He region W lies between the spheres x2+y2+z2=1 and x2+y2+z2=4 and within the cone z=x2+y2−−−−−−√ with z≥0; its boundary is the closed surface, S, oriented outward. Find the flux of F⃗ =x3i⃗ +y3j⃗ +z3k⃗ out of S
The flux of out of S is [tex]14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)[/tex].
What is Flux of the Vector Field?
Solving the flux of the vector field using the divergence theorem which has the following formula [tex]$\iint_S F \cdot d S=\iiint_E div} F(x, y, z) d V$[/tex] where F is the vector field [tex]$F=P i+Q j+R k$[/tex] and div F means the divergence of F which has the formula [tex]$F=\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}+\frac{\partial R}{\partial z}$[/tex]
Here, we let the vector field to be [tex]$\vec{F}=x i+y j+z k$[/tex]
[tex]$\vec{F}=x i+y j+z k$[/tex]
Now solving for [tex]${div} F$[/tex]
[tex]$$\begin{aligned}& {div} F=\frac{\partial x}{\partial x}+\frac{\partial y}{\partial y}+\frac{\partial z}{\partial z} \\& {div} F=1+1+1=3\end{aligned}$$[/tex]
Thus,
[tex]\iint_S F \cdot d S=\iiint 3 d V[/tex]
From the given region the limits of integrations in spherical coordinates are,
[tex]0 \leq \theta \leq 2 \pi, 0 \leq \phi \leq \frac{\pi}{4}, 1 \leq \rho \leq 2[/tex]
Thus,
[tex]\iint_S F \cdot d S=\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} \int_1^2 3 \rho^2 \sin \phi d \rho d \phi d \theta[/tex]
Integrate with respect to [tex]$\rho$[/tex]
[tex]\begin{aligned}& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 3\left[\frac{1}{3} \rho^3\right]_1^2 \sin \phi d \phi d \theta \\& =\int_0^{2 \pi} \int_0^{\frac{\pi}{4}} 7 \sin \phi d \phi d \theta\end{aligned}[/tex]
Integrate with respect to [tex]$\phi$[/tex]
[tex]\begin{aligned}& =\int_0^{2 \pi} 7[-\cos \phi]_0^{\frac{\pi}{4}} d \theta \\& =\int_0^{2 \pi} 7\left(-\frac{\sqrt{2}}{2}+1\right) d \theta\end{aligned}[/tex]
Integrate with respect to [tex]$\theta$[/tex]
[tex]\begin{aligned}& =7\left(-\frac{\sqrt{2}}{2}+1\right)[\theta]_0^{2 \pi} \\& =14 \pi\left(-\frac{\sqrt{2}}{2}+1\right)\end{aligned}[/tex]
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What is the rate of change between (3.4,-0.1) and (3.5,0.1)?
The rate of change between the points (3.4, -0.1) and (3.5, 0.1) is 2.
How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity.
Therefore,
rate of change = Δy / Δx
rate of change = y₂ - y₁ / x₂ - x₁
Hence, let's find the rate of change of (3.4,-0.1) and (3.5,0.1).
rate of change = 0.1 + 0.1 / 3.5 - 3.4
rate of change = 0.2 / 0.1
rate of change = 2
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y=-12-3x what is the answer and how do you do this
Answer:
You draw the line of the graph and every point on the line is a solution
Step-by-step explanation:
y = mx + b You graph the b which is the y intercept. This is where the graph crosses the x axis. In this case it is -12. From that point (0,-12) You follow a pattern which is the slope. In this case the slope is -3. That mans that you move three units down and then 1 unit right.
I highlighted a few points on the line. Every point on the line is a solution.
please help me ASAP MATH!
