obtain expressions in component form for the position vectors having the following polar coordinates.
Expressions in component form for the position vectors having the polar coordinates are:
a) -12 cos(40)i + 12sin(40) j = -9.19i + 7.71j
b) 3cos(40) i + 3 sin(40) j = 2.29i + 1.92j
c) -24cos(48)i - 24sin(48) j = -16.059i - 17.83j
Polar coordinates can be found in :Use one or more of the following equations: cos=xr, sin=yr, tan=yx, and r=x2+y2 to convert rectangular coordinates to polar coordinates.
What exactly are polar coordinates?The polar coordinate system is indeed a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to determine each point's location on a plane. The polar axis is the ray emanating from the pole inside the reference direction. The pole is the point of reference.
According to the Given information:Let the +x and +y represent, respectively, the unit vectors represented by I and j.
(a) 12.6 m, 130° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= m.
-12 cos(40)i + 12sin(40) j
= -9.19i + 7.71j
(b) 3.60 cm, 70.0° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= cm.
3cos(40) i + 3 sin(40) j
= 2.29i + 1.92j
(c) 24.0 in., 206° counterclockwise from the +x axis [tex]\overrightarrow{\mathrm{R}}[/tex]= in.
-24cos(48)i - 24sin(48) j
= -16.059i - 17.83j
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I understand that the question you are looking for is:
Obtain expressions in component form for the position vectors having the following polar coordinates.
(a) 12.6 m, 130° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= m
(b) 3.60 cm, 70.0° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= cm
(c) 24.0 in., 206° counterclockwise from the +x axis
[tex]\overrightarrow{\mathrm{R}}[/tex]= in.
On the double number line, 3 minutes corresponds to 180 beats.
0 ? 120 180 240 300
Beats:
Minutes:
0 1
2
3
4
5
How many beats are there in 3 minutes? Type your answer as a number.
18 Shifting the origin to another point (h,k) without Changing the directions of the axes. If P(x,y) with reference to original axes changes to P(X,Y) with reference new axes then i) x=X-h, y=Y-k ii) x=X-h,y=Y+k iii) x= x+h, y=Y+k iv)x=x-y=Y-k
If we shift the origin without changing the direction and point P(x, y) is changed to P(X, Y) then the new coordinates will be x = X + h and y = Y + k.
Shifting of origin is the phenomenon of changing the coordinates of the origin which is generally (0, 0) to another point which has coordinated (h, k). This phenomenon is usually carried out graphically. This is done when there is difficulty to solve the problems in coordinate geometry when we take the origin at (0, 0).
If we shift the origin which is at P(x, y) to another point (h, k) then the coordinates of new point P(X, Y) will be
x = X + h and y = Y + k
If h is positive, then coordinates will be x = X + h and if h is negative then coordinates will be x = X - h. If k is positive, then coordinates will be y = Y + k and if k is negative then coordinates will be y = Y - k.
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0.000000006450 in scientific notation
Answer:
[tex]6.45*10^{-9}[/tex]
Step-by-step explanation:
Twice the sum of a number and 4 is equal to three times the difference of the number and 4. Find the number.
Answer:
The number will be x
Step-by-step explanation:
2(x + 4) = 3(x - 2)
2x + 8 = 3x - 6
14 = x
q(x)=-2x-3
r(x)=-x+2
find the value of q(r(5))
Answer: q(r(5))= 3
Step-by-step explanation: sub in 5 for x in r(x). Once you do that, you'll get -3 for r(5). Now sub in the value of r(5), -3, for x in q(x). Then you'll end up with -9 once the equation has been evaluated.
1)
0.6
11
What would it be
Answer:as a fraction it would be 11 3/5
Step-by-step explanation:
Determine the largest positive interger d such that d+10 is a divisor of d^3+2011
The largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.
As given,
Divisor= d +10
Dividend= d³ + 2011
(d³ + 2011 ) ÷ ( d+ 10) = [(d² -10d +100) (d +10) +1011] ÷ ( d+ 10)
=(d² -10d +100) + [ 1011 / (d+10)]
Largest positive integer d for which d +10 is a divisor of d³ + 2011
d + 10 =1011
⇒d=1001
Therefore, the largest positive integer d for which d +10 is a divisor of d³ + 2011 is equal to 1001.
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write an equivalent expression for 2*14 / 2*2
Answer:
Step-by-step explanation:
if * means multiplication
the equivalent expression will be :
[tex]\frac{2.14}{2.2} = \frac{7}{7} = 7[/tex]
If the * means power :
then equivalent expression will be
[tex]\frac{2^{14} }{2^{2} } = 2^{(14-2)} =2^{12}[/tex]
A submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. It starts off at -340 meters.
