Think About the Process The length of cell A is 4 x 10^-5 length to cell B's length? Use pencil and paper. Is it easier to find notation or in standard form? Explain your reasoning. m. The length of cell B is 0.000002 the ratio when the numbers m. What is the are expressed ratio of cell A's in scientific
Answers
Ratio of length of cell A to the length of cell B will be 20 : 1.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
Length of cell A = 4 x 10⁻⁵
Length of cell B = 0.000002 = 2 x 10⁻⁶.
Now,
Length of cell B into scientific notation = 2 x 10⁻⁶
Hence, The ratio of the length of cell A to cell B = 4 x 10⁻⁵ / 2 x 10⁻⁶
= 2 x 10⁻⁵⁺⁶
= 2 x 10¹
= 20
Thus, Ratio of length of cell A to the length of cell B is 20 : 1.
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Related Questions
Kanesha is making scented candles to sell at the craft fair. she buys a 5 pound package of candle wax, a package of 12 small candle tins that each have volume of 4 ounces and the package of 12 medium candle tins that each have a volume of 6 oz. Kanesha knows that 1 lbs of candle wax will fill 20 oz in volume.assuming kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...____ small 4 oz candles____ medium 6 oz candleswhat is the maximum amount of money she will earn in the craft fair?
Answers
Kanesha is making scented candles to sell at the craft fair. She buys a 5-pound package of candle wax, a package of 12 small candle tins that each have a volume of 4 ounces and the package of 12 medium candle tins that each have a volume of 6 oz. Kanesha knows that 1 lb of candle wax will fill 20 oz in volume.
Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...
____ small 4 oz candles
____ medium 6 oz candles
what is the maximum amount of money she will earn in the craft fair?
________________________________________
1 lb of candle wax will fill 20 oz
She buys a 5-pound package, therefore, she will fill 20*5= 100 oz
Tin size S small (4 oz ) and M medium (6 oz)
S*4 + M*6 = 100
S*7.5 + M*9 = amount of money
_____________________
S*4 + M*6 = 100
4 S = 100 - 6M
S= 100/4 -6/4M
S= 25 -3/2M
Replacing
(25 -3/2M )*7.5 + M*9 = amount of money
187.5 - 11.25M + 9M = amount of money
187.5 - 2.25M = amount of money
According to the expression, the fewer medians sell, the higher the income will be.
Reviewing the candle values by ounces used.
7.5/ 4 = 1.875 sale price / oz
9.0/6 = 1.5 sale price / oz
_____________________________
Therefore, in order to maximize the profit, it would be necessary to make as many small ones as possible, that is, 12.
12* 4 oz = 48
100- 48 = 52
what is left after using the 4 oz tins can be used in the medium candles
52/ 6 = 8
___________________________________
Answer
Assuming Kanesha sells all of the scented candles she makes how many candle tins of each size should she use in order to maximize the amount of money she will earn at the craft fair...
__12__ small 4 oz candles
___8_ medium 6 oz candles
find an equation of the form f(x)=ax^2+bx+c. must solve algebraically and check using a calculator (state, the steps used to perform the check).
f(1)=4, f(2)=13, f(4)=46
Answers
By using algebra resolution methods for systems of linear equations, we find that the equation of the form f(x) = a · x² + b · x + c that passes through the three points is equal to f(x) = (5 / 2) · x² + (3 / 2) · x.