Answer:
A
Step-by-step explanation:
numerator = exponent of x (in this case is 1, so it can be omitted)
denominator = index of the root
√x
Help me how do I do this (221x3 + 154x2 + 228x + 41) / (17x + 4)-4
The value of x from the equation (221x3 + 154x2 + 228x + 41) / (17x + 4)-4 is 992
How to find the value of x?In general, the algebraic expression should take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left side and all the remaining values to the right side to find the value of x. To find the answer, simplify the values. In algebra, the letter "x" is frequently used to represent an unknown value. It is referred to as a "variable" or "unknown" at times.
(221x3 + 154x2 + 228x + 41) / (17x + 4)-4
Multiplying 221*3 and 154*2 =663,308
( 663+308 + 228x + 41) / (17x + 4)-4
( 971+ 228x + 41) / (17x + 4)-4
=( 971+ 228x +41)
(17x + 4)
=1012+228x
(17x + 4)
-x=-992
x=992
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Landon and Colin bought 1/2 pound of trawberrie. They are haring the trawberrie equally. How many trawberrie will each peron receive?
Using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The four basic mathematical operations, according to the majority of people, are addition, subtraction, multiplication, and division.
So, the strawberries both Landon and Colin will get are:
We know that Landon and Colin brought 1/2 strawberries.
They share is equally that is:
1/2 ÷ 2
Now, solve as follows:
1/2 ÷ 2
1/2 ÷ 2/1
1/2 * 1/2
1/4
Therefore, using mathematical operations, we can conclude that both London and Colin will get 1/4 of strawberries each.
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Richard and Teo have a combined age of 28. Richard is 13 years older than twice Teo’s age. How old are Richard and Thiago?
If Richard is 13 years older than twice Teo's age. The age of Richard and Thiago will be 23 and 5 respectively.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Richard and Teo have a combined age of 28. Richard is 13 years older than twice Teo’s age.
We have to find the age of Richard and Thiago.
Suppose the age of Richard and Teo be x,
If Richard and Teo have a combined age of 28,
T+R=28 --------(1)
If Richard is 13 years older than twice Teo’s age,
R=( 2T + 13) --------(2)
u
Substitute the value of R in eqation 1
T+( 2T + 13)=28
3T+13=28
3T=28-13
3T=15
T=5
Substitute the value of T in equation 1 to obtain R,
T+R=28
5+R=28
R=28-5
R=23
Thus, if Richard is 13 years older than twice Teo age. The age of Richard and Thiago will be 23 and 5 respectively.
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Mary' bedroom had an area of 40 feet. The length of the bedroom i 8 feet. What i the width of the bedroom?
The width of Mary's rectangular room is 5 feet.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane.
It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
A square is a rectangle
So, we consider Mary's room a rectangular room:
With an area of 40ft² and a length is 8ft.
Area of rectangle: l*w
Where l stands for length and w stands for width.
Now, calculate the width using the formula as follows:
Area = l*w
40 = 8*w
w = 40/8
w = 5ft
Therefore, the width of Mary's rectangular room is 5 feet.
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how is the accuracy rate calculated? how is the accuracy rate calculated? subtract the number of correct predictions from the total number of predictions. divide the number of true positives by the number of true negatives. divide the number of correct predictions by the total number of predictions. add the number of true positives and the number of false negatives.
Accuracy rate is equal to the difference of predicted value and true value divide it by true value and then multiply by 100 to get the rate.
Accuracy value represent the calculated value is more close to the true value.It help us to measure the statistical error.It help us to know what the error given in the measured value of the data.Divide the difference of predicted and true by the true value and then multiply it by 100 to get the accuracy rate.Accuracy test can be done different statistical methods also.Accuracy rate = [ | Predicted value - True vale|/ true value ] × 100
Therefore, the accuracy rate is the percentage of the ratio of difference of predicted value and true value to the true value.
The given question is incomplete, I answer the question in general according to my knowledge:
How is the accuracy rate calculated?
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During the two-day drive to her sister's house, Audrey drove 320 miles the first day and 280 the second day. She stopped for gas twice, paying $24 and $31. She used 27 gallons of gas.