At what depth is it after:
1 stage meters
2 stages meters
4 stages meters
How many full stages will it take to return to the surface?
Answer:
Can you only pick one answer?
Answers:
depth after 1 stage is -280 meters depth after 2 stages is -220 meters depth after 4 stages is -100 meters how many stages to return to the surface? 6 stages==========================================================
Explanation:
After 1 stage, the depth is -340+60*1 = -280 meters. In other words, it's 280 meters below the surface.
After 2 stages, the depth is now -340+60*2 = -220 meters
After 4 stages, the depth is -340+60*4 = -100 meters
After n stages, the depth is -340+60n. Set this equal to zero and solve for n.
-340+60n = 0
60n = 340
n = 340/60
n = 5.667 approximately
This rounds to n = 6
After n = 5 stages, the depth is -340+60n = -340+60*5 = -40 meters
After n = 6 stages, the depth is -340+60n = -340+60*6 = 20 meters, so the submarine is now at the surface. Of course the sub cannot fly to a height of 20 meters above the ocean's surface, so the highest it can go is 0 meters at the surface itself. This means the 6th stage is a movement of 40 meters (instead of 60 meters).
It might help to draw out a vertical number line to visually keep track of everything.
Please help me with this problem im confused.
Answer: A. D.
Step-by-step explanation:
A.
x-b-3<0
x-b-3+3<0+3
x-b<3 (yes)
B.
0>b-x+3
0+x>b-x+3+x
x>b+3
x-b>b+3-b
x-b>3 (no)
C.
x<3-b
x+b<3-b+b
x+b<3 (no)
D.
-3<b-x
-3+3<b-x+3
0<b-x+3
0+x<b-x+3+x
x<b+3
x-b<b+3-b
x-b<3 (yes)
Answer:
A and D
Step-by-step explanation:
Option A
[tex]\begin{aligned}& \textsf{Given inequality}: & x-b-3 & < 0\\& \textsf{Add 3 to both side}: \quad & x-b-3+3 & < 0+3\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]
Option B
[tex]\begin{aligned}& \textsf{Given inequality}: & 0 & > b-x+3\\& \textsf{Add $x$ to both sides}: & 0+x & > b-x+3+x\\& \textsf{Simplify}: & x & > b+3\\& \textsf{Subtract $b$ from both sides}: \quad& x-b & > b+3-b\\& \textsf{Simplify}: & x-b & > 3\end{aligned}[/tex]
Option C
[tex]\begin{aligned}& \textsf{Given inequality}: & x & < 3-b\\& \textsf{Add b to both sides}: \quad & x+b & < 3-b+b\\& \textsf{Simplify}: & x+b & < 3\end{aligned}[/tex]
Option D
[tex]\begin{aligned}& \textsf{Given inequality}: & -3 & < b - x\\& \textsf{Divide both sides by -1}: \quad & \dfrac{-3}{-1} & > \dfrac{b}{-1}-\dfrac{x}{-1}\\& \textsf{Simplify}: & 3 & > -b+x\\& \textsf{Simplify}: & x-b & < 3\end{aligned}[/tex]
Note: When multiplying or dividing by a negative number in an inequality, remember to flip the inequality sign.
I'm really confused by this; can someone help me?
Write the biconditional statement using the information given in the statement below.
"If a shape is an octagon, then it has 8 sides"
what is 2.56 - 8.9 =
Answer:
-6.34
Step-by-step explanation:
If you used a number line, it'll help! Start at 2.56, and go back (to the left) 8.9, and you will arrive at -6.34
[tex]\sqrt{x} 255\\[/tex]
The square root of 255 is approximately 15.969.
Given,
Root 255, [tex]\sqrt{255}[/tex]
We have to find the square root of the number:
Square root of a number:
A number multiplied by itself is the square root of that number. Or we may say that after adding a number to itself, we must calculate its square root in order to go back to the original number. The square root of p, if it is a positive integer, is represented by p, so that p = q.
Now,
√255 = 15.9687194227
Which is approximately equals to 15.969
That is,
The square root of 255 is approximately 15.969
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a national survey conducted among a simple random sample of 1,507 adults shows that 56% of americans think the civil war is still relevant to american politics and political life.
a)
[tex]z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}[/tex]
b) By assuming a significance level of α = 0.05 and observing that [tex]p_v[/tex] > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.
c) The confidence interval at 90% would be shown (0.527;0.593).
About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.
What is a survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.
a)
1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.
