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]
The following dot plots compare the height of the members of the basketball team and the swimming team.
Determine the mean, median, mode and range for the dot plot. Show your work.
(2pts) Mean:
(2pts) Median:
(1pt) Mode:
(2pts) Range/Spread:
I'm not confident with the Mean but the rest should be correct.
Mean - 709.6 ( All numbers added up then, divided by the numbers there are)
Median - 65 ( Number in the middle)
Mode - 65 ( Most repeated number)
Range - 8 ( Greatest number - Smallest number)
The Wanting Recognition (WR) Scale provides a quantitative measure of a person's level of need for approval and sensitivity to social situations. A random sample of 100 convicted drug dealers was scoredf on the WR scale and produced a mean WR score of 39 and a standard deviation of 6. (a) Use this information, find an interval estimate of the mean WR score for all convicted drug dealers with 99% confidence level.
Answer:
99% of the confidence level of the mean WR score for all convicted drug dealers
(37.4544, 40.5456)
Step-by-step explanation:
Step(i):-
Given that the sample size 'n' = 100
Given that the mean of the sample(x⁻) = 39
Given a standard deviation of the sample (σ) = 6
Level of significance = 0.01 or 99%
Step(ii):-
99% of the confidence level of the mean WR score for all convicted drug dealers
[tex](x^{-} - Z_{0.01} \frac{S.D}{\sqrt{n} } ,x^{-} + Z_{0.01} \frac{S.D}{\sqrt{n} })[/tex]
[tex](39 -2.576 \frac{6}{\sqrt{100} } ,39 + 2.576 \frac{6}{\sqrt{100} })[/tex]
(39 - 1.5456 , 39+1.5456)
(37.4544, 40.5456)
Final answer:-
99% of the confidence level of the mean WR score for all convicted drug dealers
(37.4544, 40.5456)
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answer:
90 degrees c
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Also can you give me brainlist???
Answer:
90 degrees celsius
Hi I need to send you a screenshot .
Solve the equation. Find all real solutions.
9r3 - 144r = 0
Answer:
r=0
Step-by-step explanation:
9r x 3 - 144r = 0
27r-144r=0
-117r=0
r=0
Help plsssssss i'm lost il give brainiest
Answer:
A 16°
B -8°
C 6°
D -16°
E -4°
Step-by-step explanation:
Look at 0° and 10°. There are 5 lines from one to the other, so each line represents 2°.
A
3 lines above 10° = 10° + 3 * 2° = 10° + 6° = 16°
B
1 lines above -10° = -10° + 2° = -8°
C
3 lines above 0° = 0° + 3 * 2° = 0° + 6° = 6°
D
2 lines above -20° = -20° + 2 * 2° = -20° + 4° = -16°
E
3 lines above -10° = -10° + 3 * 2° = -10° + 6° = -4°
Use the net to find the surface area of the regular pyramid.
YOU GET BRAINLEST IF YOU ANSWER CORRECTLY.
Answer:
the answer would be 78.6
Step-by-step explanation:
The function, f(x), is plotted below.
Evaluate the limits, if they exist. If not, write DNE.
Limit as x approaches negative 1 minusf(x) =
Limit as x approaches 3 plusf(x) =
Limit as x approaches 1 f(x) =
Answer:
1
2
DNE
Step-by-step explanation:
Solve the equation 10^(4x−1)=2^5. Round your answer to the nearest hundredth
HELPPP!!
Order the angle measures from least to greatest
help please
Answer:
m<B, m<C, m<A
Step-by-step explanation:
The length of sides and angle measures correspond. This means the angle opposite to the longest side is the largest, etc. The shortest side is AC, which is the opposite of <B, making it the smallest. Then, the same logic can be applied to <C which is the middle, and <A which is the largest. Therefore, from least to greatest the angles are m<B, m<C, m<A.
Christopher has a garden in the shape of a square with a side length of 24 feet. He plans to plant tomatoes along the
diagonal. How long is the diagonal of Christopher's garden?
A - 48 Ft
B - 24 Ft
C - 24 square root of 2
D - 24 square root of 3
9514 1404 393
Answer:
C - 24 square root of 2
Step-by-step explanation:
In case you haven't memorized the fact that the diagonal of a square is √2 times the side length, you can figure it from the Pythagorean theorem.
d² = s² + s² . . . . square of hypotenuse is sum of squares of sides
d² = 2s²
d = s√2 = (24 ft)√2 = 24√2 ft
how long will it take with 0.5kW power rating to do 1500J of work?
3 seconds
3 microseconds
3 minutes
0.3 seconds
Plzzzzz answer. Will give brainliest
Area of square = (2x-3)^2
Area = 2x-3 x 2x-3
Area = 4x^2 -6x -6x +9
Area = 4x^2 -12x + 9
Area of ovals = x-5 + x-5 = 2x-10
Area of square - area of ovals:
4x^2 - 12x +9 - 2x -10
4x^2 -14x +19 square units
The polynomial - 16 + v.t+s, represents the height (in feet) of an object, where v, is the initial vertical
velocity (in feet per second), s, is the initial height of the object (in feet), and is the time in seconds). Write a polynomial that represents the
height of the object. Then find the height of the object after 1 second.
Complete question is;
The polynomial -16t² + v_o(t) + s_o represents the height (in feet) of an object, where v_o is the initial vertical
velocity (in feet per second), s_o is the initial height of the object (in feet), and t is the time in seconds. Write a polynomial that represents the height of the object that has an initial velocity of 25 ft/s and initial height of 4ft. Then find the height of the object after 1 second.
