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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using the trap razors below find the measure of angle HMA.
In the given trapezoid, the angle ∠ HMA is 120°.
What is trapezoid?A closed polygon or geometry with four sides, four corners, and four angles is called a trapezium. Each pair of a trapezium's opposing sides is parallel to the other.
In the given trapezoid AMHT,
The angle H = 60°.
To find the angle ∠ HMA,
Since, the sum of angle MHT and angle HMA is equal to 180°.
∠ HMA + ∠ MHT = 180°
∠ HMA + 60 = 180
∠ HMA = 120
The required angle ∠ HMA is 120°.
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Diameter of cylinder A is 7 cm, and the height is
14 cm. Diameter of cylinder B is 14 cm and height
is 7 cm. Then find the ratio between their volume
The ratio of volumes of Cylinder A to Cylinder B is 1 : 2
What is a Cylinder?
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the volume of the first cylinder be = A
Let the volume of the second cylinder be = B
Now,
The diameter of first cylinder = 7 cm
Radius of the first cylinder r = 7/2 = 3.5 cm
Height of the first cylinder h = 14 cm
And ,
The diameter of second cylinder = 14 cm
Radius of the second cylinder R = 14/2 = 7 cm
Height of the second cylinder H = 7 cm
To find the ratio between the volumes of both cylinders
Volume of Cylinder A = πr²h
Substituting the values in the equation , we get
Volume of Cylinder A = π x ( 3.5 ) x ( 3.5 ) x ( 14 )
Volume of Cylinder B = πR²H
Substituting the values in the equation , we get
Volume of Cylinder B = π x ( 7 ) x ( 7 ) x ( 7 )
The ratio between volumes of A and B is given by = Volume of Cylinder A / Volume of Cylinder B
So , the ratio is
Volume of Cylinder A / Volume of Cylinder B = π x ( 3.5 ) x ( 3.5 ) x ( 14 ) / π x ( 7 ) x ( 7 ) x ( 7 )
On simplifying the equation , we get
Volume of Cylinder A / Volume of Cylinder B = 2/4
Therefore , the ratio is
Volume of Cylinder A / Volume of Cylinder B = 1 : 2
Hence , The ratio of volumes of Cylinder A to Cylinder B is 1 : 2
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What is the concentration of h ions at a ph = 2? mol/l what is the concentration of h ions at a ph = 6? mol/l how many more h ions are there in a solution at a ph = 2 than in a solution at a ph = 6?
The concentration of H+ ions at a pH = 2 is 10⁻² mol/L
Theconcentration of H+ ions at a pH = 6 is 10⁻⁶ mol/L
And there are 10,000 times more H⁺ ions in a solution of pH = 2 than that of pH = 6
In this question we have been given the pH of the solution.
We need to find the concentration of H+ ions in the given solution.
The H⁺ ion concentration can be calculated from pH values using the equation: pH = - log [H⁺]
at a pH = 2,
Using the above equation, 2 = - log [H⁺]
[H⁺] = 10⁻² mol/L
at a pH = 6,
Using the above equation, 6 = - log [H⁺]
[H⁺] = 10⁻⁶ mol/L
We need to find how many more h ions are there in a solution at a ph = 2 than in a solution at a ph = 6
Consider the ratio of [H⁺] for pH = 2 and pH = 6, we have
10⁻²/10⁻⁶ = 10⁴
Therefore, there are 10,000 times more H⁺ ions in a solution of pH = 2 than that of pH = 6
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Which expression is equivalent to the expression quantity negative 10 over 9 times t plus 1 over 8 end quantity minus expression quantity negative 6 over 18 times t plus 3 over 4 end quantity?
negative 14 over 18 times t minus 5 over 8
negative 14 over 18 times t plus 2 over 8
4 over 9 times t plus 2 over 4
16 over 18 times t plus negative 4 over 8
The expression that is equivalent to the given algebraic expression is; negative 14 over 18 times t minus 5 over 8
How to solve algebraic expressions?We are given the algebraic expression as;
-(10/9)t + (1/8) - [(-6/18)t + (3/4)]
Factorize out 1/72 to get;
(1/72)(-80t + 9 + 24t - 54)
= (1/72)(-45 - 56t)
= (-14/18)t - 5/8
We have used some basic mathematical operations in the expression, it gives us negative 14 over 18 times t minus 5 over 8
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Which inequality does the graph represent?
y>x-2
y
y > -X-2
y<-x-2
Inequality (A) "y > x-2 represents the given graph when the line passes to 2 and -2 from the x-axis and y;-axis respectively.
