The surface element is
dS = || ∂r/∂u x ∂r/dv || du dv
where
r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k
r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k
is the vector parameterization for the surface S.
The normal vector to the surface is
∂r/∂u x ∂r/dv
… = (i + j + 2 k) x (i - j + k)
… = 3 i + j - 2 k
and has norm
|| ∂r/∂u x ∂r/dv || = √(3² + 1² + (-2)²) = √(14)
Now compute the integral:
∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv
… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv
… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv
… = √(14) ∫₀¹ (8 + 2v) dv
… = √(14) (8v + 2v²) |₀¹
… = 10 √(14)
Rewrite the following quadratic equation in factored form, such as y=(x-a)(x-b)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
y = x^2 - x - 72
y = (x - 9)(x + 8)
You want two numbers that multiply to 72 -- -9 and 8
You want two numbers that differ by -1 -9 + 8 = - 1
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $200 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.]
ft (smaller value) ? ft (larger value)
ft2
Answer:
Length = [tex]5\ \text{ft}[/tex]
Breadth = [tex]5\ \text{ft}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the length of the garden
and [tex]y[/tex] be the width of the garden
From the details of the cost in the question we get
[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]
Now area of the garden is
[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]
Differentiating with respect to x we get
[tex]\dfrac{dA}{dx}=10-2x[/tex]
Equating with 0
[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]
Double derivative of the area is
[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]
So, area is maximum at [tex]x=5[/tex]
[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]
So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].
Margaret is making strawberry milkshakes for the kids party. The recipe calls for 1/3 of a cup of strawberry syrup to make 8 milkshakes. How many cups of Strawberry syrup are needed to make 48 milkshakes?
A.) 3
B.)2
C.)16
D.) 8
Answer:
B. The answer is 2 cups.
For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a standard deviation of 100. Assume that the SAT scores are normally distributed. What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
b) between 450 and 675?
Answer:
The probability that a randomly selected high school senior's score on mathematics part of SAT will be
(a) more than 675 is 0.0401
(b)between 450 and 675 is 0.6514
Step-by-step explanation:
Mean of Sat =[tex]\mu = 500[/tex]
Standard deviation = [tex]\sigma = 100[/tex]
We will use z score over here
What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
P(X>675)
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]
Z=1.75
P(X>675)=1-P(X<675)=1-0.9599=0.0401
b)between 450 and 675?
P(450<X<675)
At x = 675
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]
Z=1.75
At x = 450
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{450-500}{100}[/tex]
Z=-0.5
P(450<X<675)=0.9599-0.3085=0.6514
Hence the probability that a randomly selected high school senior's score on mathematics part of SAT will be
(a) more than 675 is 0.0401
(b)between 450 and 675 is 0.6514
what is the value of B and C
Answer:
The value of b is 6 and the value of c is also 6
Step-by-step explanation:
We know that given triangles are congruent. When two triangles are congruent then their respective sides are also equal/congruent.
So,
ΔUWV≅ΔEDF
Then
WV ≅ DF
WU ≅ DE
UV ≅ EF
So,
Putting their respective value equal:
WV = DF
[tex]9c = 10c-6\\10c-6 = 9c\\10c-6+6 = 9c+6\\10c = 9c+6\\10c-9c = 9c+6-9c\\c = 6\\and\\10b = b+54\\10b-b = b+54-b\\9b = 54\\\frac{9b}{9} = \frac{54}{9}\\b = 6[/tex]
Hence,
The value of b is 6 and the value of c is also 6
A new, healthy drink has 160% of the “recommended daily allowance” (RDA) of vitamin J. If the RDA is 40 milligrams, how much vitamin J is in the new health drink?
Answer:
80
Step-by-step explanation:
Im not really sure just the thingy says that 80 was the right anwser
Answer:
64
Step-by-step explanation:
Sorry I'm really late.
what do i need to subtract from 83/10 to make 8
Answer:
0.3
Step-by-step explanation:
Let x be what you need to subtract
[tex]\frac{83}{10} = 8.3[/tex] Plug x in: 8.3 - x = 8Re-arrange: 8.3 - 8 = x8.3 - 8 = 0.3So, you need to subtract 0.3 from 83/10 to make 8.I hope this helps!
Answer:
3/10
Step-by-step explanation:
83/10 - 3/10 = 80/10 = 8
If a wedding ring is dropped from a tall building, the distance it has fallen in feet is given by 16t2, where t is the time in seconds since the ring was dropped. How far has the ring fallen after 5 seconds?
Graph the equation on the coordinate plane.
y = 4x
HURRY!! At the snack bar, hot dogs cost $4 each and bottled water costs $2 each:
Answer: (2,1) (1,3)
Step-by-step explanation: Assume that the number of hot dogs is X and the number of water bottles is y.
write the equation in slope-intercept form of the line that passes through (6,-11) and is parallel to the graph of y=-2/3x+12
Answer:
[tex]y = -\frac{2}{3}x - 7[/tex]
Step-by-step explanation:
Given
[tex]Point = (6,-11)[/tex]
[tex]Equation: y = -\frac{2}{3}x + 12[/tex]
Required
Determine the equation of the point
First, we need to determine the slope of the point.
