Answer:It's easy for us to visualize a meter; that's about 3 feet. ... nm (10-9 m) to 100 nanometers (100 x 10-9 = 10-7 m) and the unique properties that arise.
Step-by-step explanation:
Find the absolute maximum and minimum values of the following function on the given region R. f(x,y)=5x2+5y2−10x+21; R=(x,y): x2+y2≤4, y≥0
We first compute the partial derivatives of f(x, y):
f(x, y) = 5x² + 5y² - 10x + 21
∂f/∂x = 10x - 10
∂f/∂y = 10y
The critical points of f occur where both ∂f/∂x and ∂f/∂y are equal to zero. This only happens at the point (x, y) = (1, 0). (And this point does lie inside R.)
Next, compute the Hessian matrix H(x, y) for f :
[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}10&0\\0&10\end{bmatrix}[/tex]
Since det(H(x,y)) = 100 is positive for all x and y, this means the critical point (1, 0) is a local minimum, and we have f(1, 0) = 16.
Next, we check for extrema along the boundary of R, which is comprised of a semicircle with radius 2 and the line segment connecting (-2, 0) and (2, 0).
• Parameterize the semicircular portion by
x(t) = 2 cos(t)
y(t) = 2 sin(t)
with 0 ≤ t ≤ π. Then
f(x(t), y(t)) = 20 sin²(t) + 20 cos²(t) - 20 cos(t) + 21
which is simplifies to a function of one variable t,
g(t) = 41 - 20 cos(t)
Find the extrema of g over the interval [0, π] : we have critical points when
g'(t) = 20 sin(t) = 0
which happens at t = 0 and t = π. At these points, we get local extreme values of
•• t = 0 => x = 2 and y = 0 => f(2, 0) = 21
•• t = π => x = -2 and y = 0 => f(-2, 0) = 61
• Over the line-segment portion, we take y = 0, so f(x, y) again reduces to a function of one variable:
f(x, 0) = 5x² - 10x + 21
Completing the square, we have
5x² - 10x + 21 = 5 (x - 1)² + 16
which has a maximum value of 16 when x = 1 (and this happens to be the critical point (1, 0) we found earlier).
So, over the region R, f(x, y) has
• an absolute maximum of 61 at the point (-2, 0), and
• an absolute minimum of 16 at (1, 0)
A store pays $306.56 for a refrigerator. The store marks up the price by 29%. What is the amount of the mark-up?
the numbers one through 10 are written on individual cards and place in a bag. If you reach into the bag to pull out card what is the probability that it will be a 7
Answer:
1 in 10 chance
Step-by-step explanation:
There are 10 cards, so since you reach into the bag and pull out only 1 card, there is a 1 in 10 chance.
Find the missing value using the given information
(4,p), (p,-3), m=5/3
Answer:
p = 11/8
Step-by-step explanation:
We are trying to find the slope, so use the slope formula
m = ( y2-y1)/(x2-x1)
5/3 = ( -3 -p)/ ( p-4)
Using cross products
5(p-4) = 3(-3-p)
5p-20 = -9-3p
Add 3p to each side
5p+3p -20 = -9-3p+3p
8p-20 = -9
Add 20 to each side
8p-20+20 =-9+20
8p =11
Divide by 8
8p/8 = 11/8
p = 11/8
Which relation has a domain of (2, 4) and a rang of (2, 8)
A (2, 4) (2,8)
B (2, 2) (2,8) (4,2)
C{(2,4)(8,2)(8,4)}
D{(2,2)(2,4)(4,2)(8,8)}
Six times a number plus 7 is equal to 55. What is the number?
Answer:
6x_+7=55, the answer is 13, why? well because if you add 6+7 you will have 13, now you can multiple that by 5, and you will have 55 as an answer, did I helped you?
the sum of 22 and n is equal to 45.13
Answer:
23.13
Step-by-step explanation:
On a sunny day, Jameson casts a shadow of 11 feet and the lamppost in the parking lot casts a shadow of 66 feet. If Jameson is 6 feet tall, how tall in the lamppost?
Answer:
36 feet
Step-by-step explanation:
shadow/height = shadow/height
11/6 = 66/h
h = 66 * 6 / 11
h = 36
A freight train 22.5 miles per 60 miles to its destination how far from the destination will the train be in 2.5 hour
A local hamburger shop sold a combined total of 637 hamburgers and cheeseburgers on Wednesday. There were 63 fewer cheeseburger sold than burgers. How many hamburgers were sold on Wednesday?
Anyone able to help with this?
[tex]W = 23.7°[/tex]
Step-by-step explanation:
The formula given is the statement of Snell's law of refraction. We are given the following:
[tex]I_a = 1.0003[/tex]
[tex]I_w = 1.3[/tex]
[tex]A = 31.5°[/tex]
So we need to find the angle of refraction W. Starting with Snell's law,
[tex]\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A[/tex]
Plugging in the given values, we get
[tex]\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402[/tex]
Solving for the angle W, we then get
[tex]W = \sin^{-1}(0.402) = 23.7°[/tex]
Aliyah went to the sandwich shop for lunch. She had a sandwich and a salad. Her total bill for lunch was $9.82. The salad she ordered cost $2.56. Which correctly shows how she determined the cost of her sandwich?
Answer:
9.82 - 2.56 = 7.26 is the equation
Let be an angle in quadrant I such that sin +10 Find the exact values of sec 0 and tan 0.
Answer:
just look at picture's That's the answer
Find the values of x and y.
X =
y =
Answer:
y=5
x=45
Step-by-step explanation:
I am not quite sure of x but I am positive for the value of y
6. A quadratic function has a minimum at (6,-2) and an x-intercept at (10,0).
What is the other x-intercept?
