[tex]\\ \sf\longmapsto y=2+3x+5+2x[/tex]
[tex]\\ \sf\longmapsto y=3x+2x+2+5[/tex]
[tex]\\ \sf\longmapsto y=5x+7[/tex]
Hence
m=5,b=7Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate the flux of F across S. F(x, y, z) = (x3 + y3)i + (y3 + z3)j + (z3 + x3)k, S is the sphere with center the origin and radius 3.
By the divergence theorem, the flux of [tex]\vec F[/tex] across S is equal to the volume integral of [tex]\mathrm{div}(\vec F)[/tex] over the interior of S.
We have
[tex]\vec F(x,y,z) = (x^3+y^3)\,\vec\imath + (y^3+z^3)\,\vec\jmath + (z^3+x^3)\,\vec k \\\\ \implies \mathrm{div}(\vec F) = \dfrac{\partial(x^3+y^3)}{\partial x} + \dfrac{\partial(y^3+z^3)}{\partial y} + \dfrac{\partial(z^3+x^3)}{\partial z} = 3(x^2+y^2+z^2)[/tex]
so that
[tex]\displaystyle \iint_S \vec F(x,y,z)\cdot\mathrm d\vec s = \iiint_T \mathrm{div}(\vec F)\,\mathrm dV = 3 \iiint\limits_{x^2+y^2+z^2\le3} (x^2+y^2+z^2)\,\mathrm dx\,\mathrm dy\,\mathrm dz[/tex]
To compute the volume integral, convert to spherical coordinates with
x = ρ cos(θ) sin(ϕ)
y = ρ sin(θ) sin(ϕ)
z = ρ cos(ϕ)
so that
ρ ² = x ² + y ² + z ²
dx dy dz = ρ ² sin(ϕ) dρ dϕ dθ
The region T is the interior of the sphere S, given by the set
[tex]T = \left\{(\rho,\theta,\phi) \mid 0\le\rho\le3 \text{ and } 0\le\phi\le\pi \text{ and }0\le \theta\le2\pi\right\}[/tex]
So we have
[tex]\displaystyle 3 \int_0^{2\pi} \int_0^\pi \int_0^3 \rho^4 \sin(\phi) \,\mathrm d\rho \,\mathrm d\phi \,\mathrm d\theta \\\\ = 6\pi \left(\int_0^\pi \sin(\phi)\,\mathrm d\phi\right) \left(\int_0^3 \rho^4 \,\mathrm d\rho\right) = \boxed{\frac{2916\pi}5}[/tex]
The required surface integral S, and flux across F·dS; that is [tex]\dfrac{2916\pi }{5}[/tex]
Given that,
Function;[tex]F(x, y, z) = (x^3 + y^3)\vec{i} + (y^3 + z^3)\vec{j} + (z^3 + x^3)\vec{k},[/tex]
S is the sphere with center the origin and radius 3.
We have to determine,
Use the Divergence Theorem to calculate the surface integral S, F.dS that is, calculate the flux of F across S.
According to the question,
By the divergence theorem, the flux of [tex]\vec{F}[/tex]across S is equal to the volume integral of [tex]div(\vec{f})[/tex] over the interior of S.
S is the sphere with center the origin and radius 3.
Therefore,
[tex]F(x, y, z) = (x^3 + y^3)\vec{i} + (y^3 + z^3)\vec{j} + (z^3 + x^3)\vec{k},\\\\= div\vec({F}) = \dfrac{d(x^3+y^3)}{dx} + \dfrac{d(y^3+z^3)}{dx} + \dfrac{d(z^3+x^3)}{dx} = 3(x^{2} + y^{2} + z^{2} )\\\\Then,\\\\\int \int_S \vec{F}(x, y, z) . \vec{ds} = \int \int \int _T div\vec{F}dV= 3 \int \int\int (x^{2} + y^{2} + z^{2} )dx.dy.dz[/tex]
To compute the volume integral, convert to spherical co-ordinate,
[tex]x = p\ cos\theta\ sin\phi\\\\y = p \ sin\theta \ sin\phi\\\\z = p\ cos\phi\\\\[/tex]
Therefore,
[tex]p^2 = x^{2} + y^{2} +z^{2} \\\\dx.dy.dz = x^{2} \ sin\phi \ dp\ d\phi \ d\theta[/tex]
The region T is the interior of the sphere S is given by the set,
[tex]T = {[ p,\theta,\phi}] | \ (0\leq p\leq 3 \ and \ \ 0\leq \phi \leq \pi \ and \ 0\leq 0\leq 2\pi )[/tex]
Then,
[tex]= 3 \int^2_0 \int^\pi _0 \int^3_0 p^4. sin(\phi). dp.d\phi .d\theta\\\\= 6\pi ( \int^\pi _0 sin(\phi).d\phi) (\int^3_0 p^4dp\\\\= \dfrac{2916\pi }{5}[/tex]
Hence, The required surface integral S, F·dS; that is [tex]\dfrac{2916\pi }{5}[/tex]
To know more about Integration click the link given below.