Since the point is parallel to the given equation, then they have the same slope (m).
The general form of an equation is:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m = -\frac{2}{3}[/tex]
The equation of the point in slope intercept point is:
[tex]y -y_1 = m(x-x_1)[/tex]
Where
[tex]m = -\frac{2}{3}[/tex]
[tex](x_1,y_1) = (6,-11)[/tex]
Substitute these values in the equation:
[tex]y - (-11) = -\frac{2}{3}(x - 6)[/tex]
[tex]y +11 = -\frac{2}{3}(x - 6)[/tex]
[tex]y +11 = -\frac{2}{3}x + \frac{2}{3}*6[/tex]
[tex]y +11 = -\frac{2}{3}x + 4[/tex]
Subtract 11 from both sides
[tex]y = -\frac{2}{3}x + 4-11[/tex]
[tex]y = -\frac{2}{3}x - 7[/tex]
Suppose that your school's environmental club wants to travel to the state capital to participate in an Earth Day festival. The rental of a bus for the day will cost $895. Lunch and festival activities will cost $25 per student. Your club advisor thinks that the fee for participating should not be more than $60. How many students must be recruited for the trip. Write a mathematical model for this.
Answer:
Mathematical model is:
(895/n) + 25 ≤ 60
Number of students must not be less than 26
Step-by-step explanation:
We are told that;
- the rental of a bus for the day will cost $895.
- Lunch and festival activities will cost $25 per student
If the number of students are n, then cost per student for bus rent is; $895/n
Thus, total amount per n number of students to participate is;
895/n + 25
Now, we are told that the club advisor thinks that the fee for participating should not be more than $60.
Thus in form of inequality, we have;
(895/n) + 25 ≤ 60
Subtract 25 from both sides to get;
(895/n) ≤ 60 - 25
(895/n) ≤ 35
Multiply both sides by n and then divide both sides by 35;
895 ≤ 35n
26 ≤ n
Samir usually drink 3 cups of coffee in the morning how many liters of coffee does he drink round
Answer:
0.709765 liters
Step-by-step explanation:
Is 4/10 closer to 0, 1, 1/2
Answer:
1/2
Step-by-step explanation:
Divide the denominator in half
10/2 = 5
4 is close to 5 so 4/10 is close to 1/2
Answer:
4/10 is closer to 1/2.
Think of a pie. There are 10 slices total, but only 4 slices remain, because I ate them all! Do you think that 4 out of 10 slices would be closer to a whole pie or half a pie? It would be closer half a pie.
Further explanation:
If you were to round the number 44 to the closest ten, it would be 40. If you were to round 47 to he nearest ten, it would be 50. If you were to round 45 to the nearest ten, it would also be 50. I hope this helps!
Half (1/2) is the answer.
which is closer to 0, -24 or 38
Answer:
-24
Step-by-step explanation:
Although -24 is a negative number, it still is 24 numbers away from zero. 38 is positive and is 38 digits away.
A 15 foot ladder is leaning against a building, with the base of the ladder 4 feet from the building. How high up on the building will the top of the ladder reach?
The ladder will reach
android:
nothing ft high up on the building.
(Round to the nearest tenth.)
Enter your answer in the answer box and then click Check Answer.
All parts showing
Answer: The height of the building = 14.5 feet.
Step-by-step explanation:
Given: Length of ladder = 15 feet
Distance of base of ladder from building = 4 feet
Since building is standing vertical on ground making right angle.
So with ladder a right triangle is formed , where base = 4 feet , Hypotenuse = 15 feet [Hypotenuse is side opposite to right angle]
According to the Pythagoras theorem ,
Hypotenuse² = Perpendicular² + Base²
⇒ (15)² = Perpendicular² + (4)²
⇒ 225 = Perpendicular² +16
⇒ Perpendicular² = 225 -16
⇒ Perpendicular² = 209
⇒ Perpendicular = √209 = 14.4568322948 ≈ 14.5 feet
Hence, the height of the building = 14.5 feet.
Mr. Jones got four seats on the school's trip to Grand
Canyon for his students. In how many different ways Mr.
Jones can select a group of four from his class of 36?
Answer:
D. 58,905
Step-by-step explanation:
Number of seats available for Mr. Jones had for the trip = 4
Number of students in his class = 36
Number of ways he can select a group of 4 out of 36 students from his class is calculated as follows:
[tex] C \binom{36}{4} = \frac{36!}{(36 - 4)! * 4!)} [/tex]
[tex] = \frac{36!}{(32! * 4!)} = 58,905 [/tex]
Formed from sentences P and Q, the sentence P or Q is a
A) biconditional.
