Find the trigonometric form of the complex number. Hint: Graph the complex number first to give yourself a visual representation.
Answers
First, let's graph the complex number:
The trigonometric form will be given by:
[tex]-2-2i=r(\cos \theta+i\sin \theta)[/tex]The angle θ here is 225° (5π/4), the r-value will be
[tex]\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ \\ r=\sqrt[]{4+4} \\ \\ r=\sqrt[]{8}=2\, \sqrt[]{2} \end{gathered}[/tex]Now we have the trigonometric representation:
[tex]-2-2i=2\, \sqrt{2}\mleft(\cos \mleft(\frac{5\pi}{4}\mright)+i\sin \mleft(\frac{5\pi}{4}\mright)\mright)[/tex]Therefore the correct answer is the letter D.
Related Questions
how do you multiply 120 by 1/6
Answers
The expression is,
[tex]\frac{1}{6}\times120[/tex]On solving, we have,
[tex]\begin{gathered} 120\times\frac{1}{6}\Rightarrow\frac{120\times1}{6}=20 \\ \end{gathered}[/tex]Thus, the required answer is 20.
A guy wire runs from the top of a cell tower to a metal stake in the ground. Penelope
places a 12-foot tall pole to support the guy wire. After placing the pole, Penelope
measures the distance from the stake to the pole to be 5 ft. She then measures the
distance from the pole to the tower to be 21 ft. Find the length of the guy wire, to the
nearest foot.
Answers
Answer:
68 ft
Step-by-step explanation:
You want the length of a guy wire from a stake to the top of a cell tower if the stake is 5 ft from a 12-ft pole that is 21 ft from the tower. The guy wire crosses the top of the pole.
TrianglesThe attached diagram shows the geometry. The smaller triangle is a right triangle with legs 5 and 12. Its hypotenuse is ...
c = √(5² +12²) = √169 = 13
The larger triangle is similar and has a base of 21+5 = 26 units. This means its hypotenuse, the length of the wire, will be 26/5 times the length of the hypotenuse of the smaller triangle.
guy wire length = (26/5)(13 ft) = 67.6 ft ≈ 68 ft
The length of the guy wire is about 68 feet.
The graph below represents taxi fares in the city of Chicago. If a woman travels 8.5 miles by taxi, what would you expect her fare to be? Give an estimate to the nearest dollar.
Answers
ANSWER:
$22
STEP-BY-STEP EXPLANATION:
To determine the value of the fare we use it through the graph just like this:
Therefore, the correct option is $22
What is an equation of the line that passes through the points (3, -4) and (-4, 3)
Answers
The equation of a line passing through the point (3, -4)and (-4, 3) is y = -x - 1
How to find equation of a line?The equation of a line passing through a point can be represented as follows;
In slope intercept form,
y = mx + b
where
m = slopeb = y-interceptThe line is passing through the point (3, -4) and (-4, 3).
Therefore,
slope = m = 3 + 4 /-4 - 3
m = 7 / -7
m = -1
Let's find the y-intercept using (3, -4)
-4 = -(3) + b
b = -4 + 3
b = -1
Therefore, the equation of the line is y = -x - 1
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Read the following sentence.We will go to the park tomorrow if you finish your homework.What is the connecting word in the sentence and what logical symbol represents it?
Answers
The connecting word in the sentence is If.
The logical symbol is
[tex]\rightarrow[/tex]Therefore, the correct option is Option 2.
True or False
Directions: On the line before each statement, write T if the statement is true or F if the statement is false.
6. Seafloor spreading takes place along a mid-ocean ridge.
7. Oceanic crust is older when it is closer to a mid-ocean ridge than it is when
it is farther from the ridge.
8. The high thermal-energy flow at a mid-ocean ridge comes from seawater.
9. Magnetic bands on the ocean floor are evidence that Earth's magnetic field
changes.
10. Knowledge of seafloor spreading could have helped Alfred Wegener gain more
support for his hypothesis of continental drift.
Answers
Answer:
6.T
7.F
8.F
9.T
10.T
Step-by-step explanation:
I also took the test and these where my correct answers
Given the polynomial f(x) = x4 + 3x3 − 3x2 − x, which of the following is true? (1 point)
(x + 1) is a factor since f(−1) = 0.
(x − 1) is a factor since f(−1) = 0.
(x + 1) is a factor since f(1) = 0.
(x − 1) is a factor since f(1) = 0.