Since the problem specifies that majority α=0.05 represents the significance threshold, [tex]p_0[/tex] is the number that we wish to test (no given, but is assumed)
Z would stand for the statistic (interesting variable), and [tex]p_v[/tex] for the p value (variable of interest)
P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.
2) Useful concepts and formulas
The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :
Alternative Hypothesis: p[tex]\geq[/tex] 0.5
Null Hypothesis: p[tex]\leq[/tex] 0.5
The proportion is thought to have a normal distribution.
This test for the percentage of union membership has one tail higher.
Verify whether the sample conforms to the presumptions required for the test to be applied.
a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.
b) The sample size must be sufficient.
[tex]np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10[/tex]
3. Determine the statistic.
The formula used to calculate the statistic is as follows:
[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658[/tex]
P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]
According to the alternative hypothesis, the following would be the p value:
P value= [tex]p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}[/tex]
Using this formula, the confidence interval would be determined.
p ± [tex]z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }[/tex]
With the value of [tex]\alpha[/tex] and [tex]\alpha _2[/tex], we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.
[tex]z_{\frac{\alpha }{2} }=2.58[/tex]
adding the following to the formula for the confidence interval:
[tex]0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593[/tex]
Also provided would be the 90% confidence interval (0.527;0.593).
About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.
And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.
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a charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. they sold each ticket for $45. let y represent the net profit (in dollars) when they have sold x tickets.
The equation which represents the net profit of the charity organization is y = 45x-810.
profit in math is described as the quantity gained from any commercial activity. due to the fact each ticket costs $45, the range of tickets bought ought to be accelerated by the fee of one ticket. because the question stated that x tickets had been sold, the amount could be $45 accelerated by x, which is $45x. To calculate the income, we ought to first calculate the cost of 18 tickets, which gives us the value charge, after which subtract it from the selling charge ($45x).The cost of 18 tickets is 18 x $45 = $810.profit = $45x-810y = 45x-810To learn more about profit, visit :
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Calculate the volume of this regular solid.
Intro
8 cm
What is the volume of
TL
Round at the end to the nearest tenth.
cm³
Done
The volume of the sphere is 2144.7cm³.
Given that a sphere with radius 8 cm.
As we all know that the volume of sphere is 4/3πr³.
We will find the volume of sphere by substituting the value of radius in the formula, we get
Volume=4/3 πr³
Now, we will substitute r=8 cm in above formula, we get
V=(4/3)π(8 cm)³
V=(4/3)π(512)cm³
Now, we will simplify this by multiply by 4, we get
V=(2048/3)πcm³
Now, we will simplify it by dividing it with 3, we get
V=682.66π cm³.
As we know, the value of π is 3.14.
So, we will substitute this value and simplify it, we get
V=682.66×3.14
V=2144.66 cm³
Hence, the volume of the sphere when the radius is 8cm is 2144.7 cm³.
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jean gray earns a graduated commission of 4 on her first $2000 of sales and 8 on all sales over $2000 jean's sales for the past week totaled $3925
Her commission for the week was $234.
It is given the total earning in past week = $3,925 and jean earns 4% for the first $2000
So, the commission = $2000 x 4/100 = $80
To find additional sales, the formula to refer is
Add –on sales = total sales – base sales
= 3,925 – 2000
= 1,925
For the $1,925 sales, Jeans earns 8% commission, Her commission
= 1,925*0.08 = $154
So, the total commission = $80 + $154 = $234
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find the total profit or loss for each color of T-shirt
answer:
Green t-shirt=profit of $1
White t-shirt=profit of $3
Black t-shirt=profit of $1.
To find the answer, selling price minus total money spent (shirt, printing) If the number is negative, it’s loss, and if it’s positive, it’s profit
Given that f(x)=x²- 7 and g(x)= 3x + 1, find (fg)(-1/3)
if it exists.
Answer: 7
Step-by-step explanation:
(fg)(-1/3)=
f(g(-1/3))=
f(3(-1/3) + 1)=
f(-1 + 1)=
f(0)=
0²- 7=7
a circle has a circumference of 615.44615.44615, point, 44 units. what is the radius of the circle? use 3.14 for \piπpi and enter your answer as a decimal.
A circle with a circumference of 615.44 units has a radius of 98 units.
A circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center.
The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant [tex]\pi[/tex] and the diameter of the circle.
C = [tex]\pi[/tex]D
The diameter (D) is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center. On the other hand, the radius (r) of a circle is the distance from the center of a circle to any point on the circumference of the circle. Radius is half of the diameter.
If r = 1/2 D, then
D = 2r
Evaluating the value of Din the formula of the circumference,
C = [tex]\pi[/tex](2r)
C = 2[tex]\pi[/tex]r
Using the value of [tex]\pi[/tex] as 3.14 and the circumference as 615.44 units,
evaluate the equation.
