Answer:
The area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Step-by-step explanation:
From this study,
The surface area of f(x,y) is expressed by:
[tex]A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA[/tex]
where
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 2[/tex]
Given that:
f(x,y) = 9 - x²
Thus, [tex]f_x = -2x[/tex] and [tex]f_y = 0[/tex]
However, the area becomes:
[tex]A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy[/tex]
[tex]A = \iint_R \sqrt{1+4x^2} \ dxdy[/tex]
From above, replacing x with [tex]\dfrac{1}{2} \ tan \ u[/tex]
then [tex]dx = \dfrac{1}{2} sec^2 \ udu[/tex]
∴
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu[/tex]
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu[/tex]
[tex]\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)[/tex]
Hence;
[tex]\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}[/tex]
[tex]\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Therefore, the area of the surface over R is [tex]\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}[/tex]
Question 14 Multiple Choice Worth 1 points)
(02.05 LC)
+
The amount $4.50 is 6% of what price?
O $10.50
O $13.30
O $27.00
O $75.00
Answer:
.27
Step-by-step explanation:
4.5*6/100
=.27
Answer:
$27.00
I stayed up all night studying for this test and I got the question right haha
a tourist information center is between a bus station and a train station when mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) the train station is located at point
Answer:
dfd
Step-by-step explanation:
In a survey of 18 college students, it was found that 11 were taking an
English class, 6 were taking a math class, and 4 were taking both
English and math. How many students were taking a math class only?
A.7
B.11
C.2
D.5
Answer:
C.)2
Step-by-step explanation:
6-4=2
Answer:
I am choosing C ok it close to correct
2 lines intersect. Where the 2 lines intersect, 4 angles are created. Labeled clockwise, from uppercase right: angle 1 (3 x minus 1) degrees, angle 2 is blank, angle 3 (2 x + 9) degrees, and angle 4 is blank. What are the numerical measures of each angle in the diagram? ∠1 and ∠3 measure degrees. ∠2 and ∠4 measure degrees.
Answer:angle 1 and 3 measure 29 degrees.
angle 2 and 4 measure 151 degrees.
Step-by-step explanation:
Answer:
29 and 151
Step-by-step explanation:
Marco sorted these solid figures into two groups. What is true about the groups?
Group 1
Group 2
All figures in Group 2 appear to have at
least one triangular face.
<) All figures in Group 1 are rectangular
prisms
)) All figures in Group 2 are triangular
prisms
1) All figures in Group 1 appear to have at
least one square face,
Answer:
All figures in Group 1 appear to have at
least one square face
Step-by-step explanation:
Let us examine each statement and see whether they are true or not.
The first statement is not true. Only one of the figures (square pyramid) has at least one triangular face. It has 4 triangular faces, actually.
The second statement is not true. Only one of the figures is a rectangular prism. The remaining two are triangular pyramid and triangular prism respectively.
The third statement is not true also. Only 1 figure is a triangular prism.
The fourth statement is correct. In group 1, all the figures has at least one square face.
how many minutes (min ) are in 2 hours?
Answer:
120
Step-by-step explanation:
1 hour = 60 minutes
2 hours = 2* 60 = 120 minutes
point a is at (-7,-9) and point b is at (6,3) what is the midpoint of line segment AB
Answer:
(-1/2,-3)
Step-by-step explanation:
(-7,-9) =x1, y1
(6,3) = x2, y2
now,
Mid point= x1+x2 /2 , y1+y2 /2
= -7+6 /2, -9+3 /2
= (-1/2 , -3)
Factor 5x 4 - 30x 2 - 135. 5(x2 + 9)(x2 - 3) 5(x - 3)(x + 3)(x2 - 3) 5(x - 3)(x + 3)(x2 + 3)
Answer:
Step-by-step explanation:
[tex]5x^{4} -30x^{2} -135[/tex]
We need to pull out 5 to make the rest easier to factor.
[tex]5(x^{4} -6x^{2} -27)[/tex]
Now we can factor.
Consider all combinations of how to get 27.
1 x 27
3 x 9
And that's it before you end up just switching the place i.e. 9 x 3 and 27 x 1
This makes it easy to see that 3 and 9 are our best choice because 9 - 3 is 6 which is our middle term in the equation.
