Express the complex number in trigonometric form.
-5i
A) 5(cos 270° + i sin 270°)
B) 5(cos 180° + i sin 180°)
C) 5(cos 90° + i sin 90°)
D) 5(cos 0° + i sin 0°)
Answers
It is in the form a+bi where a = 0 and b =-5
So the point (a,b) is (0,-5)
The distance from the origin to this point is 5 units, therefore r = 5. This is the magnitude.
The angle is 270 degrees as shown in the attached image. You start on the positive x axis and rotate until you reach the point (0,-5)
This is why the answer is choice A) 5(cos(270) + i*sin(270))
Related Questions
Tara is taller than Jeff. Jeff is 47 inches tall. Write an inequality that compares Tara's height in inches, t, to Jeff's height
Answers
Answer:
t > 47
Step-by-step explanation:
Tara is taller than Jeff. Jeff is 47 inches tall.
We need to write an inequality that compares Tara's height to Jeff's height
Let t be the height of Tara
and j be the height of Jeff
Tara is taller than Jeff, we use greater than symbol for taller
So inequality becomes t > j
Given Jeff is 47 inches tall, so replace 'j' with 47
Answer is t > 47
Final answer:
To compare Tara's height to Jeff's, the inequality used is t > 47, indicating Tara is taller than Jeff.
Explanation:
The question asks you to write an inequality that compares Tara's height, represented by t, to Jeff's height, which is 47 inches. To represent that Tara is taller than Jeff using an inequality, you use the 'greater than' symbol (>). Therefore, the correct inequality to show that Tara is taller than Jeff is t > 47. This inequality means that Tara's height in inches is greater than 47 inches.
The perimeter of a is 35.54 inches longer than the perimeter of a square of side 6.75 Find the perimeter of the rectangle to the nearest inches. tenth of an inch
Answers
Perimeter of rectangle: 27 + 35.54 = 62.54 inches
A pharmacist has an 18% alcohol solution. How much of this solution and how much water must be mixed together to make 10 liters of a 12% alcohol solution? Answer:
Answers
We need a table to do this. 3 rows and 3 columns. Across the top the columns are number of liters, % alcohol, and total. We will label the first row stuff with alcohol, the second row stuff with water, and the third row will be the mix of alcohol and water. In the first column we will put an x for alcohol since we don't know how much alcohol we have in the mix. In the second column we will put the decimal equivalent of the percent alcohol, which is .18. In the total column we will put the product of those 2, which is .18x. Now for the second row, water. We will put a y in the first column since we don't know how much water we have in the mix. In the second column we will put a 0, since water doesn't have any alcohol in it. In the third column we will put the product of the 2 which will be 0. In the third row, the mix row, we put a 10 since we want 10 L of this mix. We will put the decimal equivalent of how much alcohol we want in this mix which is .12. In the total column we put the product of those 2 which is 1.2. Since we are adding the alcohol and the water, x and y, to get a total of 10, this is our first equation. x+y=10. In the total column we will add the percent alcohol in the alcohol and the water to get 1.2. .18x + 0 = 1.2, or just .18x = 1.2. Let's divide both sides by .18 to find the amount of alcohol is in this mix. We get 6 2/3 liters of alcohol. If there is a total of 10 L of this mix, 10 - 6 2/3 = water, and the amount of water then is 3 1/3 L.
if the parent function is square root x. describe the translation of of the fuction square root x-1
Answers
f(x)->f(x-h)+k
when the functions has been translated h units to the right, and k units up.
Compare with
sqrt(x)->sqrt(x-1)+0
we see that h=1, k=0.
Thus it is a horizontal translation of 1 unit to the right. (zero unit up).
Final answer:
The function √(x-1) is a horizontal translation of the function √x by 1 unit to the right along the x-axis.
Explanation:
The function √(x-1) represents a horizontal translation of the parent function √x. The translation is 1 unit to the right along the x-axis.
In function transformation terms, when a function f(x) is altered to become f(x - a), this translates the graph of the function to the right by 'a' units if 'a' is positive and to the left by 'a' units if 'a' is negative.
To illustrate, the graph of f(x) = √x is translated to become g(x) = √(x-1). Compared with the graph of f(x), every point on the graph of g(x) will be 1 unit to the right.