Answer:
(2,0)
Step-by-step explanation:
The minimum is 4 units from the x intercept on the x axis.
Since this is a quadratic, values on the same y should be equidistant from the min or max on the x axis.
6+4=10
6-4=2
The other x intercept is at (2,0)
Please help if you can!
Answer:
-3
Step-by-step explanation:
that’s where the line intercepts with the y axis
Answer:
-3,0 is y intercept good luck
87 is 12.5% of what number?
Answer:
10.88
Step-by-step explanation:
PLZ HHHHHELP POINTSSS HERE
Answer:31
Step-by-step explanation:
Because
If u add 31+31=62
And 62+118=180
Brainliest please
Round 2,913 to the nearest ten
Answer:2,910
Step-by-step explanation:
Answer:
2910
Step-by-step explanation:
We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.
We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.
If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
4. Ms. Bragg is giving a test worth 100 points. The test contains a total of 40 questions. Some questions are worth 2 points and some questions are worth 4 points on the test. Write a system of equations to determine how many of each type of question are on the test. A) Define your variables. You can use any letters you want) B) Write your system of equations. (There should be 2 separate equations)
9514 1404 393
Explanation:
A)
Let t and f represent the numbers of two-point and four-point questions, respectively.
__
B) The number of points for each type of question is the product of the point-value per question and the number of questions of that type.
2t + 4f = 100 . . . . . the test is worth 100 points
t + f = 40 . . . . . . . . there are 40 questions on the test
_____
Additional comment
The test will have 30 two-point questions and 10 four-point questions.
If P = {3, 5, 7, 11, 13, 17, 19), what is n(P)?
Answer:
the n(P) of P = {3, 5, 7, 11, 13, 17, 19} is "128".
Step-by-step explanation:
n(P) is the Cardinality of the set P. Its formula is 2^k.
where k = number of elements in the set.
Hope this helps :)
If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 5.
The probability is
=====================================================
Explanation:
Refer to the dice chart below. It represents all possible ways to roll two dice and sum up the face values.
According to the table, there are...
A = 1 copy of the sum "2"B = 2 copies of the sum "3"C = 3 copies of the sum "4"D = 4 copies of the sum "5"There are A+B+C+D = 1+2+3+4 = 10 instances where we get a sum between 2 and 5. The table shows 6*6 = 36 sums total. This means there are 36-10 = 26 sums where they are between 6 and 12, aka "the sum being greater than 5".
Those 26 sums are what we focus on. Out of those 26 items, four of them are sums of "9".
The probability we want is therefore 4/26 = 2/13
The probability that the sum of the dice is 9, given that the sum is greater than 5 is 0.154
See attachment for the sample space of a roll of two dice.
From the attached sample space,
The number of sum greater than 5 is: 26The number of sum greater than 5 that is 9 is: 6Represent the events that a sum is greater than 5 with A, and a sum is greater than 5 is 9 with B.
So, we have:
[tex]n(A) = 26[/tex]
[tex]n(A\ n\ B) = 4[/tex]
The probability that the sum of the dice is 9, given that the sum is greater than 5 is then calculated using:
[tex]Pr = \frac{n(A\ n\ B)}{n(A)}[/tex]
This gives
[tex]Pr = \frac{4}{26}[/tex]
[tex]Pr = 0.154[/tex]
Hence, the probability is 0.154
Read more about probability at:
https://brainly.com/question/251701
The rabbit will never go over 75 pounds. If this rabbit is bom in July weighing 2 pounds, in which month will it weigh around 46 pounds?
At a coffee shop, a latte costs $5.50 and
hot tea costs $1.75. Each day, Parker
buys 2 hot teas and several lattes for
his office staff. Which equation can be
used to find y, Parker's total cost, if x
represents the number of lattes? (7.1A,
7.1B, 7.1D, 7.1F)
A y = 5.50x + 3.50
BY 5.50x + 1.75
C y = 1.75x + 5.50
Dy = 3.50x + 5.50
Answer:
A) y = 5.50x + 3.50
Step-by-step explanation:
2 x 1.75 = 3.50 + x number of lattes $5.50 each.
29. Which set of integers is listed in order from least to greatest?
5,8,-9, -10
-5, -3, -2,7
O-5, 4, -2, -7
O 5, 4, 2, -1
Answer:
It would be the second set of numbers.
Step-by-step explanation:
Find the missing number in the following series: __ 85 81 83 79 81 77
Answer:
83
Step-by-step explanation:
The pattern is -4 then +2
a store pays $26 for a lamp. The store marks up the price by 40%. What is the amount of the markup
Answer:
$10.4
Step-by-step explanation:
mark me brainliest if u are kind
How can you express (15 + 30) as a multiple of a sum of whole numbers with no common factor?
A. 2 x (7.5 + 15)
B. 3 x (5 + 10)
C. 5 x (3 + 6)
D. 15 x (1 + 2)
Answer:
13 24 56 23 56 78 166 Yan Lang po thank
i need help on this math problem
Answer:
[tex]\sqrt{81}[/tex] = 9
[tex]\sqrt{169}[/tex] = 13
Step-by-step explanation:
Need the answer to this pls
Answer:
0
Step-by-step explanation:
1. First, we should know the slope-intercept form of any equation: y = mx + b.
y = y-coordinatem = slopex = x-coordinateb = y-intercept2. In the equation y = -2/3(x), it appears that the variables we can see are y, m, and x. However, the y-intercept, b, is still there with the value of 0.
Additionally, this is a proportional relationship because it follows the format y = kx. Proportional relationships always have a y-intercept of 0.Therefore, the y-intercept is 0.