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HELP ME OUT PLZZZZZZ
Answer:
x=5
JK = 40 units
Step-by-step explanation:
JM=MK since the have the little red line which shows they are equal
7x+5 = 8x
Subtract 7x from each side
7x+5 -7x= 8x-7x
5 = x
JK = 7x+5 = 7(5)+5 = 35+5 = 40
Which of the following sets refer to vertical angles from the diagram?
Lines and Angles
Question 29 options:
∠AOB and ∠BOC
∠BOF and ∠HOD
∠BOD and ∠HOD
∠COD and ∠HOG
Angle ∠COD and angle ∠HOG are vertically opposite angles. Then the correct option is C.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
The diagram is given below.
Angle ∠COD and angle ∠HOG are vertically opposite angles.
Hence, Angle ∠COD and angle ∠HOG are congruent.
Then the correct option is C.
More about the angled link is given below.
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#SPJ1
Synthetic Substitution
(x+y)(x^2-xy+y^2)
Answer:
x^3 - y^3
Step-by-step explanation:
g The weight of golden hamsters follows a normal distribution with a mean weight of 4.3 ounces and a standard deviation of 0.25. What is the probability that a randomly chosen hamster weighs less than 4.4 ounces
Let X be the random variable representing the weight of a hamster. Transform X to Z, which follows the standard normal distribution. We have
P(X < 4.4) = P((X - 4.3)/0.25 < (4.4 - 4.3)/0.25) = P(Z < 0.4) ≈ 0.6554
Asap right now brainliest for the correct one
Answer:
Option BStep-by-step explanation:
The next step is the result of calculating the square roots:
[tex]4^{1/2} = 2[/tex]and
[tex]36^{1/2} = 6[/tex]This will make the step:
2 · [tex]3^{1/2}[/tex] + 6 · [tex]3^{1/2}[/tex] = 8 · [tex]3^{1/2}[/tex]Correct choice is B
eksponent
[tex]\sqrt[n]{x^n} = x[/tex][tex]\sqrt{x} = x^{1/2}[/tex]—
[tex] = 4^{ \frac{1}{2} } .3 ^{ \frac{1}{2} } + \sqrt{36} \times 3^ \frac{1}{2} [/tex]
[tex] = \sqrt{4} \times 3 {}^{ \frac{1}{2} } + 6 \times 3 {}^{ \frac{1}{2} } [/tex]
[tex] = 2 \times 2 + 6 \times 3 {}^{ \frac{1}{2} } [/tex]
[tex] = 4 + 6 \times \sqrt{3} [/tex]
[tex] = 4 + 6 \sqrt{3} [/tex]
Water freezes at 0°C. Give two examples of two temperatures at which ice could exist.
Answer:
Ice can exist at 32°F and at -34°C since they freeze at those temperature points.
Answer:
Step-by-step explanation:
It could exist at -4oC degrees and - 8oC degrees. It could exist anywhere between 0 and - 100 . All numbers are randomly chosen. The point is that they are minus.
help is really needed...
Find the volume.
A. 240 m³
B. 351 m³
C. 214 m³
D. 356 m³
Answer:
240m^3
Step-by-step explanation:
Volume = length x width x height.
5x12x4= 240
Could 3, 6 and 8 represent the lengths of the sides of a right triangle?
A. Yes, because the sum of the squares of the legs does equal the sum of the square of the hypotenuse.
B. No, because the sum of the square of the legs does not equal the square of the hypotenuse.
C. No, because the sum of the sides does not equal the hypotenuse.
D. Yes, because the sum of the legs does equal the hypotenuse.
Answer:
Step-by-step explanation:
No because the sum of the two shorter legs does not equal the square of the hypotenuse.
3^2 = 9
6^2 =36
8^2 =64
9 and 36 do not equal 64
4,582 x 10
Written in place value form
Answer:
45820
Step-by-step explanation:
the "10" means adding 1 zero to "4582" in place value
Hundred Thousand= 4
Thousand= 5
Hundred= 8
Tens= 2
Units= 0
what is the others name for false solution
Answer:
mistaken,
incorrect,
wrong,
bad,
untruthful
Answer:
Extraneous solution
Step-by-step explanation:
Extraneous solutions are solutions that come from solving a problem but are ultimately not a valid solution.
Which decimals are equivalent to(5 x 10)+( 2 x 1/100)select all that apply.
Anyone who knows this mathematic question will get the brainliest
Anyone know the answer with explanation please I would appreciate it!