There are no changes vertically, so there is no translation up or down.
which is equivalent to (9y2 – 4x)(9y2 + 4x), and what type of special product is it?
81y4 – 16x2, a perfect square trinomial
81y4 – 16x2, the difference of squares
81y4 – 72xy2 – 16x2, a perfect square trinomial
81y4 – 72xy2 – 16x2, the difference of squares
Answers
81y4 -16x, the difference of squares.
The expression (9y2 – 4x)(9y2 + 4x) is equivalent to 81y4 – 16x2, a difference of squares in mathematical terms.
Explanation:The expression you are asking about is equivalent to
81y4 – 16x2
, which is a special product known as
the difference of squares
. In mathematics, a difference of squares is a term that describes an expression of the form a^2 - b^2. It can be factored into the multiplication of two binomials: (a+b)(a-b). In your example, (9y2)^2 is 81y4 and (-2x)^2 is 16x2, so the final expression is 81y4 – 16x2.
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Identify the type of correlation shown in the scatter plot
A. Positive Correlation
B. Negative Correlation
C. No correlation.
Answers
A triangle has side lengths of 8 inches, 12 inches, and 16 inches Determine whether this is a right triangle
Answers
Answer:
No, because 8^2+12^2 doesn't equal 16^2
Step-by-step explanation:
The triangle ABC is not a right angle triangle
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of sides of the triangle are
The measure of side AB = 8 inches
The measure of side BC = 12 inches
The measure of side AC = 16 inches
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
16² = 8² + 12²
256 ≠ 64 + 144
256 ≠ 208
Therefore , it does not satisfy Pythagoras relation
Hence , the triangle is not a right angle triangle
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Solve 2x2 + x − 4 = 0. x2 + x + = 0
Answers
Answer:
1/2 and -2 are the first answers to the question
1/16 and 1/16 are the next answers
1/4 and 33/16 are the last ones
and for the multiple choice answer which is last is A
Step-by-step explanation:
To solve the quadratic equation 2x^2 + x - 4 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the given values into the formula, we find two solutions: x = (-1 ± √33) / 4.
Explanation:To solve the equation 2x2 + x - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b2 - 4ac)) / (2a)
For our equation, a = 2, b = 1, and c = -4. Substituting these values into the formula, we have:
x = (-1 ± √(1 - 4(2)(-4))) / (2(2))
Simplifying further, we get two solutions: x = (-1 ± √33) / 4.
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You are paid $13.70/hr. You work 40 hr/wk and your deductions are FICA (7.65%), federal tax withholding (11.55%), and state tax withholding (8.35%). Your housing and fixed expenses are 30% of your realized income per month and you want to save 6 months’ worth in an emergency fund. How much do you need to save?
Answers
To calculate the six-month emergency fund, we first determined the monthly net income after deductions from the gross monthly pay. Then, we found that 30% of the net income goes towards housing and fixed expenses. Multiplying this expense by six gives the total emergency fund needed, which is $2,848.20.
To calculate the amount needed for a six-month emergency fund, we first need to determine the monthly take-home pay after all deductions. The student earns $13.70 per hour and works 40 hours a week. Deductions include FICA (7.65%), federal tax withholding (11.55%), and state tax withholding (8.35%).
First, calculate the gross monthly income: $13.70/hr * 40 hrs/wk * 4 weeks/mo = $2,184/month.
Next, calculate total deductions: FICA (7.65% of $2,184) + Federal Tax (11.55% of $2,184) + State Tax (8.35% of $2,184) = $166.97 + $252.34 + $182.36 = $601.67.
Now calculate the net monthly income: $2,184 - $601.67 = $1,582.33.
The student's housing and fixed expenses are 30% of the net income, which amounts to $474.70/month. Therefore, for a six-month emergency fund, the student would need:
$474.70 * 6 months = $2,848.20 saved.
To save for a six-month emergency fund, you must first calculate your net monthly pay after deductions from your salary, which is determined to be $1,588.12. Then calculate 30% of this for your monthly fixed expenses, and finally, multiply that amount by six to determine the total savings required for the emergency fund, which amounts to $2,858.64.
