Answer:
Option D.
[tex]\mathbf{\sqrt{3}} +1}[/tex]
Step-by-step explanation:
The given integral is:
[tex]\int^d_c \int ^{h_2(y)}_{h_1(y)} f(x,y)\ dx \ dy[/tex]
The intersection curves enclosed by the surfaces:
z = 2 - x² - y² and z = 2x + 2y
This implies that:
[tex]2x +2y = 2 - x^2- y^2[/tex]
[tex](x^2 + 2x) +(y^2 + 2y) = 2 \\ \\ (x+1)^2 + (y + 1)^2 = 4 --- (1)[/tex]
We will realize that the curve of this intersection is a circle which is centered at (-1, -1) of the radius 2.
So, from equation (1)
[tex](x + 1)^2 = 4 - (y + 1)^2[/tex]
x + 1 = ±[tex]\sqrt{4 - (y + 1)^2}[/tex]
[tex]x = -1 \pm \sqrt{4 - (y+1)^2}[/tex]
Now,
[tex]h_2 (y) = -1 + \sqrt{4 - (y +1)^2}[/tex] and [tex]h_1 (y) = -1 - \sqrt{4 - (y +1)^2}[/tex]
[tex]h_2(0) = -1 + \sqrt{4-1}[/tex]
[tex]h_2(0) = -1 + \sqrt{3}[/tex], and:
[tex]At \ \ (-1, -1); \\ \\ z = 2 - (-1)^2 - (-1)^2 \\ \\ z = 2 - 1 - 1 \\ \\ z = 0[/tex]
and
[tex]z = 2x + 2y \\ \\ z = 2(-1) + 2 (-1) \\ \\ z = -2 + (-2) \\ \\ z = -4[/tex]
The surface z = 2-x²-y² lies above z = 2x + 2y in the region of intersection
∴
[tex]f(x,y) = (2 - x^2 - y^2) - (2x + 2y) \\ \\ f(0,0) = 2 - 0 \\ \\ f(0,0) = 2[/tex]
So, h₂ (0) + f(0,0) = [tex]\sqrt{3}} - 1 + 2[/tex]
h₂ (0) + f(0,0) = [tex]\mathbf{\sqrt{3}} +1}[/tex]
Write an equation that passes through the points (0,-5) and (8,-5)
Answer:
Equation of the line: [tex]y = -5[/tex].
Step-by-step explanation:
Let [tex](x_0,\, y_0)[/tex] and [tex](x_1,\, y_1)[/tex] denote the coordinates of these two points, respectively.
Calculate the slope [tex]m[/tex] of this line:
[tex]\displaystyle m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{(-5) - (-5)}{8 - 0} = 0[/tex].
Notice that the slope is zero because the two points have the same [tex]y[/tex]-coordinates ([tex]y_0 = y_1 = -5[/tex]) even though their [tex]x[/tex]-coordinates are distinct ([tex]x_0 \ne x_1[/tex].)
Equation for this line in point-slope form:
[tex]y - y_0 = m\, (x - x_0)[/tex].
[tex]y - (-5) = 0\, (x - 0)[/tex].
Rewrite and simplify to obtain the equation of this line in slope-intercept form:
[tex]y = -5[/tex].
The [tex]x[/tex]-term was eliminated because the slope was zero.
I GIVEEEEEE BRAINLILSTER
Answer:
D 54 I did this
Step-by-step explanation:
I need help. (5+5)/2
Answer:5
Step-by-step explanation:10/2=5
Answer: the answer is 5
Step-by-step explanation
Determine the x-intercept of the line whose equation is given: Y = 4x + 2
a. (0, 2)
b. (-2, 0)
c. (0, - 1/2
d. (- 1/2, 0)
Answer:
d
Step-by-step explanation:
Of the following sets, which represents a function?
Situation A = {student's name, all the colors that the student likes}
Situation B = {student's name, the student's favorite math teacher}
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
Answer:
Situation B is a function.
Step-by-step explanation:
We know that,
A function is a relation in which every element in the domain i mapped to a unique element in the co-domain.