Answer:
[tex]\displaystyle QR = 12[/tex]
Step-by-step explanation:
First, it's never a bad idea to draw the line and see what it looks like! This is shown below (not to scale).
We are given that PS = 18 and PR = 15, and we want to determine QR.
PS is the sum of PR and RS:
[tex]\displaystyle PS = PR + RS[/tex]
Substitute:
[tex]\displaystyle (18) = (15) + RS[/tex]
Solve for RS
[tex]\displaystyle RS = 3[/tex]
Since RS ≅ PQ:
[tex]\displaystyle RS = PQ = 3[/tex]
PS is also the sum of PQ, QR, and RS. Hence:
[tex]PS = PQ + QR + RS[/tex]
Since PS = 18 and RS = PQ = 3:
[tex](18) = (3) + QR + (3)[/tex]
Solve for QR:
[tex]QR = 12[/tex]
In conclusion, QR measures 12 units.
Solve quadratic equation by factoring.
Answer:
x = -5 and x = -9.
Step-by-step explanation:
To factor this, we need to find two numbers that add to 14 and multiply to 45. These are 5 and 9. Therefore, this equation factors to (x + 5)(x + 9) = 0. The two x values that would make this true are -5 and -9 because they would make (x + 5) and (x + 9) equal to 0 respectively.
While on a walk in the country, you pass a field full of horses and chickens. After a quick count, you determine there are 43 heads and 122 feet in the field. How many of each animal are there?
Horse = x = 1 head and 4 feet
Chicken =y = 1 head and 2 feet
Horse + chicken = x + y = 43 ( total heads)
Horse = 43 - y
4x + 2y = 122
4(43-y) + 2y = 122
Simplify:
172-4y + 2y = 122
Combine like terms
172-2y = 122
Subtract 172 from both sides
-2y = -50
Divide both sides by-2
Y = 25
X + y = 43
X + 25 = 43
X = 18
There are 18 horses and 25 chickens.
please help me
integrate In x
[tex] \frac{ lnx ^{2} }{x}[/tex]
Answer:
On the pic
Step-by-step explanation:
Sorry if my handwriting is bad
The sun is about 93 x 10 6 miles from earth. What’s is this distance written as a whole number
This distance would be written as a whole number as 93,000,000.
Three times the sum of a number and 18 is at least-30
Answer:
the sum of the number is 16 and it is al least 20 points
ME has the endpoints of M(-6,4) and E (5,-2) find the midpoint and distance of ME
Answer:
(-0.5, 1)- the midpoint, the distance is sqrt157
Step-by-step explanation:
The midpont is O
x0= (-6+5)/2= -0.5
yo= (4-2)/2=1
(-0.5, 1)
The distance is sqrt ((5-(-6))^2+(-2-4)^2)=sqrt 157
Find the total surface area of the pyramid with base length and height be 10 cm and 12 cm respectively.
Answer:
Hence, total surface area of the pyramid is 360 cm².
Step-by-step explanation:
We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:
L²=H²+(s/2)²=122+(10/2)²=122+5²
=144+25=169⇒
L=(169)^1/2=13
The perimeter of the base is P=4s, since it is a square, therefore,
P=4×10=40 cm
The general formula for the lateral surface area of a regular pyramid is LSA=1/2Pl where P represents the perimeter of the base and l is the slant height.
Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:
LSA=1/2Pl=1/2×40×13=260 cm²
Now, the area of the base B=s² with s=10 cm is:
B=s²=10²=100 cm²
The general formula for the total surface area of a regular pyramid is TSA=1/2Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.
Since LSA=1/2Pl=260 cm² and area of the base is B=100 cm², therefore, the total surface area is:
TSA=1/2Pl+B=260+100=360 cm²
Hence, total surface area of the pyramid is 360 cm².
Ive been having this question for a while "what do you use first PEMDAS or Order of Operations". Well you might say it doesn't matter because a problem like this 5(3+8)=x if you use PEMDAS u first add the eight and the three and you would get eleven then you times the eleven with the five to get fifty five. So x=55. If you use Order of Operations you would multiply the three and eight by five to get 15+40=x you would add the fifteen and the forty to get fifty five making x=55. But if you took the problem {3(525/4π)}^1/3=R
then its a different situation heres the problem solved with PEMDAS.
{3(525/4π)}^1/3
{3(525/12.57)}^1/3
{3•41.77}^1/3
125.30^1/3=4.90
R=4.90
Now this is a step by step explanation on how to do order of operations.
{3(525/4π)}^1/3
(1575/12•9.40)^1/3
(1575/112.80)^1/3
13.90^1/3=2.30
R=2.30
So as you see these two equations have different answers. Now agin which of the two of them do i use Order of Operations or PEMDAS.