So now we have:
[tex]5(x^{2} -9)(x^{2} +3)[/tex]
We can break down [tex]x^{2} -9[/tex] even further because it's a perfect square.
(x - 3)(x + 3)
Our final factor is
5(x - 3)(x + 3)[tex](x^{2} +3)[/tex]
Which phrase should be inserted in the line to make a true statement? 2/3 is _____ 8/12 A. Is greater than B. Less than C. Cannot be compared.D.is equal to (HELP I NEED THIS HURRYY PLSSSS)
Answer:
the answer is equal because 8/12=2/3 so 2/3=8/12 (2/3)
Step-by-step explanation:
I bought three pencils costing 18 cents each. how much change did I get from $1
Answer:
15 pencils
Step-by-step explanation:
18c/3
x/1
cross multiply then divide
Answer:
46 cents
Step-by-step explanation:
18 x 3 = 54
100 - 54 = 46
What degree is the polynomial function shown on the graph? A) third B) fourth C) fifth D) sixth
Answer:
Step-by-step explanation:
Question 3 Write each fraction as an equivalent fraction with the denominator 30. Then write the
original fractions in descending order
1/15, 5/6 , 7/10, 1/2
Answer: 5/6, 7/10, 1/2, 1/15
Step-by-step explanation:
5/6=25/30, 7/10=21/30, 1/2=15/30, 1/15=2/30
jim's bookshelf has 24 inches remain in. each of his notebooks is 3/4 inches wide. how many notebooks will fit in the remaining space
Answer:
32 notebooks will fit.
Step-by-step explanation:
Write the name of the
period that has the
digits 913.
One sample has a mean of M=7.2 and a second sample has a mean of M=12.8. The two sample are combined into a single set of scores. a. What is the mean for the combined set if both the samples have n=5? b. What is the mean for the combined set if the first sample has n=5 and the second sample had n=35?
Answer:
a. M = 50
b. M = 242
Step-by-step explanation:
mean = [tex]\frac{sum of scores}{number of samples}[/tex]
⇒ sum of scores = mean x number of samples
Let the mean be represented by M, and the number of samples be represented by n,
sum of scores = M x n
a. When n = 5 for both samples,
The first sample's sum of scores = M x n
= 7.2 x 5
= 36
The second sample's sum of scores = M x n
= 12.8 x 5
= 64
The mean for the sum of scores of the combined set = [tex]\frac{36 + 64}{2}[/tex]
= 50
When both samples have n = 5, the mean of the combined set is 50.
b. When the first sample has n = 5, the sum of scores = 36.
If n = 35 for the second sample, the sum of scores = M x n
= 12.8 x 35
= 448
The mean for the sum of scores of the combined set = [tex]\frac{36 + 448}{2}[/tex]
= 242
10/r - 7 - 6b if r = 5 and b = -6
Steps to solve:
10/r - 7 - 6b when r = 5 and b = -6
~Substitute
10/5 - 7 - 6(6)
~Simplify
5 - 7 + 36
~Subtract
-2 + 36
~Add
34
Best of Luck!
If your exponent on your power 10 is positive, is your number larger or smaller than 10?
Answer:
See below.
Step-by-step explanation:
The number maybe less than 10, equal to 10, or larger than 10.
Examples:
A.
exponent: 1/2
10^(1/2) = sqrt(10) (less than 10)
B.
exponent: 1
10^1 = 10 (equal to 10)
C.
exponent: 2
10^2 = 10 * 10 = 100 (larger than 10)
Simplify the expression: 7 + 24 / 6 * 10 *
Answer:
47
Step-by-step explanation:
Since we are following PEMDAS and doing the problem left to right, first you would divide 24/6 which is 4 and then multiply by 10 which is 40. Then add the remaining 7 and your answer is 47. Simple.
What is the value of the digit 5 in the number 4.105
Answer:
thousanths place
Step-by-step explanation:
Answer:
4.105
5-hundredths place if I’m correct
104 percent of 102 is what
Answer:
106.08
Step-by-step explanation:
Answer:
106.08 percent
solve system
a = 5 - 2b; a +2b = 6
Answer:
This System has no solutions.
What number should be added to 78to get a sum of 97
THE ANSWER TO THAT PROBLEM IS SIMPLY 175
Answer:
19
Step-by-step explanation:
All you need to do is subtract 78 from 97 to find the "remainder." Or you can also add until you get to 97.