That is, every element in the domain must have a unique image.
So, we see that,
Situation A = {student's name, all the colors that the student likes}
Here, the students can have more than one color which they like.
Thus, this relation is not a function.
Situation B = {student's name, the student's favorite math teacher}
Here, the students can have only one favorite math teacher.
So, this relation is a function.
Answer:
D
Step-by-step explanation:
Given ΔMNO, find the measure of ∠MNO.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
28 degrees
38 degrees
52 degrees
76 degrees
I know the answer is 28 degrees , I just am not sure how to work out this problem .
Answer:10907
Step-by-step explanation 10907
Answer:
The answer is 28
Step-by-step explanation:
Hope this helps,
have a great day
The temperature in Tampa increased from 4 a.m. to 4 p.m. on one day in February the tables of values below represents temperatures as a function of time
Answer:
from 6:53 a.m. to 8:53 a.m.
Step-by-step explanation:
:)
Divide. Give the Divide. Give the quotient and remainder.
254 divided 8
Quotient:
Remainder:
Step-by-step explanation:
254 = 8 * 30 + 8 * 1 + 6
= 8(30 + 1) + 6
= 8 * 31 + 6.
Hence the quotient is 31 and the remainder is 6.
Answer:
254/8=31.75
Step-by-step explanation:
The remainder of 254 divided by 8 is 6
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a
congruence statement,
If no, justify your answer.
Step-by-step explanation:
Angle ACB = Angle ZXY (given)
AB = XY (given)
CB = ZY (given)
Since they both display the SSA postulate, it does not guarantee that the triangles are congruent.
Answer:
NoStep-by-step explanation:
Given
Two sides and non-included angle of one triangle is congruent to same on another triangleIt doesn't match any congruency postulates and therefore is not enough to proof that the triangles are congruent
Assume the random variable x is normally distributed with mean u=89 and standard deviation o=4. Find the indicated probability.
Answer:
4
Step-by-step explanation:
becouse is the rii asewei feel mw
what is the diameter of a circle of area 3850 m square
Answer:
70.01
steps by-step explanation:
Two cars start from the same point and move in a straight line, one east at a speed of 60 km per hour and the other west at a speed of 80 km per hour. After what time will they live at a distance of 770 km?
Answer:
5.5 hours
Step-by-step explanation:
Given that :
Speed of A = 60 kmphr
Speed of B = 80 kmphr
After what time will distance = 770 km
Speed * Time = Distance
Let time = x
Distance A + Distance B = 770
(60 * x) + (80 * x) = 770
60x + 80x = 770
140x = 770
x = 770 / 140
x = 5.5 hours
Alan jogged 3.2 miles to school and then 2.2 after school each day for 5 days. Jennifer jogged a total of 45 miles. Who jogged the most and by how much?
Answer:
Jennifer jogged the most, by 18 miles
Step-by-step explanation:
Given
Alan:
[tex]To\ School = 3.2\ miles[/tex]
[tex]After\ School = 2.2\ miles[/tex]
[tex]Days = 5[/tex]
Jennifer:
[tex]Total= 45\ miles[/tex]
Required
Who jogged most?
First, we calculate the distance covered by Alan daily
[tex]Daily = To\ School + After\ School[/tex]
[tex]Daily = 3.2\ miles + 2.2\ miles[/tex]
[tex]Daily = 5.4\ miles[/tex]
Next, we calculate the distance covered in 5 days
[tex]Distance = 5.4\ miles * 5[/tex]
[tex]Distance = 27\ miles[/tex]
By comparison, Jennifer jogged the most because 45 > 27
And the difference is:
[tex]Difference = 45\ miles - 27\ miles[/tex]
[tex]Difference = 18\ miles.[/tex]
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 9 cm
Answer:
8 cm and 9 cm
Step-by-step explanation:
This is the answer because:
1) The other two sides have to equal somethinng that is bigger than 13.
2) 5 cm + 8 cm = 13 cm, therefore, 5 cm and 8 cm is not the correct answer.