To calculate how much you need to save for an emergency fund, we first need to determine your monthly take-home pay after deductions. Your gross pay per week is $13.70 per hour multiplied by 40 hours, which equals $548. Your gross pay per month is then $548 times 4 weeks, totaling $2,192. We will then subtract the deductions: FICA (7.65%), federal tax (11.55%), and state tax (8.35%). Let's calculate each:
FICA: $2,192 x 7.65% = $167.68
Federal Tax: $2,192 x 11.55% = $253.17
State Tax: $2,192 x 8.35% = $183.03
Your total deductions are $167.68 + $253.17 + $183.03 = $603.88.
So, your net monthly pay is $2,192 - $603.88 = $1,588.12.
Next, we calculate your fixed expenses which are 30% of your net income: $1,588.12 x 30% = $476.44.
To determine the amount needed for a six-month emergency fund, you multiply your monthly fixed expenses by six:
$476.44 x 6 = $2,858.64.
Therefore, you need to save $2,858.64 for your emergency fund.
1.64*10^0/2.0*10^2 in scientific notation
Answers
[tex]1.64 * 10^0 : 2.0 * 10^2= (1.64:2.0) * 10^0:10^2= 0.82 * 10 ^{0-2} = \\ \\ 0.82 * 10 ^{-2} =0.82 * \frac{1}{10^2} =0.82 * \frac{1}{100} =0.0082= \boxed{ 8.2 * 10^{-3} } [/tex]
The student's expression is simplified by dividing 1.64 by 100 then expressing the result in scientific notation as 1.64 imes 10⁻².
The student's question involves simplifying a mathematical expression that uses scientific notation. The expression is 1.64 times 10⁰ divided by 2.0 times 10². Here's a step-by-step breakdown:
Identify the powers of ten: The denominator has 10 to the power of 2, which is 10 squared or simply 100. The numerator has 10 to the power of 0, which equals 1.
Simplify the expression: Divide 1.64 by 100 (2.0 times 10²), which gives a result of 0.0164.
Express in scientific notation: 0.0164 can be written as 1.64 times 10⁻².
If you had an hour a week to spend with a low-achieving 3rd grader, over say, six weeks, what would you focus on with them?
Answers
You can't do much with an hour in a week for six weeks, even with a 3rd grader. That's the bad news. The good news is that if you get him or her to work with you, and give them a second hour, you might be able to do something. What I would focus on depends on what I find out about what they can do. It also depends on how they take in information. Most people (almost all) learn either by hearing or seeing. Most younger children learn better by doing than by being told.
Always try and make some of what you do physical. You didn't mention the subject area, but I'm assuming mathematics because that's where you listed it.
Find out what your jurisdiction expects a third grader to do. Talk to the teacher if you are the parent of such a child. The process of learning is an extremely complex task. Don't take it on if you are flying blind and are unable to talk to the teacher. You need to be the parent or you need to take the parent along. In almost every place, no teacher will talk to someone who is unrelated to the child.
When you know more about the child, post again. I don't know exactly how you can contact me again (perhaps making me a friend), but when you know more, you are perfectly welcome to contact me again.
How to simplify this expression
Answers
Answer:
[tex]\dfrac{x+2}{x+1}[/tex]
Step-by-step explanation:
Factor the numerator and cancel common factors from numerator and denominator.
[tex]\dfrac{x^2-4}{(x-2)(x+1)}=\dfrac{(x-2)(x+2)}{(x-2)(x+1)}=\dfrac{x+2}{x+1}[/tex]
Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.
Answers
40 divided by 2 =20
and thats all i got xD
40/2=20
with a new price of that bagel drop is 50%
(40/40+60=80
and 20$ is the money that Deborah income reducing
Find the sum of the geometric series with a1 = -1, r = -2 And a10 = 512
Answers
[tex]S_n=a_1+a_2+\cdots+a_{n-1}+a_n[/tex]
[tex]S_n=a_1+ra_1+\cdots+r^{n-2}a_1+r^{n-1}a_1[/tex]
[tex]rS_n=ra_1+r^2a_1+\cdots+r^{n-1}a_1+r^na_1[/tex]
[tex]\implies S_n-rS_n=a_1-r^na_1\iff(1-r)S_n=(1-r^n)a_1\implies S_n=\dfrac{1-r^n}{1-r}a_1[/tex]
You're given that [tex]a_1=-1[/tex] and [tex]r=-2[/tex], so
[tex]S_n=\dfrac{1-(-2)^n}{1-(-2)}(-1)=-\dfrac{1-(-2)^n}3[/tex]
The fact that you're given [tex]a_{10}[/tex] makes me think you're supposed to find [tex]S_{10}[/tex], which is just a matter of setting [tex]n=10[/tex] in the formula above.
