639[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{} & {USA\ 1} & {Japan\ 2} & {\bar x} & {64.6} & {67.5} &{n} & {30} & {30} & {\sigma} & {4.0} & {4.5} \ \end{array}[/tex]
See attachment for data
Required
Determine the test statistic
The test statistic is calculated using:
[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}[/tex]
So, we have:
[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{4.0^2}{30} + \frac{4.5^2}{30}}}[/tex]
[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00}{30} + \frac{20.25}{30}}}[/tex]
[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{16.00+20.25}{30}}}[/tex]
[tex]t = \frac{64.6 - 67.5}{\sqrt{\frac{36.25}{30}}}[/tex]
[tex]t = \frac{-2.9}{\sqrt{1.2083}}[/tex]
[tex]t = \frac{-2.9}{1.099}[/tex]
[tex]t \approx -2.639[/tex]
The absolute value is:
[tex]t \approx 2.639[/tex]
I need someone to write me a narrative on how to solve this problem please!
Need the answer to x and y !
Answer:
x=5, y=3
Step-by-step explanation:
7x-11=24: 7x=35: x=5
3(5)+9=8x: 24=8x: x=3
The radius of a circle is 16 cm. Find its area in terms of \piπ
Answer256pi
Step-by-step explanation:
Area=pi*r^2
=pi*16^2
256pi
Which sign makes this number sentence true?
|866| __ |-866|
A. >
B. <
C. =
D. +
Answer:
>
Step-by-step explanation:
Answer:
c for me
Step-by-step explanation:
hope that helps you
3x+5y=30 complete the table of values
Answer:
O
Step-by-step explanation:
Vincent began his weekly chores on Saturday morning at 11:20 he worked for 1 hour and 15 minutes with a 10 minute break at what time did Vincent finish his chores
Answer:
12:45
Step-by-step explanation:
Step One: An hour after 11:20 is 12:20, plus 15 minutes is 12: 35.
Step Two: Just add 10 minutes, because it doesn't matter when you add the ten minutes.
,........................................................................................l
what is the remainder when the polynomial f(x) = x³ - x² + 3x - 2, is divided by 2x - 1
Answer:
Equate the divisor to 0
2x-1=0
2×=1
×=1/2
Putting onto the polynomial
f(1/2) = (1/2)³-1/2)²+3(1/2)-2
=-5/8
the difference between the squares of two numbers is 32. twice the square of the first number increased by the square of the second number is 76. find the numbers.
Answer:
The numbers are 6 and 2
6 squared = 36
2 squared = 4
So 36-4 = 32
And 36 x 2 = 72 + 4 = 76
4
Brad goes to bed at 21 25.
He is in bed until 0708 the next day.
Work out the length of time that Brad is in bed.
Answer:
Step-by-step explanation:
Which is greater 3/5 or 7/10
Answer:
7/10
Step-by-step explanation:
Use the butterfly method:
3/5 7/10
multiply the denominator and numerator to each other sides:
3 * 10 = 30
5 * 7 = 35
35 > 30
35 belongs to 7/10 so:
7/10 is greater
How high is the end of the ladder against a building
round off all answer in to two decimal places A=p(1+in) Steven won a portion of the local lottery.the price money is to the value of R18000.he wants to invest the money but does not know which bank to choose. FNB offers Steven 5,6/% for 8 years simple interest per annum, Nedbank offers Steven 6,6% for 6 years simple interest per annum and standard bank offers 7,2% for 5 years simple interest determine each bank future value to help Steven decide which bank he should choose FNB NEDBANK STANDARD BANK
Answer:
FNB bank
Step-by-step explanation:
FNB = 18000 * 0.056* 8 = 8064
Nedbank = 18000*0.066* 6 = 7128
Standard = 18000*0.072*5=6480
FNB is the best choice for Steven