Please give a step by step explanation why i should use either or. All these problems were rounded to the nearest hundredth.
Answer:
Order of Operations was aught at a younger age for those just grasping the idea of multiplication and division. Exposing PEMDAS at a young age would confuse them too much, hence the order of operation groups, addition/subtraction and multiplication/division. So for the second example problem, PEMDAS would be correct because it does involve you to use parentheses as well as exponents to solve for. Very easy to mix up between order of operations and PEMDAS, but just look at it as if Order of operations is a beginner level of PEMDAS.
Step-by-step explanation:
The students at a school assembly
were divided into 4 equal groups.
There were 73 students in each
group. Write and solve an equation
to determine the number of students
that were at the assembly.
Answer:
292
Step-by-step explanation:
73 students in 1 group
4 groups all together
73 Students times 4 groups = amount of students all together
so 73x4=292
A recipe calls for 4 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
Answer:
5 walnuts = 4 cups of pecans
8 walnuts = 9 cups of pecans
Answer:
10 cups of pecans.
Step-by-step explanation:
The ratio between pecans and walnuts are: [tex]\frac{4}{5}[/tex]×8
So if we make a smaller batch with 1 cup of walnuts, we will need [tex]\frac{4}{5}[/tex] cup of pecans.
So for 8 cups of walnuts, we will need [tex]\frac{4}{5}[/tex] x 8 = 6,4 cups or [tex]6 \frac{2}{5}[/tex] cups of pecans.
I'm vietanh and good luck studying!
sketch the curve of y=x² with conclusion.
Step-by-step explanation:
I have attached pictures. Hopefully they are visible.
:)
Answer equation in photo, show work please and thanks
Answer:
19
Step-by-step explanation:
There are 38 points total, each field goal is 2 points.
If we do 38/2 we get 19.
Image has work...
[tex]\frac{38}{2}[/tex]
A light aircraft travels 6 miles per hour less than three times the speed of a van. If the van can travel 72 miles in the same time it takes the aircraft to travel 204 miles, then what is the average speed of each?
Answer:
Van: 36 mph.
Plane: 102 mph.
Step-by-step explanation:
x = speed of van
y = common time value
(3x - 6) * y = 204 // plane
x * y = 72 // van
3xy - 6y = 204 // plane simplified
We can now substitute 72 for xy in the equation above.
3*72 - 6y = 204 --> 216 - 6y = 204
We now subtract 216 from both sides.
-6y = -12
We now divide both sides by -1 to get rid of the negative sign & then divide both sides by 6 to simplify.
y = 2
If x*y = 72, then x = 72/y = 72/2 = 36.
Thus, the speed of the van is 36 mph.
We can find the speed of the plane by using the equation from earlier, 3x - 6.
3x - 6 = 3*36 - 6 = 108 - 6 = 102.
Define diameter and radius of a circle with a diagram
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer....
Radius : a straight line from the centre to the circumference of a circle or sphere.Diameter : a straight line passing from side to side through the centre of a body or figure, especially a circle or sphere.(Diagram attached)
Hope it helps!
Brainliest pls!
Follow me! :)
the full segment of half of the circle is diameter and half segment us called radius
m-2=1.97 and explain how to do it im lowkey kind of confused on how to do this.
9514 1404 393
Answer:
m = 3.97
Step-by-step explanation:
Your equation is written as a "one-step" linear equation.
m -2 = 1.97
It is solved by adding 2 to both sides of the equation. (This is the "one step.")
m -2 +2 = 1.97 +2
Simplifying gives ...
m = 3.97
_____
If this is supposed to be an equation where -2 is a exponent, then the rules related to exponents apply. In plain text, this would be written m^-2 = 1.97.
[tex]m^{-2}=1.97\\\\\dfrac{1}{m^2}=1.97\qquad\text{write using a positive exponent}\\\\\dfrac{1}{1.97}=m^2\qquad\text{multiply by $m^2/1.97$}\\\\\sqrt{\dfrac{1}{1.97}}=m\approx0.71247050\qquad\text{take the square root}[/tex]
Which expression does this power represent?
109
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9
10 × 9 × 10 × 9 × 10 × 9 × 10 × 9 × 10 × 9 × 10 × 9 × 10 × 9 × 10 × 9 × 10 × 9
10 × 9
9514 1404 393
Answer:
(a) 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Step-by-step explanation:
You may recall that we use a multiplier to signify repeated addition:
x + x + x = 3x
In a similar way, we use an exponent to signify repeated multiplication:
10 × 10 × 10 = 10³
__
The exponent 9 in 10⁹ means the factor 10 appears 9 times in the product:
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10⁹
Answer:
a 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
Step-by-step explanation: