The rectangular form of the polar expression [tex]12(cos\pi+ isin\pi)[/tex] is -12
The given equation is:
[tex]12(cos\pi+ isin\pi)[/tex]
The above equation is in polar form
Note that:
[tex]cos \pi = -1\\\\sin\pi = 0[/tex]
Substituting [tex]cos \pi = -1[/tex] and [tex]sin \pi = 0[/tex] into the expression [tex]12(cos\pi+ isin\pi)[/tex] in order to get the rectangular form of the expression
[tex]12(cos\pi+ isin\pi)[/tex]
= 12(-1 + 1(0))
= 12 ( -1 + 0)
= 12(-1)
= -12
Therefore, the rectangular form of the polar expression [tex]12(cos\pi+ isin\pi)[/tex] is -12
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Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = yj − zk,
S consists of the paraboloid
y = x2 + z2, 0 ≤ y ≤ 1,
and the disk
x2 + z2 ≤ 1, y = 1.
Since S is closed, you can use the divergence theorem, which says
[tex]\displaystyle\iint_S \vec F(x,y,z) \cdot \mathrm d\vec S=\iiint_R \mathrm{div}\vec F(x,y,z)\,\mathrm dV[/tex]
where R is the interior of the surface S.
We have
div F (x, y, z) = ∂/∂x (0) + ∂/∂y (y) + ∂/∂z (-z) = 1 - 1 = 0
so the flux would be 0.
In this exercise we have to calculate the flux by the divergent theorem:
The flux would be ZERO
Since S is closed, you can use the divergence theorem, which says:
[tex]\int\limits\int\limits_s {F(x,y,z} \, ds= \int\limits \int\limits\int\limits_R {divF(x, y, z)} \, dv[/tex]
where R is the interior of the surface S. We have:
[tex]\nabla F (x, y, z) = 1-1= 0[/tex]
so the flux would be ZERO.
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1+9 help me now plssssss
Answer:
10
Step-by-step explanation:
you do the one plus the nine which gives you 11 then subtract 2 which gets you 9 then add 4 which gets you 13 then minus 3 which gets you 10.
a cyclist travels 14 hours in per hour. what is the cyclists speed in feet/ minute. 1 mile= 5280 feet
Answer:
1,232 ft/min (feet per minute)
Step-by-step explanation:
14 miles = 73,920 feet
1 hour = 60 minutes
73, 920 / 60 = 1,232 feet/minute
7. Find the value of x and y:
x=
y=
(10x - 61)
(18y + 5)º
(x + 10)
Answer:
y = 8º
y = 8º
Step-by-step explanation:
Given:
(10x - 61)º
(18y + 5)º
(x + 10)º
Find:
x and y
Computation:
(10x - 61) + (x + 10) = 180
11x - 51 = 180
11x = 231
x = 21º
(10x - 61)º = (18y + 5)º [Vertical opposite angle]
10x - 61 = 18y + 5
10x - 18y = 66
5(21) - 9y = 33
y = 8º
One number is 4 more than 3 times another. Their sum is 16. Find the two numbers.
1. Given the equation Ax + By = 600 and the x-intercept is (60,0) and the y-intercept is (0,25)
what are the values of A and B?
A =
B=
-25.63+ -30.59 ??? Can someone let me know what this equals?
Answer:
= -56.22
Step-by-step explanation:
have a great day
pls mark as brainliest!
hope this helped!
Answer:
-56.22
just calculated it (:
Five more than a number is equal to seven-halves of the number What is the number?
HELP
Answer:
The number is 2
Step-by-step explanation:
To attempt this question, we need to represent the number with (x).
Let the number be x
Five more than the number is:
5 + x
Seven-halves means 1/2 × 7 = 7/2
Mathematically, the question is saying:
5 + x = 7/2 × x
5 + x = 7x/2
Cross multiply;
2(5 + x) = 7x
10 + 2x = 7x
We collect like terms;
10 = 7x - 2x
10 = 5x
x = 10/5
x = 2
The number represented by x is 2
We want to convert the given sentence into an equation, and then solve it. We will see that the number is 2.
Finding the equation
We start with the sentence:
"Five more than a number is equal to seven-halves of the number"
if we define x as the number, we can write:
5 + x = (7/2)*x
Now we can solve this equation for x, we will get:
5 + x = (7/2)*x
5 = (7/2)*x - x = (7/2 - 1)*x
5 = (7/2 - 2/2)*x = (5/2)*x
(2/5)*5 = x
2 = x
So the number is 2.
