Answer:
[tex]y =-x[/tex] ---- critical point
local minima
Step-by-step explanation:
Given
[tex]f(x,y) = x^2 + y^2 + 2xy[/tex]
Required
Determine the critical point
Differentiate w.r.t x
[tex]f_x =2x + 2y[/tex]
Differentiate w.r.t y
[tex]f_y =2y + 2x[/tex]
Equate both to 0
[tex]2x + 2y =0[/tex]
[tex]2y =0-2x[/tex]
[tex]2y =-2x[/tex]
Divide by 2
[tex]y =-x[/tex] ----- in both equations
Hence:
The critical point is: [tex]y =-x[/tex]
Solving (b):
We have:
[tex]f_x =2x + 2y[/tex]
[tex]f_y =2y + 2x[/tex]
This is represented as:
[tex]D = \left[\begin{array}{cc}2&2\\2&2\end{array}\right][/tex]
Calculate the determinant
[tex]|D| =2 * 2 -2 * 2[/tex]
[tex]|D| = 4-4[/tex]
[tex]|D| = 0[/tex]
The critical point is at local minima
There are approximately 1.2×10 to the eighth household in the US if the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day
Answer:
[tex]Total = 4.8 * 10^{10}[/tex]
Step-by-step explanation:
Given
[tex]h = 1.2 * 10^8[/tex] --- households
[tex]g = 400[/tex] --- gallons
Required
The number of households
To do this, we simply multiply the average households by the gallons.
[tex]Total = g* h[/tex]
[tex]Total = 400 * 1.2 * 10^8[/tex]
[tex]Total = 480 * 10^8[/tex]
Rewrite as:
[tex]Total = 4.8 * 10^2 * 10^8[/tex]
[tex]Total = 4.8 * 10^{10}[/tex]
A group of 12 friends bought tickets for an afternoon concert. However, not all of the friends were able to sit together. Tickets for floor seats cost $15 each, and tickets for tier seats cost $70 each. The total cost of the tickets was $345. How many tickets for tier seats did they purchase
Answer:
3 tier seats tickets
Step-by-step explanation:
Let the friends that bought floor seats be x and let the friends that bought tier seats be y.
Thus;
x + y = 12 - - - (eq 1)
Floor seats tickets cost $15 each, and tier seats tickets cost $70 each. The total cost of the tickets was $345. Thus;
15x + 70y = 345 - - - (eq 2)
Let's make x the subject in eq (1)
x = 12 - y
Putting this for x in eq 2 gives;
15(12 - y) + 70y = 345
180 - 15y + 70y = 345
55y = 345 - 180
55y = 165
y = 165/55
y = 3
Put 3 for y in x = 12 - y to get;
x = 12 - 3
x = 9
Thus, they purchased 9 floor seats tickets and 3 tier seats tickets
what are the two types of probability
Answer:
The two "types of probability" are: 1) interpretation by ratios, classical interpretation; interpretation by success, frequentist interpretation. The third one is called subjective interpretation.
HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
No solution
Step-by-step explanation:
Given
[tex]|x| = -1[/tex]
Required
The solution
The above equation has no solution.
This is because [tex]|x| \ge 0[/tex]
In otherwords, the absolute value of a number is always positive.
8b - 5a + 4 for a = -4 and b = 7
If anyone gets this tysm
Answer:
80Step-by-step explanation:
Given Question,
8b - 5a + 4
Given Values:
a = -4 and b = 7
Solution,
8(7) - 5(-4) + 4
= 56 + 20 + 4
= 80 (Ans)
Answer:
80
Step-by-step explanation:
8b - 5a + 4
a = - 4
b = 7
8(7) - 5(- 4) + 4
56 - (- 20) + 4
56 + 20 + 4
60 + 20
80
Tasta's bank account was. She deposited a check into her bank account and her new total is. How much was the check that Tasta deposited into her account?
Answer:
Step-by-step explanation:
New Total equals Previous Total plus the Check value
New Total minus Previous Total equals the Check value
Her new total is - Tasta's bank account was = Check value
Find the distance between the points (0, -3) and (4, 0).
A. 7
B. 1
C. 25
D. 5
9514 1404 393
Answer:
D. 5
Step-by-step explanation:
The distance formula is good for finding the distance between two points.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((4 -0)² +(0 -(-3))²) = √(16 +9) = √25
d = 5
The distance between the points is 5 units.
_____
You may notice that the line between the points makes a 3-4-5 right triangle with the coordinate axes.