3) 6 cm + 7 cm = 13 cm, therefore, 6 cm and 7 cm is not the correct answer.
4) 7 cm + 2 cm = 9 cm, therefore, 7 cm and 2 cm is not the correct answer.
5) Finally, 8 cm + 9 cm = 17 cm, therefore, it is the correct answer since it has a bigger value than 13.
Hope this helps! :D
Answer:
8 and 9
Step-by-step explanation:
because
A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). In this study, the explanatory variable is the
A. amount of eroded soil.
B. rate of water flow.
C. depth of the soil bed.
D. size of the soil bed.
E. None of the above.
Answer:
B. rate of water flow.
Step-by-step explanation:
Given that in a research study the explanatory variable is a form of a variable that is independent and it is used by the researcher to make predictions or analyze variations in other variables known as response variables.
Hence, in this case, the Explanatory variable is the "rate of water flow" because it is the variable researcher wishes to utilize in predicting the amount of soil washed away.
Maya's penny bank is 3/4 full. After she removes 280 pennies, it is 1/2 full. How many pennies can Maya's bank hold?
Answer:
1120
Step-by-step explanation:
write a function for the table
please help I don't get it
Answer:
y=2(x-2.5)
Step-by-step explanation:
Answer:
y = 2x - 5
Step-by-step explanation:
Let us consider the points (- 2, - 9) & (0, - 5)
Equation of line in two point form is given as:
[y-(-9)]/[-9-(-5)] = [x - (-2)]/[-2 - 0]
(y + 9)/(-9 +5) = (x + 2)/ (-2)
(y + 9)/(-4) = (x + 2)/(-2)
(y + 9)/(2) = (x + 2)/(1)
(y + 9) = 2(x + 2)
y + 9 = 2x + 4
y = 2x + 4 - 9
y = 2x - 5
This is the required function.
Simplify to create an equivalent expression6(7-3y)+6(y+1)
Answer:
48-12y
Step-by-step explanation:
6(7-3y) + 6(y+1)
distribute the 6 on both parentheses
42-18y+6y+6
combine like terms
42-12y+6
combine like terms again
48-12y
Javier is considering two options for college.
Option A: Complete the first two years of schooling at a community college
and then transfer to a university.
Option B: Complete all four years of schooling at the university.
Community College Financial Analysis
Costs per Year
Financial Aid Package per Year
Tuition & Fees
Scholarships & Grants
$3,000
$1,000
Room & Board
$1,000
University Financial Analysis
Costs per Year
Financial Aid Package per Year
Tuition & Fees
Scholarships & Grants
$10,000
$15,000
Room & Board
Work-Study
$11,500
$4,000
Which statement about the cost of the options is true?
Option B will save him $1,000.
Option B will save him $2,000.
Option A will save him $14,000.
Option A will save him $17,500.
Answer:
A
Step-by-step explanation:
I got it right in Edginuity.
Answer:
A
Step-by-step explanation:
Identify whether each phrase is an expression, equation, or inequality
Answer:
Top stays the same
Middle and bottom switch
Step-by-step explanation:
ABCDE is aregular pentangon
X=?
Answer:
x = 5.2
Step-by-step explanation:
Measure of interior angle of a regular polygon = [tex]\frac{(n-2)\times180}{n}[/tex]
Here n = number of sides of the polygon
Interior angle of a regular pentagon = [tex]\frac{(5-2)\times180}{5}[/tex]
= 108°
By applying cosine rule in ΔABK,
(BK)² = (AK)² + (AB)² - 2(AK)(AB)cos(108)°
(x + 3)² = 4² + 6² - 2(4)(6)cos(108)°
x² + 6x + 9 = 16 + 36 - (-14.83)
x² + 6x = 57.83
x² + 6x - 57.83 = 0
x = [tex]\frac{-6\pm \sqrt{6^2-4(1)(-57.83)}}{2(1)}[/tex]
x = [tex]\frac{-6\pm16.35}{2}[/tex]
x ≈ -11.2, 5.2
Since, x can't be negative,
x = 5.2 will be the answer.
What is 4/5 as a decimal and what is 4/5 as a percent representation
Solve the inequality for y.
y-5<-14
the standard ratio of a photo's width to it's length is 2/3. what is the length of a photo that has a width of 14 inches?
A. 9.3
B. 17
C. 20
D.21
Answer:
The answer is D.21.
Step-by-step explanation:
You have to divide 14 by 2/3 and you get 21.
PLZ mark me Brainliest!
Find the distance between the points (-12.3, 15.1) and (17.5, 2). Round your answer to the
nearest hundredth.
Answer:
32.55
Step-by-step explanation:
d = 32.552266
For:
(X1, Y1) = (-12.3, 15.1)
(X2, Y2) = (17.5, 2)
Distance Equation Solution:
d=(17.5−(−12.3))2+(2−15.1)2−−−−−−−−−−−−−−−−−−−−−−−−−√
d=(29.8)2+(−13.1)2−−−−−−−−−−−−−−−√
d=888.04+171.61−−−−−−−−−−−−−√
d=1–√059.65
d=32.552266
could be confusing.
What is the awnser please!! -5r + 6 < -5(r + 2)
i)1-2(2x+1)=1-(x-1)
ii)3.6x-6.1=5.9_2.4x
question from equation and inequality
Answer:
1)Solving the expression [tex]1-2(2x+1)=1-(x-1)[/tex] we get [tex]\mathbf{x=-\frac{1}{3}}[/tex]
2) solving the equation [tex]3.6x-6.1=5.9-2.4x[/tex] we get [tex]\mathbf{x=2}[/tex]
Step-by-step explanation:
We need to solve the expressions:
1) [tex]1-2(2x+1)=1-(x-1)\\[/tex]
Solving
[tex]1-2(2x+1)=1-(x-1)[/tex]
First solving the brackets
[tex]1-4x-2=1-x+1[/tex]
Simplifying
[tex]-1-4x=-x[/tex]
Adding 4x on both sides
[tex]-1-4x+4x=-x+4x\\-1=3x[/tex]
Switching the sides
[tex]3x=-1[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=-\frac{1}{3}\\x= -\frac{1}{3}[/tex]
So, Solving the expression [tex]1-2(2x+1)=1-(x-1)[/tex] we get [tex]\mathbf{x=-\frac{1}{3}}[/tex]
2) [tex]3.6x-6.1=5.9-2.4x[/tex]
Solving:
[tex]3.6x-6.1=5.9-2.4x[/tex]
Adding 6.1 on both sides
[tex]3.6x-6.1+6.1=5.9-2.4x+6.1\\3.6x=12-2.4x[/tex]
Adding 2.4x on both sides
[tex]3.6x+2.4x=12-2.4x+2.4x\\6x=12\\[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{12}{6}\\x=2[/tex]
So, solving the equation [tex]3.6x-6.1=5.9-2.4x[/tex] we get [tex]\mathbf{x=2}[/tex]
Maria and Jane set up a lemonade stand one summer to earn money for a trip to the beach. They noticed that the hotter the day, the more glasses of lemonade they sold. They mixed up the lemonade exactly the same way every day: the same amount of sugar, lemon juice, and water. They added ice to the glass when they poured the drink. They always used the same size glass. They decided to chart their sales in order to figure out how much lemonade to make each day, using the weather forecast as their guide. Identify the independent, dependent, and controlled variables in the girls' experimental data.
Answer:
When its hotter people loose water by sweating (de-hydrating) and they replenish their bodies with Lemonade. PLEASE MARK ME BRAINLIEST!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Find the amount of simple interest that $400 would earn at 8% per year by the end of 3 1/2 years.
Answer:
$32
Step-by-step explanation:
The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.
Answer:
The best model is hypergeometric distribution.
Step-by-step explanation:
The probability would be best modeled with hypergeometric distribution.
Hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws, without replacement, which is often employed in random sampling for statistical quality control.
The hypergeometric distribution differs from the binomial distribution in the lack of replacements.
Thus, the best model is hypergeometric distribution.