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Allison traveled a distance of 130 miles in 2
1
hours. What was Allison's average driving
speed, in miles per hour?
Allison's average driving speed in miles per hour is 65.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
130 miles = 2 hours
Divide 2 on both sides.
130/2 miles = 1 hour
65 miles = 1 hour
Thus,
The average speed is 65 miles per hour.
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Convert 0.49494949 into a fraction. Show all work.
Answer:
0.49 49
=
49 this is a fraction
99
Step-by-step explanation:
Let
XXX
x
=
0.49
¯¯¯¯
49
then
XXX
100
x
=
49.49
¯¯¯¯
49
and
XXX
99
x
=
100
x
−
x
=
49
XXX
x
=
49
99
Where would you locate √6 on the number line?...
Between 2.75 and 3.0
Between 2.5 and 2.75
Between 2.0 and 2.25
Between 2.25 and 2.5
Answer:
Between 2.25 and 2.5
Step-by-step explanation:
The square root of 6 is 2.4494.... which is closer to 2.5
PLEASE ANSWER what are the slopes to these graphs ?
Answer:
13. 1/4x
14. -2/4x or -1/2x
15 1/3x or 2/6x
16. Zero
Step-by-step explanation:
13. goes up once and goes to the side 4 times
14. goes down twice and goes to the side 4 times
15. goes up one time and three to the side
16. zero slope, the line is horizontal
Answer:
13. 1/4
14. -1/2
15 1/3
16. Zero
Step-by-step explanation:
A device runs until either of two comonents fails, at which point the device stops running. The joint density function of the lifetimes of the two components, both measured in hours, is f(x,y) = x + y/8 for 0 < x < 2 and 0 < y < 2Calculate the probability that the device fails during its first hour of operation.
Answer:
The probability that the device fails during its first hour of operation is 0.625.
Step-by-step explanation:
The joint density function of the lifetimes of the two components, both measured in hours, is:
[tex]f(x,y)=\frac{x+y}{8};\ 0<x<2,\ 0<y<2[/tex]
Compute the probability that the device fails during its first hour of operation as follows:
[tex]P[(X<1)\cup (Y<1)]=1-\int\limits^{2}_{1} {\int\limits^{2}_{1} {\frac{x+y}{8}} \, dx } \, dy[/tex]
[tex]=1-\int\limits^{2}_{1} {\frac{x^{2}+2xy}{16}}|^{2}_{1} \, dy\\\\=1- \int\limits^{2}_{1}[{\frac{4+4y}{16}-\frac{1+2y}{16}}] \, dy\\\\=1-\int\limits^{2}_{1}{\frac{3+2y}{16}}\, dy\\\\=1-[\frac{3y+y^{2}}{16}]^{2}_{1}\\\\=1-0.375\\\\=0.625[/tex]
Thus, the probability that the device fails during its first hour of operation is 0.625.
The slipe of the line passing through the points (7, 5) and (21, 15) is
Answer:
5/7
Step-by-step explanation:
You find a slope by using the equation y2-y1/x2-x1.
In this case: 15-5/21-7
10/14
5/7
What is the slope of the line whose equation is y-6=2(x+3)?
Answer:
2
Step-by-step explanation:
y=mx+n m is slope
y-6=2(x+3) so y=2x+12 m=2 is slope.
(7w - 6) +5 (-2.4w + 1)
Answer: The answer would be -5w-1
Step-by-step explanation:
Answer:
xcgvb vgjbnnnnnnnnnn vbjn bvh
Step-by-step explanation:
You have asked to design a rectangle box with a square base and an open top. The volume of the box must be620 cm to the 3rd power. the cost of the material for the base is $0.40 per square cm and the cost of the material for the side is $0.10 per square cm.How to determine the dimension of the box that will minimize the cost of manufacturing. What is the minimum cost? in dollars and rounded to the nearest cent.
Answer:
$69.21
Step-by-step explanation:
Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]
Let h be the height of the box
V = Volume of the box = [tex]620\ \text{cm}^3[/tex]
[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]
Now surface area of the box with an open top is given
[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]
Differentiating with respect to x we get
[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]
Equating with zero
[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]
Double derivative of the function
[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]
So, x at 10.74 is the minimum value of the function.
[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]
So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.