Which of the following cannot be determined using the information given?
A. cost of gas
B. how many gallons the gas tank holds
C. miles driven
D. miles per gallon of gas
The value not predicted for the given information is "how many gallons the gas tank holds".
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.
Here,
How many gallons the gas tank holds is the value that could not be predicted based on the information provided.
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The top of a ladder rests at a height of 12 feet against the side of a house. If the base of the ladder is 9 feet from the house, what is the length of the ladder? Round to the nearest foot.
Answer:
16 ft
Step-by-step explanation:
The length of the ladder is 16\ ft16 ft
Step-by-step explanation:
Let
L ----> the length of the ladder
we know that
Applying the Pythagoras theorem
L^{2}=15^{2} +6^{2}L
2
=15
2
+6
2
L^{2}=261L
2
=261
L=\sqrt{261}\ ftL=
261
ft
L=16\ ftL=16 ft
the perimeter and the width of a rectangle are 64 m and 2 m, respectively. what is the area of the rectangle?
Area of the given rectangle as per given perimeter and width is equal to 60m².
As given in the question,
Perimeter of the given rectangle = 64m
Width of the given rectangle 'w' = 2m
Let us consider 'l' be the length of the rectangle
Perimeter of the rectangle = 2 ( l + w )
Substitute the values
64 = 2 ( l + 2)
⇒32 = l + 2
⇒l = 32 - 2
⇒l = 30m
Area of the given rectangle = l × w
= 30 × 2
= 60m²
Therefore, the area of the given rectangle as per given dimensions is equal to 60m².
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In the year 2000, the company made $2. 2 million in profit. For each conecutive year after that, their profit increaed by 13%. How much would the company' profit be in the year 2003, to the nearet tenth of a million dollar?
Rounded to the nearest tenth of a million dollars, the company made $3.2 million in profit in the year 2003.
What is meant by Profit?Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. It is, in other words, the difference between income and costs. Profit is an important aspect in a company's performance and is often quantified in monetary terms, but it may also be viewed .For example, for each consecutive year after that, their profit increased by 13%.
Profits may be divided into two categories: net profit and gross profit. After deducting all costs, taxes, and expenses, a company's net profit is the overall profit it has made. In contrast, gross profit is the profit made by a firm before expenses and costs are deducted.
How to solve?
In the year 2001, the company made $2.2 million * 1.13 = $2.486 million in profit.
In the year 2002, the company made $2.486 million * 1.13 = $2.82778 million in profit.
In the year 2003, the company made $2.82778 million * 1.13 = $3.1987314 million in profit.
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Naturalized citizens include individuals who
A) can become president or vice president one day
B) we’re under 18 when their parents were naturalized
C) have received formal permission to remain in the country
D) entered the United States in order to settle here
Answer:
b). were 18 when their parents were naturalized
Step-by-step explanation
I know I am right because I believe this is Civics or U.S History. I did Civics in 7th, and U.S History I am currently doing. hope this helps!
A one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of
carbohydrates. Determine how many servings of each would be required to obtain 160 calories and 20 grams of carbohydrates
How many serving(s) of spaghetti would be required?
(Round to the nearest tenth.)
For 160 calories and 20 grams of carbohydrates 0.61 cups are required.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates.
For 160 calories the number of cups will be calculated as,
1 cup = 260 calories
160 calories = ( 160 ) / 260 cups
160 calories = 0.61 cups
Therefore, for 160 calories and 20 grams of carbohydrates 0.61 cups are required.
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How to write the equation of the line with m = - 3/4 that goes through (2, –5) in
Slope–Intercept Form.
Answer: y=-3/4x-3.5
Step-by-step explanation:
First, set up the equation based on the information we already know. The slope-intercept form is y=mx+b (m being the slop and b is the y-intercept)
We already know the slope, so we can substitute it.
y=-3/4x+b
Now, the only variable we need to find is b (the y-intercept)
To do this we can substitute the point that was given, (2,-5)
Substitute -5 in for y and 2 in for x.