How to determine the quadratic equation that passes through three points
In this problem we must determine the coefficients of a quadratic equation that passes through the points (x₁, y₁) = (1, 4), (x₂, y₂) = (2, 13) and (x₃, y₃) = (4, 46). First, we need to create a system of linear equations by substituting on y and x thrice:
(x₁, y₁) = (1, 4)
a · 1² + b · 1 + c = 4
a + b + c = 4
(x₂, y₂) = (2, 13)
a · 2² + b · 2 + c = 13
4 · a + 2 · b + c = 13
(x₃, y₃) = (4, 46)
a · 4² + b · 4 + c = 46
16 · a + 4 · b + c = 46
Then, we find a system of three linear equations with three variables that offers an unique solution:
a + b + c = 4 (1)
4 · a + 2 · b + c = 13 (2)
16 · a + 4 · b + c = 46 (3)
There are different methods to find the solution to this system, we proceed to use algebraic substitution:
By (1):
c = 4 - a - b
(1) in (2) and (3):
4 · a + 2 · b + (4 - a - b) = 13
3 · a + b = 9 (2b)
16 · a + 4 · b + (4 - a - b) = 46
15 · a + 3 · b = 42 (3b)
By (2b):
b = 9 - 3 · a
(2b) in (3b):
15 · a + 3 · (9 - 3 · a) = 42
15 · a + 27 - 9 · a = 42
6 · a = 15
a = 15 / 6
a = 5 / 2
By (2b):
b = 9 - 3 · (5 / 2)
b = 9 - 15 / 2
b = 18 / 2 - 15 / 2
b = 3 / 2
By (1):
c = 4 - 5 / 2 - 3 / 2
c = 4 - 8 / 2
c = 4 - 4
c = 0
The coefficients of the quadratic equation are (a, b, c) = (5 / 2, 3 / 2, 0).
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To rent a certain meeting room, a college charges a reservation fee of $13 and an additional fee of $4 per hour. The chemistry club wants to spend at most $33 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answers
13+4(t)=33
Subtract the 13 from both sides leaving
4(t)=20
Then divide by 4 to get your variable by itself leaving
t=5
So the maximum amount the chemistry club can rent the meeting room would be 5 hours
On a horizontal number line, -43 is located to the left of -35.
Answers
Step-by-step explanation:
On a horizontal number line, -43 is located to the left of -35. TRUE because -43 is farther away (to the left) from 0 than -35.
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
Answers
The value of x such that f(x) and g(x) have equal values is 3
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of x?From the question, we have
f(x) = -2x + 4
g(x) = 2x - 8
The question implies that the functions have equal values
This means that
f(x) = g(x)
Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms
2x + 2x = 8 + 4
Evaluate the like terms
4x = 12
Divide both sides of the equation by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsSee attachment for the graph of the functions
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If x² = 16, find x³.
Answers
Answer:
64
Step-by-step explanation:
If x² = 16, x is the square root of 16.
Therefore, x = 4
Now plug x in:
x³ = 4³ = 64
X^2 =16 , X is the square root of 16
X=4
Then you plug it in
X^3=4^3 =64
Please help I’ll mark you as brainliest if correct!!!
Answers
Answer:
[tex]a=22\\b=6\\c=14\\d=8[/tex]
Step-by-step explanation:
So (Didn't even know what it was until now), is a square where all rows, columns, and diagonals sum up to the same number.
So, from the diagonal of 7, 15, and 23, but adding them up, we can tell that each row, column, and diagonal should sum up to 45.
If we know that, you can solve it either arithmetically or algebraically (I'm going to sovle them algebraically)
Here are the equations I used to solve for each:
[tex]7+16+a=45\\23+a=45\\a=22\\\\24+15+b=45\\39+b=45\\b=6\\\\15+16+c=45\\31+c=45\\c=14\\\\14+23+d=45\\37+d=45\\d=8[/tex]
Any further questions? Just leave a comment.
In angle VWX, VX is extended through point X to point Y,
m/VWX = (x + 14)°, m/XVW = (x +9)°, and
m/WXY = (5x - 10)°. What is the value of x?
Answers
Answer:
11
Step-by-step explanation:
This will form triangle VWX. So we have values for ∠VWX and ∠XVW but we don't have value for ∠WXV.
Since ∠WXV and ∠WXY are supplementary angles
=> ∠WXV + ∠WXY = 180
=> ∠WXV = 180 - ∠WXY
So the angles of triangle VXY
∠VWX + ∠XVW + ∠WXV = 180
(x + 14) + (x + 9) + (180 - (5x - 10)) = 180
x + x - 5x + 14 + 9 + 180 + 10 = 180
-3x + 213 = 180
-3x = - 33
x= 11
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To
make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts
that cost $3.00 per pound. He mixes 10 pounds at a time.
How many pounds of Virginia peanuts does Sergio use? How many pounds of Spanish peanuts does Sergio use?
Answers
How many pounds of Virginia peanuts does Sergio use?