What are graphs?In discrete mathematics, more specifically in graph theory, a graph is a structure that resembles a collection of objects where some object pairs are conceptually "connected."
Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
To calculate the slope m and the y-intercept, write the equation y = MX + b.
The slope and y-intercept can then be used to graph the equation (0, b).
So, to find which inequality represents the given graph, simply plot the inequalities on the graph.
After plotting, we can conclude that inequality "y > x-2" represents the graph shown in the question.
(Refer to the image attached below)
Therefore, inequality (A) "y > x-2 represents the given graph when the line passes to 2 and -2 from the x-axis and y'-axis respectively.
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Complete question:
Which inequality does the graph represent?
a. y > x-2
b. y > -X-2
c. y <-x-2
d. y <x-2
kendra rides her bike to school each day. it takes her 10 minutes to ride 30 blocks. what unit rate expresses the speed of kendra's bike ride? 2 block
The unite rate of the kendra's bike ride is found as 3 blocks / min.
Explain the meaning of the term unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with the number one as the denominator. A particular kind of ratio is a unit rate (or called a single-unit rate). One unit of one quantity will be compared to an unique number of units of another quantity.The given question is-
Total blocks covered = 30.Total time taken = 10 minutesUnit rate = number of blocks/ total time
Unit rate = 30 / 10
Unit rate = 3 blocks / min
Thus, the unit rate of the kendra's bike ride is found as 3 blocks / min.
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write y=2/5+1 in standard form
Answer: Because the standard form is y=mx+b, and you are already in that form
Step-by-step explanation: y=mx + b is the standard form!
y=2/5x+1 is already in standard form if you compare 2 equations!
First try was incorrect
What is the value of x? Your answer may be exact or rounded to the
nearest tenth.
(4x-8)"
131*
61"
Answer: 19.5
Step-by-step explanation:
obtuse + acute = 180
131 + t = 180
t = 49 degrees for the top angle
49 + 61 + 4x-8 = 180 degrees in a triangle
110 + 4x - 8 = 180
102 + 4x = 180
4x = 78
x = 19.5
Answer:
x = 19.5
Step-by-step explanation:
The interior angles of a triangle will ALWAYS have a sum of 180°
PLEASE ASAP PLEASE I NEED IT IN A STATEMENTS AND REASONS
In a Kite ABCD the diagonals AC and BD can be proved perpendicular by linear pair perpendicular theorem.
What is linear pair perpendicular theorem?
This theorem states that if two straight lines intersect at a point, and the linear pair of angles they form have an equal measure, then the two lines are perpendicular to each other.
According to the given question:
ABCD is a Kite //Given
AB=BC //Given
BE=BE //Common side, reflexive property of equality
∠ABE ≅ ∠CBE // in a kite the axis of symmetry bisects the angles at
those corners
△ABE≅△CBE //Side-Angle-Side postulate
∠AEB ≅ ∠CEB //Corresponding angles in congruent triangles (CPCTC)
AC⊥BD //Linear Pair Perpendicular Theorem
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laura has saved her babysitting money for the past two weeks. currently has 5 time her weekly pay. this week she spent a less then 2 times her weekly pay and now has 156. how much does laura earn each week
Answer:
To find out how much Laura earns each week, you can set up an equation using the information given. Let's call Laura's weekly pay "W".
You know that Laura has saved 5 times her weekly pay, so you can write this as 5W.
You also know that she spent less than 2 times her weekly pay this week, so you can write this as 2W - X, where X is the amount that she spent less than 2 times her weekly pay.
Finally, you know that she has 156 left after spending some money, so you can write this as 156.
You can now set up the equation:
5W + (2W - X) = 156
Combining like terms, you get:
7W - X = 156
Adding X to both sides, you get:
7W = 156 + X
Dividing both sides by 7, you get:
W = (156 + X) / 7
Thus, Laura's weekly pay is equal to (156 + X) / 7. You know that she spent less than 2 times her weekly pay this week, so X must be less than 2W. However, you don't know the exact value of X, so you can't find the exact value of Laura's weekly pay.
:
If laura has saved her babysitting money for the past two weeks then Laura earns 52 dollars per week.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let Laura earns x dollars per week.
According to the problem, after two weeks of saving, she has 5 times her weekly pay, which means she has saved 5x dollars.
This week, she spent less than 2 times her weekly pay, which means she spent less than 2x dollars.
Now, she has 156 dollars left, so we can set up the equation:
5x - 2x = 156
Simplifying this equation, we get:
3x= 156
Divide both sides by 3
x = 52
Hence, Laura earns 52 dollars per week.