Answers
The factor of the polynomial is (x-1)
f(x)=x4 + 3x3 − 3x2 − x
At x=1 the value of the polynomial is 0
so this is factor of the polynomial (x-1)
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a car travels 100 miles at a speed of 40 mph
calculate how long the journey lasts give answers in hours and minutes
Answers
Answer:
2 Hours and 20 Minutes
Step-by-step explanation:
100/40 = 2.5
2 Hours and 20 Minutes
Which complex number's graph is shown? 1 2 3 4 -1 و زر زر مع -3 37 O A. 2J7(cos 3* i sin O + 32T 4 O B. 2.2(cos 225° + i sin 225º) O C. 2lcos 2(cos 7+isin 4 4 D. -2(co 5135° + i sin135)
Answers
The point (-2,2), we need to evaluate each case
In this case, for the real part we need to obtain -2
[tex]_{}2\sqrt[]{2}(\cos (\frac{3\pi}{4}))=-2[/tex]For the imaginary part, we need to obtain 2
[tex]2\sqrt[]{2}(\sin (\frac{3\pi}{4}))=2[/tex]As we can see the complex number that is shown in the graph is
[tex]2\sqrt[]{2}(\cos (\frac{3\pi}{4})+i\sin (\frac{3\pi}{4}))[/tex]ANSWER
A.
Trees in the backyard need soil around their roots. ?Chris buys 4 pounds of soil. How many ounces of soil does he have for the trees?
Answers
Answer:
64 ounces.
Step-by-step explanation:
You multiply the mass amount by 16 since there are 16 ounces in 1 pound. 16*4=64.
Is the relation a function?
Choose the answer that is entirely correct.
Responses
This relation is a function because each input has exactly one output.
This relation is a function because each input has exactly one output.
This relation is not a function because an output has two different inputs.
This relation is not a function because an output has two different inputs.
This relation is not a function because an input has two different outputs.
This relation is not a function because an input has two different outputs.
This relation is a function because all of the outputs have exactly one input.
Answers
The correct option is
This relation is a function because each input has exactly one output.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
From the figure the input are distinct and no input get coincide with output.
So, A function is a relation that states that there should only be one output for each input.
Alternatively, we could say that a function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.
Hence, This relation is a function because each input has exactly one output.
This relation is a function because each input has exactly one output.
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C. $3,006D. $3,135given, compute40 answer3. Which function has the largest value forf(-3)?) puug - 3 functionA f(x) = 2x - 5-786-33-5B. f(x) = 2 - 4x7Q-10-30C. f(x) = 6 - 3*-76-363)D. F(X) = 2* + 10 20-07104. When Mack left the bank, the temperature was 25°C. When he got htomnarature was 730F. If CA=f-32, about how many degrees
Answers
To know which function has the largest value for f(3), we need to substitute x=-3 in each function:
A. f(x)=2x-5
f(-3)=2(-3)-5=-11
B. f(x)=2-4x
f(-3)=2-4(-3)=14
C. f(-3)=6-3^(-3)
f(-3)=6-1/27
f(-3)=161/27
D. f(x)=2^(x)+10
f(-3)=2^(-3)+10
f(-3)=1/8+10=81/8
The largest value for f(-3) is 14, The answer is B f(x)=2-4x
Jenna has been keeping an eye on an emerald ring she likes. Its original price was
$35,450. After being marked down for a clearance sale, it is now $24,815. By what percent
has the price of the ring gone down?
Answers
Answer: look at the explanation
Step-by-step explanation:
It goes down by 40%
Which of the following trigonometric values are negative? 1. sin(-292°) II. tan (2pi/3°) III. cos (153°) IV. cot (222°)a. 2, 3, and 4b. 2 and 3c. 3 onlyd. 1 and 3
Answers
Therefore, the answer is:
b. 2 and 3
Find the area of the trapezoid.A trapezoid with the top base labeled two feet and the bottom base labeled ten feet. The height is labeled four feet.
Answers
To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{1}{2}(B+b)h,[/tex]where B and b are the lengths of the bases and h is the height.
Substituting B=10 ft, b=2 ft, and h=4 ft in the above formula, we get:
[tex]A=\frac{1}{2}(2ft+10ft)4\text{ ft.}[/tex]Simplifying we get:
[tex]A=24ft^2\text{.}[/tex]Answer:
[tex]24ft^2\text{.}[/tex]Find all solutions of the following equation in the interval [0, 2pi).2cos^2 x = 2- sin
Answers
Step 1: problem
[tex]2\cos ^2x\text{ = 2 - sinx}[/tex]Step 2: Concept
[tex]\text{cos}^2x=1-sin^2x[/tex]Step 3: Method
[tex]\begin{gathered} 2\cos ^2x\text{ = 2 - sinx} \\ 2(1-sin^2x)\text{ = 2 - sinx} \\ 2-2sin^2x\text{ = 2 - sinx} \\ 2-2=2sin^2x\text{ - sinx} \\ 2\sin ^2x\text{ - sinx = 0} \\ \sin x\text{ (2sinx - 1 ) = 0} \end{gathered}[/tex][tex]\begin{gathered} \sin x\text{ = 0 or 2sinx - 1 = 0} \\ x\text{ = }\sin ^{-1}0\text{ or 2sinx = 1} \\ \text{ x = 0 or sinx = }\frac{1}{2} \\ \text{ x = }\sin ^{-1}(\frac{1}{2})\text{ = 30} \end{gathered}[/tex][tex]x\text{ = 0, }\pi,\text{ }\frac{\pi}{6},\text{ }\frac{5\pi}{6}[/tex]Final answer
Find AC
Picture has math problem
Please hurry
Answers
The measure of side AC from the triangle ABC is 57 units.