In a group of students. 20 study Account. 21 Study mathematics 18 study history 7 study account only 10 study mathematics only 6 study account and mathematics only and 3 study mathematics and history only.how many student are there altogether
Answer:
In total there are 50 students.
Step-by-step explanation:
Since in a group of students 20 study account, 21 study mathematics, 18 study history, 7 study account only, 10 study mathematics only, 6 study account and mathematics only and 3 study mathematics and history only, to determine how many student are there altogether the following calculation must be performed:
7 + 10 + 6 + 3 = 26
Account = 20 - 7 - 6 = 7
Mathematics = 21 - 10 - 6 - 3 = 2
History = 18 - 3 = 15
26 + 7 + 2 + 15 = X
50 = X
Therefore, in total there are 50 students.
please help! (listing BRAINLIST and giving points) :D
Answer:
x = 50 + 95 = 145
.........
Answer:
x = 145°
Step-by-step explanation:
Given,
Measure of the first angle = 50°
Measure of the second angle = 95°
We know,
Sum of 3 angles of a triangle is equals to 180°
∴ The third angle = 180° - (50+95)°
= 180° - 145°
= 35°
Again,
Straight angle = 180°
∴ x = 180° - 35°
= 145°
∴x = 145°
An angle whose measure is - 102° is in standard position in which quadrant does the terminal side of the angle fall?
O Quadrant
O Quadrant il
Quadrant III
O Quadrant IV
find the slope of the graph
Answer:
We count across to 4 on y axis = 2
and count down from 4 to -2 on x axis = -6
-6/2 = -3
m = -3
We know its minus because the reciprocal is the perpendicular imaginary line and if -3 is for the descending line then any ascending perpendicular line would show m = -1/-3 = 3
Step-by-step explanation:
WILL MARK BRAINLIEST PLEASE HELP
a survey of boys and girls in second grade was conducted asking whether or not they like pizza. The partially completed two-way table shows results of the survey. How many boys were included in the survey?
Step-by-step explanation:
answer is in the above photo
there are 29 boys total
Sydney is cutting the crust from the edges of her sandwich. The dimensions, in centimeters, of the sandwich is shown.
Answer:
The answer is B) x = 8x² + 34; 45.52 centemiters
Step-by-step explanation:
Rewrite the equation by completing the square.
4x² + 20r + 25 = 0
(x+...)^2=...
Answer:
The equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] is equal to [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex].
Step-by-step explanation:
Let be the equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex], we proceed to rewrite the equation solely by algebraic means:
1) [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] Given
2) [tex](2\cdot x)^{2} + 10\cdot (2\cdot x) + 25 = 0[/tex] Definition of power/Associative property
3) [tex](2\cdot x + 5)^{2} = 0[/tex] Perfect square trinomial
4) [tex]2^{2}\cdot \left(x + \frac{5}{2} \right)^{2} = 0[/tex] Distributive property/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
5) [tex]4\cdot (x + \frac{5}{2} )^{2} = 0[/tex] Definition of power
6) [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex] Compatibility with multiplication/Commutative and modulative properties/[tex]a\cdot 0 = 0[/tex]
A bag holds 20 red marbles and 40 green ones, for a total of 60 marbles. Ryan picks one marble from the bag at random, hoping to pick a red marble. Which of the following statements is true?
a. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.
b. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.
c. The probability that Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble decreases.
d. The probability that Ryan will pick a red marble on the first try is 67%. If he keeps this marble and picks another from the bag, the probability that he will pick a green marble increases.
Answer:
C
Step-by-step explanation:
The probability Ryan will pick a red marble on the first try is 33%. If he keeps this marble and picks another from the bag, that % will decrease.
The probability of picking a red marble on the first try is 33%, and if Ryan keeps this marble and picks another from the bag, the probability of picking a green marble decreases.
Thus, option (C) is correct.
In this case, there are 20 red marbles out of a total of 60 marbles.
So the probability of picking a red marble on the first try is 20/60, which simplifies to 1/3 or 33%.
If Ryan keeps the red marble and picks another one from the bag, the total number of marbles becomes 59.
The number of green marbles remains the same at 40.
Therefore, the probability of picking a green marble on the second try is 40/59, which is less than the probability of picking a green marble on the first try.
Hence, the probability of picking a red marble on the first try is 33%.
Thus, option (C) is correct.
Learn more about Probability here:
brainly.com/question/32117953
#SPJ4
Solve the inequality −14z<−37, and write the solution in interval notation.
Answer:
z is greater than 27/14
z € ( 37/14 ∞)
Choose the linear inequality that describes the graph the grey area represents the shaded region
Answer:
Explain to me how you expect anyone to do this,
as you haven't provided the graph or the inequalities.