Assume he is making 10 lb of the $3.40 mixture
Let x = no. of pounds of the Virginia ($3.50) peanuts
Then (10-x) = no. of pounds of the Spanish ($3) peanuts
The Equation:
3.5x + 3(10-x) = 3.4(10)
3.5x + 30 - 3x = 34
.5x = 34 - 30
x = 4/.5
x = 8 pounds of Virginia peanuts
:
(b)How many pounds Spanish peanuts does Sergio use?
Spanish peanuts must be 2 pounds since the total is 10 pounds
:
Check:
3.5(8) + 3(2) = 3.4(10)
28 + 6 = 34
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.5 MB.
Yesterday, there were 870 downloads of the song, for a total download size of 2946 MB. How many downloads of the high-quality version were there?
Number of high-quality version downloads:
X
Answers
The number of high-quality version downloads is 300.
Given:
Size of the standard version = 2.8 megabytes (MB).
Size of the high-quality version = 4.5 MB.
Total number of downloads = 870
Total download size = 2946 MB
Let the number of high-quality version downloads be x.
Then the number of standard version downloads will be 870 - x.
Now the sum of the number of downloads of each type multiplied by their sizes equals 2946 MB.
So the equation is,
4.5x + 2.8(870 - x) = 2946
4.5x + 2436 - 2.8x = 2946
1.7x = 2946 - 2436
1.7x = 510
x = 510/1.7
x = 300
Therefore, the number of high-quality version downloads is 300.
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Vec a and vec b are two unit vectors. If vec 5a + vec 3b and vec a- vec b are perpendicular to each other, find the angle between a and b.
Answers
[tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] are two unit vectors. If [tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex] are perpendicular to each other, then the angle between a and b is ( 2n + 1)π/2.
As given in the question,
Given two unit vectors are : [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex]
|a| = 1 and |b| = 1
Vectors which are perpendicular to each other are :
[tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex]
( [tex]\vec{5a} + \vec{3b}[/tex] ). ( [tex]\vec {a} - \vec {b}[/tex] ) = 0
⇒ 5|a|² -2a.b - 3|b|² = 0
⇒ 5(1)² - 2a.b - 3(1)² = 0
⇒ 5 - 2a.b - 3 = 0
⇒ 2[tex]\vec{a}[/tex].[tex]\vec{b}[/tex] = 2
⇒ [tex]\vec{a}.\vec{b}[/tex] = 1
Let θ be the angle between two vectors
|a||b|cosθ = 1
⇒ (1)(1)cosθ = 1
⇒cosθ = 1
⇒θ = (2n+1)π/2
Therefore, [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] are two unit vectors. If [tex]\vec{5a} + \vec{3b}[/tex] and [tex]\vec {a} - \vec {b}[/tex] are perpendicular to each other, then the angle between a and b is
( 2n + 1)π/2.
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HelloI’m having trouble on the *calculus* portion on my ACT PREP GUIDEI need help solving this
Answers
First, we find the value of r:
[tex]\begin{gathered} a_n=\frac{2^n}{5^{n+1}\cdot n} \\ a_{n+1}=\frac{2^{n+1}}{5^{n+1+1}\cdot(n+1)} \\ a_{n+1}=\frac{2^{n+1}}{5^{n+2}\cdot(n+1)} \end{gathered}[/tex]Then r is calculated as follows:
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{a_{n+1}}{a_n}| \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{5^{n+2}\cdot(n+1)}\text{ / }\frac{2^n}{5^{n+1}\cdot n} \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{5^{n+2}\cdot(n+1)}\times\frac{5^{n+1}\cdot n}{2^n}| \end{gathered}[/tex]Multiplying
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{2^{n+1}\cdot5^{n+1}\cdot n}{5^{n+2}\cdot(n+1)\cdot2^n} \\ r=\lim _{n\to\infty}|\frac{2^{n+1}}{2^n}\cdot\frac{5^{n+1}}{5^{n+2}}\cdot\frac{n}{n+1}| \\ r=\lim _{n\to\infty}|2^{n+1-n}\cdot5^{n+1-(n+2)}\cdot\frac{n}{n+1}| \end{gathered}[/tex]Simplify
[tex]r=\lim _{n\to\infty}|2^1\cdot5^{-1}\cdot\frac{n}{n+1}|[/tex]Apply exponential properties
[tex]\begin{gathered} r=\lim _{n\to\infty}|\frac{2}{5}\cdot\frac{n}{n+1}| \\ r=\lim _{n\to\infty}|\frac{2n}{5\cdot(n+1)}| \\ r=\lim _{n\to\infty}|\frac{2n}{5n+5}| \end{gathered}[/tex]Applying the limit, the solution is
[tex]r=\frac{2}{5}=0.4[/tex]So, r = 0.4 and since r is less than 1, the series converges.