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When Jas is solving the system of equations of {y=3x-3 2x+2y=8,she graphs the system and her result is shown below and identifies the solution to be (2.75,5.25).Did Jas graph and find the solution correctly? If not, what was her mistake?
Jas is incorrect, and that may be because she graphed incorrectly one of the functions.
The correct solution for the system is: (1.75, 2.25)
Did Jas graph and find the solution correctly?To solve a system of equations graphically, we need to graph the two equations on the same coordinate axis and find the points where the two graphs intercept.
Here the system of equations is:
y = 3x -3
2x + 2y = 8
The graph is below. There we can see that the intercept is at (1.75, 2.25)
So Jas got an incorrect answer, and that may be because she graphed incorrectly one or both of the equations.
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help plase guys please
Step-by-step explanation:
52×7 = 50×7 + 2×7
why?
because 52 = 50 + 2
so,
52×7 = (50 + 2)×7 = 50×7 + 2×7
Answer
The third option 52 x 7 = 50 x 7 + 2 x 7
Step-by-step explanation:
First of 52 x 7 = 364, so whichever other equation is equal to 364 is the correct option
50 x 7 + 2 x 7
350 + 2 x 7
350 + 14
= 364
How can you use the point-slope form of a line when only given two points?
Answer:
YEEAH bro its called a graph you should try it
Step-by-step explanation:
There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer:
the answer will be the option b
hope this helps you
If a 2b - 10 and b= 3a -5, then what is a?
Answer:
a=4
Step-by-step explanation:
we fill in b to find a
a=2(3a-5)-10
a=6a-10-10
a=6a-20
+20 +20
a+20=6a
-a. -a
20=5a
/5. /5
4=a
hopes this helps
PLEASE HELPPPPPPPPPPPPPP ME ISTG I AM DYING
The solutions of the equation are given as,
1. 7, 2. 5, 3. 5, 4. 5, 5. 7, 6. -4, 7. 8, 8. 3.
Given that,
A number of equations are given we have to determine the solution of the equaiton,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here
1) 3x + 4 = 25
simplify,
3x + 4 = 25
3x = 25 - 4
x = 21 / 3
x = 7
Similarly, the Solution of the other equation is given as,
2. 5, 3. 5, 4. 5, 5. 7, 6. -4, 7. 8, 8. 3.
Thus, the solutions of the equation are given as,
1. 7, 2. 5, 3. 5, 4. 5, 5. 7, 6. -4, 7. 8, 8. 3.
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please help meeeee!!!!
Answer:
(-8(-4) + 3) - 7 = 32
Step-by-step explanation:
-8 * -4 = 8 * 4 = 36
36 + 3 = 39
39 - 7 = 32
Solve each system by elimination: 8x-3y=-11 2x-5y=27
Answer:
(-4,-7)
Step-by-step explanation:
8x - 3y = -11
2x - 5y = 27
8x - 3y = -11
4(2x - 5y) = 27 (4)
8x - 3y = -11
8x - 20y =108
8x - 8x = 0
-3y - (-20y) = 17y
- 11 - 108 = -119
17y = -119
17/17 y = -119/17
y = - 7
2x - 5(-7) = 27
2x + 35 = 27
2x = 27 - 35
2x = - 8
2/2 x = -8/2
x = -4
Yancy rents a car for $20 per day plus 12 cents per mile. He had the car for one day and was charged $63.68.
Answer:
he drove 30 miles
Step-by-step explanation:
Kyle ran the width of a field, a ditance of 35 meter. Then he ran the length of the field, a ditance of 84 meter. Finally, he ran diagonally acro it to get back to hi tarting point. How far did Kyle run?
By using Pythagoras theorem, Kyle run for the distance of 210 m.
What is the Pythagorean theorem ?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.
Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
The given length of the field is 84 m.
And, the width is 35 m.
Now, the diagonal of the field can be calculated using Pythagoras theorem as below,
Diagonal = √((84)² +(35)²)
= 91
Then, the total length is found by summing the length, width and the diagonal as below,
= 84 + 35 + 91
= 210
Hence, Kyle run for the distance of 210 m.
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1. two-column proof
Given: AB ≅ XY, AC ≅ XZ, BC ≅ YZ
Prove: ∆ABC ≅ ∆XYZ
The other information that must prove by the triangle is that ∠A ≅ ∠X.
How do you understand "ABC" and "DEF"?
The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. applying labels Triangle ABC is congruent to triangle DEF if, in triangles ABC and DEF, angle A = angle D, angle B = angle E, and angle AB = DE.