Step-by-step explanation:
Destiny has borrowed $8 from 7 different friends. Write an integer that
represents Destiny's total debt to her friends.
Answer:
56
Step-by-step explanation:
7×8=56
Hope this helps! :)
What is The sum of b and 11
Help ASAP pls I will give brainlist
Answer:
Step-by-step explanation:
There is a issue here...
is the spotted blue section considered "a blue sector"?
Assuming that "blue" or "red" is only a solid blue or red, this is the answer...
1) (1/10)* (3/10) = .03
2) (3/10) * (3/10) = 9/100 = .09
3) (3/10) * (1/10) = 3/100 = .03
4) (4/10) * (3/10) = 12/100 = .12
if the spotted blue and the solid blue are considered blue then this would be the result ...
1) (1/10)* (3/10) = .03
2) (4/10) * (3/10) = 12/100 = .12
3) (3/10) * (1/10) = 3/100 = .03
4) (8/10) * (3/10) = 24/100 = .24
Use the correct function to find the missing angle y measurement to the
nearest whole degree. Then using the checkboxes, select the function you
used, and the answer you found rounded to the nearest degree. (SELECT
2 ANSWERS - READ CAREFULLY) Work points are build into the results. *
18 in
yo
20 in.
Cos
Tan
64 degrees
Sin
42 degrees
26 degrees
Answer:
Cos;
26 degrees
Step-by-step explanation:
Recall: SOH CAH TOA
Reference angle = y°
Adjacent side = 18 in.
Hypotenuse = 20 in.
We would apply the trigonometric function CAH since we are dealing with the Adjacent side (A) and the Hypotenuse (H). Thus:
Cos y° = Adj/Hyp
Cos y° = 18/20
Cos y° = 0.9
y° = cos^{-1}(0.9)
y = 25.8419328° ≈ 26 degrees (nearest whole degree)
The answers are:
Cos and 26 degrees
help answer please help
Answer:
The best was to display a set of data with a wide range would be
a histogram.
Step-by-step explanation:
It's a graphical display of bars which will help you measure the central tendency.
Помогите пожалуйста
y= sinx/cosx ; y=?
Answer:
[tex]\frac{1}{cos^2x}[/tex]
Step-by-step explanation:
[tex]y'=\frac{(sinx)'*cosx-(cosx)'*sinx}{cos^2x}=\frac{1}{cos^2x}.[/tex]
what are the domain and range of this function
Answer:
The domain is all real numbers
The range is y ≥ -8
Step-by-step explanation:
The domain is the values that x can take
The domain is all real numbers
The range is the values that y can take
The range is y ≥ -8
A. 40
B. 60
C. 140
D. 80
Answer:
measure of 4=360-(100+120)
=360-220
=140
so option C is the answer
Answer:
D. 80 is your answer
Step-by-step explanation:
If ∠6 is 120 and ∠5 is 100 we see a pattern forming for example, if we divide 120 by 6 we get 20 this is the same for if we divide 100 by 5, we get 20. Now all we need to do for ∠4 is to multiply it by 20 = 80, which is your answer!
Have a great day and I hope this helps!
for what values of x are these functions defined x - 1
Answer:
The function is defined for all real numbers.
which can be denoted as >> R
Can y’all help me on question 11?!
Answer:
The correct answer is choice C.
Step-by-step explanation:
To find the area of the arrow, we must add together the areas of the rectangle and the triangle that make up the arrow. The rectangle has a length of 10 inches and a width of 4 inches, and the triangle has a base of 8 inches and a height of 2 inches. Using this information, we can plug numbers into the following formula:
Area of arrow = area of rectangle + area of triangle
Area of arrow = (10*4)+(1/2*8*2)
Area of arrow = 40 inches squared + 8 inches squared
Area of arrow = 48 inches squared
Therefore, the correct answer is option C, 48 square units (in this case, inches).
Hope this helps!
The summit of a volcano is 5 kilometers (km) above sea level, as shown below.
If the ocean floor has an elevation of -5 kilometers, which statement describes
the distance of the summit and the ocean floor?
It's not 0 or 5
Which of the following is equal to the rational expression
below when x+2 or 9?
4(x - 2)
(x - 2)(x-9)
Answer:4/x-9
Step-by-step explanation:
!!!!!!!1I WILL GIFT YOU MANY POINTSSSSS
Answer:
The third one down
Step-by-step explanation:
m, Slope is negative
b, Y-intercept is positive