Answer: From the ratio test, r = 0.4. The series converges.
nees helo on thus pl6
Answers
Assest
Cash = 39000
Owned land = 460000
Savings land = 207000
Jewerly = 3000
Total assests = 39000+460000+207000+3000
Total assests = 709000
Liabilities
Bank loans = 350000
Student loan debt = 25000
Total liabilities = 350000+25000
Total = 375000
Net worth = Total assets - Liabilities
Net worth = 709000 - 375000
Net worth = $334,000
The membership of a gym from 2000 to 2017 is given by the function:
M(x)= 180x + 125
where M is the number of members and x is the number of years after 2000 (when the gym was
founded). Show your work to receive credit. (6)
a)
What was the membership of the gym in 2007?
Answers
The membership of the gym after 7 years is 1385 .
What is a function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable ). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
Given: The function : M(x)= 180x + 125
where x is the number of years so in this case we have to find the value of M when x= 7 years
Thus the given function on substituting the value becomes
M (7)= 180× 7 + 125
= 1385.
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What is the value of 6a + 9b?
Answers
Step-by-step explanation:
Simplifying
6a + -9b = 0
Solving
6a + -9b = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9b' to each side of the equation.
6a + -9b + 9b = 0 + 9b
Combine like terms: -9b + 9b = 0
6a + 0 = 0 + 9b
6a = 0 + 9b
Remove the zero:
6a = 9b
Divide each side by '6'.
a = 1.5b
Simplifying
a = 1.5b
Suppose the monthly charges for cell phone plans are normally distributed with mean and standard deviation $.(a) Draw a normal curve with the parameters labeled.(b) Shade the region that represents the proportion of plans that charge than $.(c) Suppose the area under the normal curve to the of X$ is 0.1587. Provide an interpretation of this result.
Answers
SOLUTION
(a) From the information given in the question,
We will select a curve with 58 at its center which represents the mean and
[tex]\begin{gathered} 58-17=41 \\ 58+17=75 \end{gathered}[/tex]41 and 75 at the left and right sides. That is gotten by subtracting and adding the standard deviation of 17.
Hence the answer is Graph D
(b) The region that represents less than 41 is seen in graph B
Hence graph B is the answer
(c) Option A
The probability is 0.1587 that a randomly selected cell phone plan in this population is less than $41 per month
F(x)=2x-2, find f(-3)
Answers
Answer:
F (-3) = -8
Step-by-step explanation:
We start by substituting x = -3 into F (x) = 2x - 2
That gets us to: F ( -3) = 2 * (-3) - 2
Then we calculate the equation, bringing us to:
F (-3) = -6 - 2
When we add -6 + -2 we get: F (-3) = -8
It is estimated that 29% of the earths surface isn’t covered by water what percentage of the earths surface is water-covered
Answers
Answer: 71%
Explanation:
100% - total earth surface
29% - earth surface uncovered by water
100 - 29 = 71% of surface covered by water
In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43) and matching the number on the gold ball (1 through 31). If one ticket is purchased, what is the probability of winning the jackpot?
Answers
oris is playing a game. She rolls three six-sided number cubes to tell her how many squares to move. If two number cubes show 4 and 3, how many different possible numbers of squares may she move on her turn?
Answers
6 possible values of squares that she can move.
What is possibility or probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.
Hence she has 6 different possible numbers of squares she can move.
The possibilities are:
-8 squares (if she rolls a 1)
-9 squares (if she rolls a 2)
-10 squares (if she rolls a 3)
-11 squares (if she rolls a 4)
-12 squares (if she rolls a 5)
-13 squares (if she rolls a 6)
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I do not understand this can someone please help?