[tex]S_{10}=-\dfrac{1-(-2)^{10}}3=-\dfrac{1-1024}3=341[/tex]
What is 1/4 as a whole number?
Answers
Janice earns $3,750 per month. If she works all 12 months of the year, what’s her yearly salary?
Answers
Answer: $45000
Answer:
The answer is 45, 000. if you multiply 3,750 times 12 thats what her yearly salary.
The data set represents a progression of hourly temperature measurements.Use the regression equation to predict the temperature during the sixth hour. x 0 1 2 3 4 5 y 20 16 10 0 -7 -20
Answers
Answer:
the answer is C: y = -0.875x^2 - 3.956x + 20.179
Step-by-step explanation:
To predict the temperature during the sixth hour, we need to find the regression equation of the line that best fits the given data. Using the slope and y-intercept, we can substitute x = 6 into the equation to find the predicted temperature, which is -3.42.
Explanation:To predict the temperature during the sixth hour using the regression equation, we need to find the equation of the line that best fits the given data. The regression equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to calculate the slope (m) and the y-intercept (b) using the given data points. Then, we can substitute x = 6 into the equation to find the predicted temperature.
Using the formula for the slope (m) and the y-intercept (b), we find that m = -5.07 and b = 22.2. Substituting x = 6 into the regression equation, we get y = -5.07(6) + 22.2 = -3.42. Therefore, the predicted temperature during the sixth hour is -3.42.
What is the difference of 54.59 and 26.61?
Answers
what is the square root of 4 multiplied by 16
Answers
the answer is 32.
how many runners ran times of six to seven minutes?
Answers
Give the equivalent numerator if the denominator is x³y².
Answers
Final answer:
To find the equivalent numerator, we can multiply both sides of the equation by the denominator.
Explanation:
The equivalent numerator can be found by multiplying both sides of the equation by the denominator, which is x³y². This will cancel out the denominator on the right side. The result will be the equivalent numerator.
For example, if we have the equation 2x³y² = 6, we can multiply both sides by x³y² to get rid of the denominator:
equation * (x³y²) = 6 * (x³y²)
The x³y² on the left side will cancel out, leaving us with the equivalent numerator:
equivalent numerator = 6 * (x³y²)
So, the equivalent numerator is 6x³y².
The diameter of the base of a cylinder cookies is 8 inches. The volume of the cookie jar is 160 cubic inches. What is the height of the cookie jar?
Answers
To calculate the height of the cookie jar, we must use this formula.
FORMULA FOR HEIGHT:
H = V ÷ 3.14 × r × r
First, let's fine the radius. The radius of a circle is always half of the diameter. This means we must divide the diameter by 2.
r = d ÷ 2
r = 8 ÷ 2
r = 4 inches
The radius is 4 inches. Now, let's use the formula and find that height!
FORMULA:
H = V ÷ 3.14 × r × r
V = 160 cubic inches
Pi = 3.14
r = 4 inches
h = ?
First, square the radius.
160 = (3.14(4 × 4))h
160 = (3.14 (16))h
Now multiply that by pi.
160 = 50.24h
Finally, divide this by the volume:
160 ÷ 50.24 = 3.18 (Repeating Decimal)
Just round the repeating decimal to 3.2
A N S W E R:
The height of the cookie jar is about 3.2 inches.
what is the solution to -9×<63
Answers
I'm assuming that the multiplication sign is x.
When you are multiply something by x, you divide -9 on both sides. When you divide a negative number in an equality, you switch the signs.
x>-7 <== solution
I hope this helps!
~kaikers
In matrix T, what is the value of element t13?