By SAS or Side-Angle-Side Postulate, the corresponding two sides and it's included angles should be congruent.
Therefore, based on the illustration, the included angle for ∆ABC is ∠A while the included angle for ∆XYZ is ∠X.
Therefore, the other information that must prove by the triangle is that ∠A ≅ ∠X.
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A googol is the number 1 followed by 100 zeros. Earths mass is 5.972 x 10 to the 24 power kilograms. How many earths are needed to have a total mass of 1 googol kilograms?
To have a total mass of 1 googol kilograms, 1.674480911 × 10 ⁷⁵ earths are needed
How to determine how many earths are needed to have a total mass of 1 googol kilograms?
Given that:
1 googol = 10¹⁰⁰
Earth's mass is 5.972×10²⁴ kilograms
In order to find how many earths are needed to have a total mass of 1 googol kilograms, you need to divide 1 googol kilograms by Earth's mass (5.972×10²⁴ kilograms). Thus:
Number of earths needed = 10¹⁰⁰ / 5.972×10²⁴
Number of earths needed = 1.674480911 × 10 ⁷⁵ earths
Therefore, 1.674480911 × 10 ⁷⁵ earths are needed to have a total mass of 1 googol kilograms
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please help me I'm not smart !!
The correct response is option 3 i.e n = 6.
What is a Sequence?
A sequence is a list of items arranged in a stepwise order, with members coming either before or after.
We know that,
aₙ = a₁ + (n-1)×d .............................(Arithmetic sequence formulae)
here,
aₙ = -13
a₁ = 7
d = -4
Substituting the values we get,
-13 = 7 + (n-1)×(-4)
∵ (-4)×(n-1) = -20
=> n-1 = 5
=> n = 6
Thus, the final value of n is 6.
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Need help with this ASAP, this is my last class and I need to finish it by Today
for the 2015 general social survey, a comparison of females and males on the number of hours a day that the subject watched tv gave the following results.
After a comparison of females and males on the number of hours of a day that the subject watched the TV.
The hypotheses of a significance test to analyze whether the population means differ for females and males would be as follows:
(a) H0: μ1 = μ2 (the population means are equal for females and males)
Ha: μ1 ≠ μ2 (the population means are not equal for females and males)
(b) In order to conduct the significance test, we would need to calculate the t-statistic and the P-value. However, the question does not provide the necessary information to do so (e.g. sample means, standard deviations, sample sizes). Without this information, we cannot conduct the significance test and interpret the P-value(c) Without conducting the significance test, we cannot conclude anything about whether there is a gender difference in TV watching.
(d) Similarly, without conducting the significance test and calculating the confidence interval, we cannot determine whether the confidence interval would contain 0 or not.
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Can someone Please help me
Answer:
B. none of other works. Only hue rate of change of Function F is higher than Function G
I need to find out what’s given and what’s the reasoning for this statement
If a figure i dilated by a cale factor of 10, the area of the figure will change by a factor of how much?
If a figure is dilated by a scale factor of 10, the area of the figure will change by a factor of 100.
What is meant by the term area?The size of a two-dimensional form or a region in a plane is described by the mathematical notion of area. Square units like square inches, square feet, or square metres are frequently used figure to measure it. The total space a form takes up in a plane is known as its area. The length and breadth of the shape may be multiplied to compute it, or intricate forms like circles, triangles, formulae can be used. Finding the dimensions of a form, calculating area ofcircle or rectangle, or area of three-dimensional object are just a few of the many issues that may be solved using the geometry concept of area.
How to solve?
If a figure is dilated by a scale factor of 10, its area will change by a factor of 100.
When a figure is dilated, its area changes by the square of the scale factor. In this case, the scale factor is 10, so the area will change by a factor of 10^2 = 100.
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A square table has a perimeter of (16x-40) feet. Write an expression that represents the side length of the table in feet
Answer:
4x -10
Step-by-step explanation:
You want the side length of a square whose perimeter is (16x -40) feet.
PerimeterThe four sides of a square are all the same length. The perimeter is the sum of those lengths, so is 4 times the side length. Conversely, the side length is 1/4 of the perimeter.
s = P/4 = (16x -40)/4
s = 4x -10
The side length of the square table is 4x -10 feet.
best answer gets brainliest! please explain
Answer: t = 11
Step-by-step explanation:
f(11)= 5(11) -7
f(11) = 55 - 7
f(11) = 48
Answer:
f(11) = 48
Step-by-step explanation:
f(t) = 5t-7
we have to find out what t is
5t - 7 =48
+7 +7
5t = 55
/5 /5
t = 11