Then you get the equation -5=-3/4(2)+b
Multiply -3/4 and 2 and you get -5=-3/2+b
Add -3/2 from both sides to isolate b
You then get b=-3.5
Substitute b back in the original equation
Your final answer is y=-3/4x-3.5
Match the variable and angle with the correct value to create the angle measures for the exterior angle theorem.
x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.
In the given figure, ∠DBC=7y°, ∠CBA=5y°, ∠C=3y° and ∠D=x°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Here,
∠DBC+∠CBA=180° (Sum of adjacent angles is 180°)
⇒ 7y°+5y°=180°
⇒ 12y°=180°
⇒ y°=15°
∠DBC=7y°=105°, ∠CBA=5y°=75° and ∠C=3y°=45°
Now, ∠DBC=∠C+∠A
⇒ 105°=45°+∠A
⇒ ∠A=60°
Therefore, x=60°, y=15°, angle C is 45°, angle DBC is 105° and angle CBA is 75°.
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A family i going to on an trip for 3 day the total cot for the hotel i $336. One hundred dollar for the day wa budgeted for food. How much will each day of the the trip will cot?
The each day of the trip will cost the family $212 .
In the question ,
it is given that ,
a family is going on 3 day trip ,
the cost for hotel for 3 days is = $336 ,
So , the cost for the hotel for 1 day is = $336/3 = $112 ,
the amount budgeted for the food is one hundred dollar
the cost for the food for 1 day is = $100 .
So , the cost for each day is = cost of food + cost of hotel
Substituting the values of food and hotel ,
we get ,
= 100 + 112
Adding both the terms ,
we get ,
= 212
Therefore , the cost for each day is = $212 .
The given question is incomplete , the complete question is
A family is going to on a trip for 3 days the total cost for the hotel is $336. One hundred dollar for the day was budgeted for food. How much will each day of the the trip will cost ?
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Which graph shows a system with no solutions?
The wavelength of green light in a spectrum is about 0.000003 feet. Which
number best approximates this length as a power of 10?
The scientific notation of the wavelength of green light in a spectrum
is 3×10⁻⁶ feet.
What is scientific notation?In scientific notations numbers are written in the form of a base that is
0 ≤ b < 10 and multiplied by 10ⁿ where n represents integers.
We write large standard numbers in scientific form in a compact manner.
Given, The wavelength of green light in a spectrum is about 0.000003 feet.
Now, the decimal is 6 places before so we have to move the decimal 6 places to the right, and to maintain the actual value we'll raise it to 10⁻⁶.
Therefore, 0.000003 feet,
= 3×10⁻⁶ feet.
So, the wavelength of green light is 3×10⁻⁶ feet.
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Write the equation of the line passing through the points (-1,4) and (-4,1).
The equation of the line is
I need help with this please i don’t understand
Answer:
99
Step-by-step explanation:
Since the triangles are similar, we know the ratio of the sides is a constant. We know that SQ is 55, and the corresponding side on the other triangle is 10. This lets us find the ratio for the whole triangle! The ratio is 55/10, or 5.5.
To solve for RS, consider the corresponding side on the other triangle(LS) which is 18. We multiply that by the ratio to get 18 * 5.5 = 99, which is the length of RS.
I don't know if you need to solve for x, but if you do, here it is! We have [tex]99 = 12x+3[/tex] (the equation for side RS). subtracting 3 from both sides results in [tex]96 = 12x[/tex], and dividing by x gives us that x = 8.
Thank you! Feel free to ask me any questions about my answer. I hope this helps!