The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]
The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]
Cost of the base is $0.40 per square cm
Cost of the side is $0.10 per square cm
Minimum cost would be
[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]
The minimum cost of the box is 69.21 dollars.
! Find the slope using the formula.
(9,-5) and (-2,9)
Answer:
[tex]m=\frac{-14}{11}[/tex]
General Formula and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (9, -5)
Point (-2, 9)
Step 2: Find slope m
Substitute: [tex]m=\frac{9+5}{-2-9}[/tex]Add/Subtract: [tex]m=\frac{14}{-11}[/tex]Rewrite: [tex]m=\frac{-14}{11}[/tex]Name a street that is perpendicular to Hwy 64/40 . Can you help with all these questions
Answer:
no puedo alludar te perdón
a piece of metal has a mass of 2210g the volume of the metal is 260cm3 what is the density of the piece of metal
Answer:
The density is 8.5 g/cm³
Step-by-step explanation:
The density formula is density = mass/volume
When we plug our numbers into the formula, we get:
Density = 2210 / 260
We can then solve and get our answer 8.5 g/cm³
It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³.
How are density, volume and mass of a substance related?Suppose that a finite amount of substance is there having its properties as:
The mass of substance = m kg
The density of substance = d kg/m³
The volume of that substance = v m³
Then, they are related as:
[tex]d = \dfrac{m}{v}[/tex]
It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 .
density = mass/volume
When we substitute our numbers into the formula, we get:
Density = 2210 / 260
Density = 8.5 g/cm³
It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³
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Find the value of x.
930
45°
X=
help please
Answer:
45 Degrees
Step-by-step explanation:
Compare to its other side
What is the reciprocal of 8 5/6
Answer:
6/53
Step-by-step explanation:
Anna worked worked 37 hours this week at £8.97 hour. she then worked nine hours overtime at time and a half. how much does she get paid in total? round your answer to the nearest pound.
417
Step-by-step explanation:
I hope this helps :)
The graph of a proportional relationship will always be a straight line that passes through the origin. Why?
Answer:
Being proportional between two entities, refers to the 'Constant of Proportionality' that would be fixed between them which establishes a relationship between them when multiplied or divided.
If we considered it on a graph, the 'Constant Of Proportionality' may take any real values between the coordinate pairs x and y [x,y]. As even 0 is a real number, it will surely be a constant of proportionality when multiplied since its product would result in itself (0). Hence, both x and y turns 0.
As the coordinates of the origin are always (0,0), the graph (Or the slope) would surely pass through the origin.
Example :
If we consider a graph such that x=y.
And if we multiply or divide any real number (a) between them.
ax=ay
As a is a variable, and can take the value of 0, the graph can pass through the origin as x and y nullify becoming the coordinates of the origin.
Please help me really need help please please will mark brainiest it’s due today at 3:30pm please help me please
Answer:
8 Hours.
Step-by-step explanation:
Will spent $3.75 for 5 1/2 pounds of granola. What is his unit rate in dollars per pound to the nearest cent?
Answer:
Unitary cost (per pound)= $0.682
Step-by-step explanation:
Giving the following information:
Total cost= $3.75
Total pounds= 5.5 pounds
To calculate the unitary cost of each pound, we need to use the following formula:
Unitary cost= total cost / total pounds
Unitary cost per pound= 3.75 / 5.5
Unitary cost per pound= $0.682
The original price of a bottle
of dish soap is $2. How much
will Sasha PAY if she buys it
during the sale when it is 50%
off?
Answer:
$1
Step-by-step explanation:
i hope i read it right
Answer:
1
Step-by-step explanation:
cuz half of 2 is 1
help me with this question if you don’t mind❗️
Answer:
12m by 3m
Step-by-step explanation:
lol please mark brainliest
please help me solve this
Answer:
A) 7 and 8
Step-by-step explanation:
root of 7 is 2.64575..... then when u multiply by 3
3*2.64575=7.93725
someoneeeeee pleaseeeeee help meeee
Answer: x=60
Step-by-step explanation:
x+22+x+6+x−28=180
Step 1: Simplify both sides of the equation.
x+22+x+6+x−28=180
x+22+x+6+x+−28=180
(x+x+x)+(22+6+−28)=180(Combine Like Terms) 22+6=28 and then 28-28=0
3x=180
3x=180
Step 2: Divide both sides by 3.
3x/3 = 180/3
x=60
hope this was helpful.