Answers
Answer:
1. x = 18
2. x = 154
Step-by-step explanation:
2 12
------- = -------
3 x
3 × 12 = 36
2 × x = 2x
36 = 2x
÷2 ÷2
---------------
x = 18
----------------------------------------------------------------------------------------------------------
6 84
------- = -------
11 x
6 × x = 6x
84 × 11 = 924
6x = 924
÷6 ÷6
-----------------
x = 154
I hope this helps!
Can someone help me with this please and thank youuu
Answers
The correct answer is:
[A]: " ∡2 is supplementary to ∡3 " .
___________________
The other answer choices given—which are correct statements—only prove that " a || b " {that is: "Line A" is parallel to "Line B".}
___________________
Find the difference.
(-3x²-xy-3y²) - (6x²-4xy+y²)
Enter the correct answer.
Answers
The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is
(-9x²+3xy-4y²).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Numerical ExpressionNumbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
Algebraic ExpressionUnknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
= (-3x²-xy-3y²) - (6x²-4xy+y²)
= -3x²-xy-3y² - 6x²+4xy-y²
= (-9x²+3xy-4y²)
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In a certain instant lottery game, the chances of a win are stated as "4 in 25." Express the indicated degree of likelihood
as a probability value between 0 and 1 inclusive
The probability is
Answers
the probability of winning a lottery game out of all the games played is 0.16.
We are given that:
In a lottery game, the chances of win are = 4 in 25
So, this means that:
if a person plays 25 games of lottery, then he will probably win 4 games out of them.
So, we get that:
Total games = 25
Win games = 4
Probability = win games / total games
Substituting the values, we get that:
Probability = 4 / 25
P = 0.16
Therefore, we get that, the probability of winning a lottery game out of all the games played is 0.16.
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7.5.PS-13 Identify the solid from its net. Choose the correct answer below. o triangular prism o rectangular prism o square pyramid O triangular pyramid Click to select your answer and then click Check Answer.
Answers
The net image of a figure is a visual representation of the original figure.
From the given net image, the solid that has the net image can be said to be a traingular
pls help me with my question
Answers
Given the figure of an object consists of a cylinder and a rectangular prism.
We will find the volume of the cylinder using the following formula:
[tex]V=\pi r^2h[/tex]As shown, the diameter of the base = d = 3 ft
So, the radius = r = d/2 = 3/2 = 1.5 ft
And the height = h = 4 ft
Use π = 3
so, the volume of the cylinder will be as follows:
[tex]V=3*1.5^2*4=27\text{ }ft^3[/tex]Now, we will find the volume of the rectangular prism using the following formula:
[tex]V=l*w*h[/tex]As shown, the length = l = 7 ft
The width = w = 4 ft
The height = h = 4 ft
So, the volume of the rectangular prism will be as follows:
[tex]V=7*4*4=112\text{ }ft^3[/tex]So, the total volume of the object will be =
[tex]27+112=139\text{ }ft^3[/tex]So, the answer will be V = 139 ft³
solve similar triangles (advanced) khan academy. solve for x
Answers
Answer: 10/3
Step-by-step explanation:
[tex]\frac{2}{6}=\frac{x}{10}\\\\x=\frac{10}{3}[/tex]
In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?
a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer: ?
b) Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer: ?
Answers
1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.
2) After 8 years of straight-line depreciation, the car's value will be $19,080.
What is depreciation?Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.
Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.
Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.
Price of an automobile in 2003 = $30,600
Annual depreciation = $1,440
The car's value after t years = $19,080.
Equation Solution:Value after t years = 30,600 - 1,440t
If 19,080 = 30,600 - 1,440t
1,440t = 30,600 - 19,080
1,440t = 11,520
t = 8 (11,520/1,440)
t = 8
= 8 years
Check:
x = 30,600 - 1,440t
x = 30,600 - 1,440(8)
x = 30,600 - 11,520
x = 19,080
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Hello I need help please
Answers
olution
e have the following statement:
If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:
A) supplementary angles
Only #29,33,37,41,49 please show work THANK YOU
Answers
29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i
33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i
37) – 4 i = 4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 4 i = 0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] = 4[tex]e^{\frac{3\pi}{2}i}[/tex]
41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]
49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex] = [tex]\sqrt{26}e^{-0.197i}[/tex]
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