Find the slope of the li
16.) (5,-3), (5,8)
Answer:
slope = undefined
Step-by-step explanation:
Find the slope of the line: (5,-3), (5,8)
slope = change in y / change in x
slope = ( -3 - 8) / (5 - 5)
slope = -11/0
slope = undefined
These points graph a vertical line.
answer:
the slope is undefined.
step-by-step explanation:
there is an equation (y2-y1)/(x2-x1) that allows for you to determine the slope. since this line is vertical, the slope is defined because if you plug the points into the equation, you would be dividing by 0.
The cost of having one pizza delivered is $14. Each additional pizza cost $9 more. Write the explicit and recursive formula to represent the situation.
Answer:
14+9(x-1)=y
Step-by-step explanation:
If x is the number of pizza's being delivered and the first pizza costs $14 then that pizza is already accounted for by the 14 in the equation, so you subtract x by 1 before multiplying it by 9, then add the 14 to the product you then get the total cost: y
Find the value of y. Round to the nearest tenth.
The value of y after solving the triangle using sine rule is 46.15.
What is sine rule?Sine rule is a rule that relates the sides of a triangle with the sine of their opposite angles.
To calculate the value of y, we use the sine rule formula
Formula:
Sina/A = Sinb/B............... Equation 1Where:
a, b = The values of the two included angle of the triangleA,B = The values of the two included sides of the triangleFrom the question,
Given:
a = 42°b = 85°A = 31B = ySusbtitute these values into equation 1 and solve for y
sin42°/31 = sin85°/yy = 31×sin85°/sin42°y = 46.15Hence, the value of y is 46.15.
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write an equation of a line perpendicular to the givin equation using the given point givne (8,2); x = -4
y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
In the perpendicular lines the product of slopes will be -1
m1m2=-1
y=x+4 is the given line, it has slope of 1, so the perpendicular line will have slope -1.
The line is passing through (8,2)
2=-1(8)+b
2=-8+b
2+8=b
10=b
Hence, y=-x+10 is the equation of a line perpendicular to the givin equation using the given point given (8,2) and x = -4
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Sharon started with $42 in her bank account and
added $16 per week. Neil started out $70 in debt and deposited $30 per week. Determine how many weeks it will take them to have saved the same amount of money.
The number of weeks it will take them to have saved thesame amount is 8 weeks
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.
if x represents the the number of weeks for saving and y represents the equal saved amount, then
42+16x = y equation 1
-70+ 30x = y equation 2
subtract equation 1 from 2
-70-42+16x- 30x= 0
-112+14x= 0
collect like terms
-112=-14x
divide both sides by 14
x= -112/-14
x= 8weeks
therefore it will take them 8 weeks to have equal savings
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What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
Answer: 95 percent confidence interval
Step-by-step explanation: "you have a 5 percent chance of being wrong. with a 90 percent confidence interval, you have a 10 percent chance of being wrong a 99 percent confidence interval would be wider than a 95 percent confidence interval for example plus or minus 4.5 percent instead of 3.5 percent"
please help me with find x in the diagram below
Answer:
x = 125
Step-by-step explanation:
Given a heptagon with 60° and 90° angles marked, one marked 2x°, and the remaining angles marked x°, you want o know the value of x.
Sum of anglesThe sum of the interior angles of a heptagon is ...
180° × (7 -2) = 900°
Using the given values, this tells us ...
90° +x° +x° +x° +x° +60° +2x° = 900°
6x = 750 . . . . . . . divide by °, subtract 150
x = 125 . . . . . . divide by 6
The value of x is 125.
__
Additional comment
The attached figure is drawn with correct angles.
The sum of interior angles of an n-gon is 180°×(n -2).
(4x-7.2)+(-5.3x-8) please help!
Answer:
−1.3x − 15.2
Step-by-step explanation:
step 1: simplify
4x−7.2−5.3x−8
=4x+−7.2+−5.3x+−8
step 2: combine like terms
=4x+−7.2+−5.3x+−8
=(4x+−5.3x)+(−7.2+−8)
=−1.3x+−15.2