B) complementary.
C) conditional
D) disjunction.
Answer c I think
Step-by-step explanation:
Geometry please help!!!!!!!?
Answer:
It is same as the length of YX =8 inches so the length of VW=8 inches
A train stops at Atlanta, then at Bayville, and then at Colleyville. The
distance from Atlanta to Colleyville is 25.5 miles, and the distance from
Atlanta to Bayville is 10 2/3 miles.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as what is required of the question is not stated.
However, since the question is only limited to distance, a likely question could be to calculate the distance from Bayville to Colleyville.
Represent the distance from Atlanta to Colleyville with AC
Represent the distance from Atlanta to Bayville with AB
Represent the distance from Bayville to Colleyville with BC
So, we have that:
[tex]AC = 25.5\ miles[/tex]
[tex]AB = 10\frac{2}{3}\ miles[/tex]
The relationship between AB, AC and BC is:
[tex]AC = AB + BC[/tex]
Make BC the subject of formula:
[tex]BC = AC - AB[/tex]
[tex]BC = 25.5 - 10\frac{2}{3}[/tex]
Convert fraction to decimal
[tex]BC = 25.5 - 10.7[/tex]
[tex]BC = 14.8[/tex]
Hence, the distance from Bayville to Colleyville is 14.8 miles
(1 pt)What is the vertex of the graph of
the function f(x) = x2 + 6x + 9?
Answer:
(-3,0)
Step-by-step explanation:
Question 2 options: A consumer advocate group selects a random sample of 205 snack foods and finds that 174 of them contain more fat grams than what is indicated in the snack's nutritional information. Create a 90% confidence interval for the population proportion for snack foods that contain more fat grams that what is indicated in the snack's nutritional information.
Answer:
156 snack foods.
Step-by-step explanation:
205 - 174 = 31
To find 90% of 174, multiply 174 by 0.90.
174 x 0.90 = 156
The answer is 156 snack foods.
A square has a perimeter of 72 cm what is the length of each side
Answer:
each side is 12 cm
Step-by-step explanation:
This is a simple equation, since a square is equal an all 4 sides, all you have to do it divide 72 by 4 to get your answer.
May I have brainliest please? :)
What is the solution to the inequality f + 4 < 2?
Answer: f=-2
Step-by-step explanation:
math
Answer:
f < -2
Step-by-step explanation:
what is an odd number
Answer:
An odd number is any number than can't be divided by two ! Some examples are 1, 3, and 5.
Any integer (not a fraction) that cannot be divided exactly by 2. The last digit is 1, 3, 5, 7 or 9. Example: −3, 1, 7 and 35 are all odd numbers.
PLEASE HELP I WILL GIVE YOU A BRAINLIEST! During a basketball game, Tom attempted 25 shots and made 9. He says he made 40% of the shots he took. Is Tom correct? Explain your reasoning using complete sentences.
Answer:
Correct I think
Step-by-step explanation:
9 is nearly half of 25. (12.5) Half is equal to 50%. 40 is close to 50 and 9 is close to 12.5. So, he is correct. I think, hope this helps.
What number divided by−3 gives 12 as the result?
Answer:
-36
Step-by-step explanation:
x / (-3) = 12
x = 12*(-3)
x = -36
plz do this ill mark brainly
Answer:
7+(−2) = 7 − 2 = 5
Step-by-step explanation:
Answer:
The Positive number has to be greater than the negative number you are adding with.
Example(s):
-30 + 35 = 5
-65 + 70 = 5
Sandy has around $245 in her pocket but she thinks she could have up to $25 more or $25 less. Write and solve an absolute value equation that can show the maximum and minimum amount of money that Sandy has in her pocket.
Answer:
The absolute value equation is |x - 245| = 25The maximum amount of money in Sandy's pocket is $270The minimum amount of money in Sandy's pocket is $215Step-by-step explanation:
The absolute value equation for the amount of money in Sandy's pocket is given as;
|x - 245| = 25
The equation for the maximum amount of money in Sandy's pocket is given as;
x - 245 = 25
x = 25 + 245
x = $270
The equation for the minimum amount of money in Sandy's pocket is given as;
x - 245 = -25
x = -25 + 245
x = $215
A crew of highway workers paved 1/5 mile in 1/8 hour. If they work at the same rate, how much will they pave in one hour?
Answer:37.5
Step-by-step explanation:
The work a crew will pave in an hour will be 8/5 miles.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a crew of highway workers paved 1/5 mile in 1/8 hour. The amount of work will be calculated as,
1 / 8 hours ⇒ 1 / 5 miles
1 hour ⇒ 8 x (1 / 5 ) miles
1 hour ⇒ 8 / 5 miles
Therefore, the work a crew will pave in an hour will be 8/5 miles.
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