97 - 78 = 19
78 + 19 = 97.
Simplify: (5x2 - 3x - 4)(3x - 7) A. 15x3 - 44x2 + 9x - 28 B. 15x3 - 44x2 + 9x + 28 C. 15x3 + 26x2 - 33x - 28 D. 15x3 - 26x2 - 33x + 28
Answer:
A. 15x^3 -44x^2 +9x +28
Step-by-step explanation:
(5x^2 -3x -4)(3x - 7)
first, distribute by multiplying the terms in each parenthesis with each other:
(5x^2 * 3x) - (3x * 3x) - (4 * 3x) - (5x^2 * 7) + (3x * 7) + (4 * 7)
simplify:
15x^3 -35x^2 -9x^2 +21x -12x +28
Now combine like terms:
15x^3 -44x^2 +9x +28
need a answer for all of them
Suppose a charity event serves a prix fixe dinner that consists of one from each category: (1) soup or salad (not both), (2) appetizer, (3) entree, (4) dessert, and (5) beverage. The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages. How many different prix fixe dinners are possible
Answer:
3840
Step-by-step explanation:
Using the fundamental counting principle
The restaurant is offering five kinds of soup, three kinds of salad, four kinds of appetizers, six entrees, five desserts, and four beverages.
There are 5 independent events happening (5 prixe dinners)
(1) soup or salad (not both)
We have five kinds of soup, three kinds of salad
soup or salad (not both), = 5 + 3
= 8
(2) appetizer = 4
(3) entrees = 6
(4) dessert = 5
(5) Beverage = 4
Hence,
8 × 4 × 6 × 5 × 4
= 3840
The number of different prix fixe dinners are possible is 3840
a company's budget increase from 29 million to 133 million over a period of 10 years. growing by the same percent each year. What was the annual percent increase? Express your answer as a common fraction
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor, Maine. The temperature in Miami is 82 degrees. Write an equation to determine the temperature in Bangor.
Answer:
See Explanation
Step-by-step explanation:
Let the temperatures of Miami and Bangor be M and B degrees respectively.
According to the given information:
M = 3B + 22... (required equation)
Plug M = 82
82 = 3B + 22
82 - 22 = 3B
60 = 3B
B = 60/3
B = 20 degrees
Thus, the temperature in Bangor is 20 degrees.
The required temperature in Bangor is 52 degrees and the required equation is 82 = 3B + - 22.
Given that,
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor, Maine.
The temperature in Miami is 82 degrees.
An equation to determine the temperature in Bangor is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the temperature in Bangor be B
The temperature in Miami is 82 degrees.
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor. Implies,
82 = 3B + - 22
3B = 82 + 22
3B = 104
B = 52 degrees
Thus, the required temperature in Bangor is 52 degrees.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Find Cos N 73 48 E 55
Answer:
1. cos73 is 0.29
2. cos48 is 0.67
3. cos55 is 0.57
These are the answers for cos. Hope this helps!
You want to get an idea of how much your children will benefit from the education system in a state. Which column of numbers will you use for your analysis? Why?
use the Per-Pupil Expenditure column to compare how much each state spends on average for each student. Total expenditure for the state can be misleading. A state with a high number of students could have a high overall expenditure, even if it doesn't spend very much on each student. I'm more concerned about how much the state is likely to spend on each of my children, not how much they spend overall.
Step-by-step explanation:
Answer:
I'd use the Per-Pupil Expenditure column to compare how much each state spends on average for each student. Total expenditure for the state can be misleading. A state with a high number of students could have a high overall expenditure, even if it doesn't spend very much on each student. I'm more concerned about how much the state is likely to spend on each of my children, not how much they spend overall.
-PLATO
Which point on the graph could represent the ratio of 2 white flowers for every 3 pink flowers that will be in one row of Molly’s garden?
Answer: It’s B
Step-by-step explanation:
I just did the quiz
Answer:
The answer would be B
Step-by-step explanation:
take a look at your question.
If you look at the x axis you can see that it is 12 but c is also that.
Now take a look at the y axis, you can see that the letter B is connected to 18.
If you remember your previous problems you would remember that that was an answer (12, 18). But for those who do not remember you can multiply 2x6(which you got your 12 from) and 3x6 ( which is where the 18 is from)
So there for you are left with the answer B.
Let me know if this helped!!! :))))