Answer:
A) Polynomial is h(t) = -16t² + 25t+ 4
B) h(1) = 13 ft
Step-by-step explanation:
A) We are given;
h = -16t² + v_o(t) + s_o
Where;
v_o = the initial vertical velocity
s_o = the initial height of the object
t = the time
We are given;
v_o = 25 ft/s
s_o = 4 ft
Thus, polynomial that represents the height is;
h(t) = -16t² + 25t+ 4
B) after a time of 1 second, height is;
h(1) = -16(1²) + 25(1) + 4
h(1) = -16 + 25 + 4
h(1) = 13 ft
find the lateral surface area of the prism. geometry hw
Answer:
250
Step-by-step explanation:
Hello There!
The prism shown is a pentagonal prism
And we need to find the lateral surface area ( pretty much area of everything except for the bases.)
We can calculate the lateral surface area by using this formula
[tex]la=5ah[/tex]
where a (on the right hand side) equals the base edge length and h = height
(btw the 5 represents the number of sides)
so the base edge length of the shown figure is 5 and the height is 10
having found this information we plug it into the formula
[tex]la=5*5*10\\10*5=50\\50*5=250[/tex]
so we can conclude that the lateral surface area of the shown pentagonal prism is 250 cm²
What is the value of 3 1⁄4 increased by 2 1⁄6?
in how many ways can 4 mangoes and 3 apples be distributed among 7 children if each child receives only 2 fruit?
solution
this is what I did. total number of ways without any restriction =900. we have to subtract the case when at least one child doesn't get any fruit. let that be C1∪C2∪C3 and we use the principle of mutual inclusion and exclusion to find that. C1∪C2∪C3=C1+C2+C3−(all two intersections)+3 intersections (no one gets a fruit case) =3⋅60−3+1=178 so case where each child gets at least one fruit =900−178=722.
Is this right, someone saying answer =49
Express the quantity of the Cayennepepper im lemon juice in form one
Answer:
HUH
Step-by-step explanation:
Melissa can ride 20 miles on her bike in 8 hours how many miles can she ride an a hour
Answer:
2.75 miles in 1 hour
Step-by-step explanation:
On a super clearance sale, bathing suits were marked 85% off. What is
the sale price of a bathing suit that was originally priced $60?
Answer: $9
Step-by-step explanation: 85% off means when you multiply the number by 0.85 you subtract that from the original number, 60 times 0.85 is 51 and 60-51=9! Hope this helps!
What is the quotient of (x^3 + 3x^2 - 4x - 12) divided by (x^2 + 5x + 6)
Answer: The quotient is (x-2)
Answer:
x-2
Step-by-step explanation:
Isabella took a taxi from her house to the airport. The taxi company charged a pick-
up fee of $4.70 plus $2.25 per mile. The total fare was $58.70, not including the tip.
Write and solve an equation which can be used to determine , the number of miles in the taxi ride.
Answer:
Equation: 2.25x+4.7=58.70
Answer: x = 24x=24
Hope this helps
What is the value of B?
Answer:
The value of B is 0 because going down from the middle is all negative and going up from point B is all positive so the answer is 0 degrees
Step-by-step explanation:
Answer:
in linear pair
90+a+24=180
a=180-90-24=66°
B°=90+a=90+66=156°
the value of B°=156°
geometry 10 long 2.75 wide triangle what is the area?
What is 6 7/13 divided by 5
Answer:
17/13
Step-by-step explanation:
Answer:
[tex]\frac{17}{13}[/tex] or 1 [tex]\frac{4}{13}[/tex]
Step-by-step explanation:
1. A luge race is very dangerous, and a crash can cause serious injuries. The league requires anyone who has a crash to have a thorough medical screening before they are allowed to race again. A certain performer has an independent .04 probability of a crash in each race. a) What is the probability she will have her first crash within the first 30 races she runs this season
Answer:
0.7061 = 70.61% probability she will have her first crash within the first 30 races she runs this season
Step-by-step explanation:
For each race, there are only two possible outcomes. Either the person has a crash, or the person does not. The probability of having a crash during a race is independent of whether there was a crash in any other race. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A certain performer has an independent .04 probability of a crash in each race.
This means that [tex]p = 0.04[/tex]
a) What is the probability she will have her first crash within the first 30 races she runs this season
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
When [tex]n = 30[/tex]
We have that:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.04)^{0}.(0.96)^{30} = 0.2939[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2939 = 0.7061[/tex]
0.7061 = 70.61% probability she will have her first crash within the first 30 races she runs this season
A birdbath holds 4 liters of water. How many milliliters does it hold?
Answer:
4000
Step-by-step explanation:
Answer:
4000
Step-by-step explanation:
You have to multiply the volume value by 1000. So 4 x 1000=4000
geometry multiple choice
(will mark brainliest)
4 in.
3 in.
2 in.
2 in.
6 in.
Find the surface area.
square inches
(Hint: The rectangular faces
are different sizes.)
Answer:
The correct answer is 5in
Step-by-step explanation:
6+4=10÷2=5in
ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !
The dot isn’t shaded so > or <
From -55, it’s showing small than
From -49, it’s showing greater than
x < -55 or x > -49
Answer: x < -55 or x > -49
Step-by-step explanation:
x < -55 or x > -49
They both start with an opened circle, and also these two opened circle dots do not connect to each other. On the left side, the number is going from -55 to the smaller side, -57 or less, so we can say that x is smaller than -55. On the right side, the number goes from -49 to the bigger number, we can say that x is greater than -49.