Answers
in the matrix T the element t(13) refers to the element in row 1 and column 3
therefore
the answer is 7
Answer:
[tex]t_{13} =7[/tex]
Step-by-step explanation:
[tex]t_{13}[/tex] here 1 represents that it is in 1st row whereas 3 represents that it is in 3rd column so the element placed in 1st row and 3rd column is 7
therefore answer is
[tex]t_{13} =7[/tex]
Do you know the answer???????? Help!!!!!
Answers
The area of a triangle is [tex]A _{t} = \frac{1}{2} (base)(height)[/tex], and we know from our figure that our triangle has base=10 feet and height=5 feet, so:
[tex]A_{t} = \frac{1}{2} (10feet)(5feet)[/tex]
[tex]A_{t} = 25feet^{2} [/tex]
The area of a rectangle is [tex]A_{r} =(length)(width)[/tex]. We have tow rectangles in our figure, so for our first one:
[tex]A _{r1} =(10feet)(1feet)[/tex]
[tex]A_{r1}=10feet^{2} [/tex]
for our second one:
[tex]A_{r2} =(8feet)(2feet)[/tex]
[tex]A_{r2} =16feet^{2} [/tex]
Now that we have the areas of all out figures, lets add them to find the area of the shaded region:
[tex]A _{total} =25feet^{2} +10feet^{2} +16feet^{2} [/tex]
[tex]A _{total} =51feet^{2} [/tex]
We can conclude that the area of the shaded region is 51 square feet.
What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months?
a. $25.47
b. $202.55
c. $611.20
d. $4,861.20
Answers
Answer: Option c. $ 611.20 will be correct.
Explanation:
Since, the total amount of finance charge is [tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex]
Where P is the principle, r is the rate, n is the times of compound interest (monthly or quarterly etc.) .
Here P=$4250 r=13.25%, and n=24.
So according to the formula So, the finance charge= [tex]4250\frac{13.25(1+13.25)^{24}}{(1+13.25)^{24}-1}[/tex] = $ 611.20
The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months is c) $611.20.
To calculate the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months, we can use the following formula:
Total finance charge = Principal * (1 + Monthly interest rate)^Number of months - Principal
Where:
Principal is the amount of the loan ($4,250)
Monthly interest rate is the annual interest rate divided by 12 (13.25% / 12 = 1.1042%)
Number of months is the term of the loan in months (24)
Total finance charge = 4250 * (1 + 0.011042)^24 - 4250
Total finance charge = 611.20
Therefore, the answer is c. $611.20.
Note that this formula is for calculating the total finance charge over the entire term of the loan. If you want to calculate the monthly finance charge, you can simply divide the total finance charge by the number of months in the loan term. For example, the monthly finance charge for this loan would be $611.20 / 24 = $25.47.
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The least natural number that is divisible by three different primes is
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1) We start by writting down natural numbers one by one. Then we check for it's divisors that are prime numbers. We continue doing this until we find the solution. This approach could take quite some time to complete but it will eventually give the correct answer.
2) We need to find natural number that is divisible by three primes. And it needs to be smallest possible. This means that the product of these numbers is our solution.
We can not take any three random primes as they will not give us the requested solution. 7* 11 * 31 = 2387
We need to take three lowest primes. Those are 2, 3 and 5. 1 is not considered to be a prime.
2 * 3 * 5 = 30
So our solution is 30. All lower numbers do not have three primes as divisors.
The least natural number that is divisible by three different primes is 30.
The positive whole numbers are termed as natural Numbers.
Numbers that have only two factors are termed as Prime Numbers.
According to the question, the least natural number that is divisible by three different primes is calculated by multiplying three least prime numbers as-
[tex]2\times 3\times 5=30[/tex].
Here, the natural number should be the least so, you need to take lowest three prime numbers only.
Hence, The least natural number that is divisible by three different primes is 30.
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Solve 4y - 8 -2y + 5 = 0
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Lori is running in a marathon which is 26.2 Miles long so far she has run 1/10 of a marathon how far has Lori run
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If she has run 1/10 of the marathon, we can divide 26.2 by 10.
26.2/10= 2.62
She has run 2.62 miles.
I hope this helps!
~kaikers
The sum between two numbers is 170 and their difference is 110, what is the larger of the two numbers
Answers
x - y = 110 Add these two equations.
2x = 280 Divide by 2
x = 280/2
x = 140