C = 2[tex]\pi[/tex]r
615.44 = 2(3.14)r
r = 615.44/ (2*3.14)
r = 98 units
Therefore, the radius of the circle is 98 units.
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AB =
Round your answer to the nearest hundredth.
В
40
C
5
А
The length of the hypotenuse AB is approximately 6.53 units.
In a right angled triangle the side opposite the right angle or the largest side is called the hypotenuse of the triangle.
The length of the hypotenuse is calculated using trigonometric ratios. If in a right-angled triangle, the base angle is θ then:
sin θ = perpendicular ÷ hypotenusecos θ = base ÷ hypotenusetan θ = perpendicular ÷ baseIn the given figure we see in ΔABC
AB is the hypotenuse. ∠BAC = 40 ° AC is the base and BC is the perpendicular.
(The side that contains the given angle is the base and the side opposite the given angle is taken as perpendicular)
Now cos ∠BAC = BC ÷ AB
or, cos 40° = 5 ÷ AB
or, AB = 6.527...
or, AB ≈ 6.53
Hence the value of AB is approximately 6.53 units.
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This probability distribution shows the
typical distribution of pitches thrown to a
batter in a given "at-bat" in a baseball game.
Pitches
1
2 3 4 5
Frequency 15 20 40 15 10
Find the probability that the pitcher will
throw 4 or fewer pitches to a batter.
p = [?]
Enter
D
the sum of four numbers is 1,764. oneof the numbers, n, is 40% more than the sum of the other three numbers. what is the value of n?
Four numbers has a sum of 1764 and the value of one of those numbers is 1029.
Use algebraic expressions to solve for the value of n.
Algebraic expression is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc).
One of the four numbers is already denoted as variable n. Let m be the sum of the three other numbers.
If the sum of the four numbers is 1,764, then:
n + m = 1764
If n is 40% more than the sum of the other three numbers, then:
n = 40% m + m
n = 1.4 m
Substitute n from the 2nd equation to the 1st equation.
n + m = 1764
1.4 m + m = 1764
2.4 m = 1764
m = 735
Recall that n = 1.4 m.
n = 1.4 (735)
n = 1029
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Draw this Venn diagram. Classify the following numbers. 45, 24, 52, 30, 66, 15, 85, 90, 72, 60, 20, 38 What can you tell about the numbers in the intersection?
PLEASE HELP I NEED ANSWER PLSS I OFFER 45 POINTS
Answer:
put 244 add 7e8ue
Step-by-step explanation:
i53838 divede 73838
the hawaii visitors bureau collects data on visitors to hawaii. the following questions were among 16 asked in a questionnaire handed out to passengers during incoming airline flights.
Using sampling concepts, the population being studied is all visitors that are flying to the state of Hawaii.
What is the missing information?The problem is incomplete, but researching it on a search engine, it asks for us to identify who is the population of this study.
What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.In this problem, a set of visitors traveling to Hawaii were sampled, hence the population being studied is all visitors that are flying to the state of Hawaii.
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5x+3 is greater than or equal to x-9
The solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3
How to determine the inequality solution?The statement is given as:
5x+3 is greater than or equal to x-9
Express as an inequality
5x + 3 >= x - 9
Collect the like terms
5x - x >= -9 - 3
Evaluate the like terms
4x > = -12
Divide both sides by 4
x >= -3
Hence, the solution to the mathematical statement 5x+3 is greater than or equal to x-9 is x >= -3
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solve (3-4i) (6i+7) - (2-3i)
show solving steps-- picture is provided.
Answer:
-7 i + 43
Step-by-step explanation:
Simplify the following:
(-4 i + 3) (6 i + 7) - (-3 i + 2)
(3 - 4 i) (7 + 6 i) = 3×7 + 3×6 i - 4 i×7 - 4 i×6 i = 21 + 18 i - 28 i + 24 = 45 - 10 i:
(-10 i + 45) - (-3 i + 2)
-(-3 i + 2) = 3 i - 2:
45 - 10 i + (3 i - 2)
45 - 10 i - 2 + 3 i = (45 - 2) + (-10 i + 3 i) = 43 - 7 i:
Answer: -7 i + 43
Help please (work provided )
Answer:
150 degrees
Step-by-step explanation:
Vertical angles
A delivery person is carrying two packages. One package contains a 4-pound textbook and 5 identical workbooks. The other package contains a 6-pound textbook. The two packages weigh the same amount. What is the weight, in ounces, of each workbook? pls answer quick