Given that, ∠BTC=(3x+3)°, CT=x+8 and TA=x-9.
What is the altitude length?The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex.
Here, BT is an altitude
The altitude of a triangle is the perpendicular to the opposite side of triangle.
Now,
(3x+3)°=90°
⇒ 3x=87
⇒ x=29
So, CT=x+8
= 29+8=37
TA=x-9
=29-9=20
So, AC=CT+TA
= 37+20
= 57 units
Therefore, the measure of side AC from the triangle ABC is 57 units.
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the diameter of a circle is 14 centimeters what is the radius? give the exact answer in simplest form
Answers
The radius is half the diameter, that is:
[tex]r=\frac{D}{2}[/tex]In this case D=14 cm, hence:
[tex]r=\frac{14}{2}=7[/tex]therefore the radius is 7 cm.
Two angles are supplementary.
The measure of the larger angle is four more than three times the measure of the smaller angle. Find the measures of both angles.
Answers
Answer:
44° and 136°
Step-by-step explanation:
let x represent the smaller angle then larger angle is 3x + 4
supplementary angles sum to 180° , so
x + 3x + 4 = 180
4x + 4 = 180 ( subtract 4 from both sides )
4x = 176 ( divide both sides by 4 )
x = 44
3x + 4 = 3(44) + 4 = 132 + 4 = 136
then
smaller angle = 44° and larger angle = 136°
how to solve this problem? Result from step 1: Expected value is -$3.23.
Answers
The expected value was already calculated as:
[tex]E=-3.23[/tex]The expected value is the mean value you would get per try.
Since we played 623, the expected value is 623 times the expected valu for a single play, so:
[tex]E_{623}=623\cdot E=623\cdot(-3.23)=-2012.29[/tex]So, the expected value after playing 623 times is to -$2012.29, that is, lose $2012.29.
ILL GIVE A HUNDRED POINTS Some friends go to an amusement park in one car. They must pay a $6.00 parking fee plus $29.99 per
person for tickets.
If n is the number of tickets purchased and c is the total cost, which is the independent variable and
which is the dependent variable? Is the relationship between the variables a function?
What are you being asked or told to do? _________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
What information do you know? ____
Answers
By using the concept of linear equation, it is obtained that
c = 6 + 29.99n is the required equation involving cost and number of persons
n is the independent variable and c is the dependent variable.
The above relation involves a polynomial, so the above relation is a function.
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Let the number of persons be n
They must pay a $6.00 parking fee plus $29.99 per person for tickets.
Total cost of the ticket = $(6 + 29.99n)
By the problem,
c = 6 + 29.99n
Here on putting the value of n, the value of c can be obtained.
So n is the independent variable and c is the dependent variable.
Since the above relation involves a polynomial, so the above relation is a function.
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Find the rate of change of the line that contains the two points (-1, 4) and (5, 4). Be sure to show all calculations and reduce your slope to a fraction in simplest form.
Answers
The slope of the given points is 0
The given points are (-1, 4) and (5, 4)
Let the two points be A ( - 1, 4 ) and B ( 5, 4 )
The point A is present in the second quadrant and the point B is present in the first quadrant .
The slope of the given points can be calculated by the formula
m = y₂ - y₁ / x₂ - x₁
here y₂ = 4
y₁ = 4
x₂ = 5
x₁ = - 1
The slope is equal to 4 -4 / 5 - ( - 1 ) = 0
thus the slope of the given points is 0.
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The post office can send packages that weigh at most 70 pounds. Marcus wants to send as many 6-pound bags of macadamia nuts as possible in one package. Which inequality can be used to determine the number of bags, b, of nuts Marcus can send in one package?
Answers
Answer: 11
Step-by-step explanation: 70 divided by 6 is 11.6
what are expressions that are equivalent to 2²×7²
Answers
The value equivalent to the expression 2² × 7² is 196.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have the following expression -
2² × 7²
The given expression is -
2² × 7²
Solving, we get -
(2 x 2) x (7 x 7)
4 x 49
196
Therefore, the value equivalent to the expression 2² × 7² is 196.
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Tonio works for a website that sells theater tickets and receives a base salary of $18,200 per year. He earns a commission of 2.3% for all ticket sales, which average $15,500 per week. He also gets a "viewed” fee of 3 cents each time someone comes to the website, whether or not any tickets are purchased. The number of visitors to the website averages 12,400 per month a) what is the total commission Tonio will earn this year. b) What is the total amount Tonio earns from visits to the website?c) What are Tonio’s total earnings for the year?
Answers
Tonio's salary is composed by:
- A base value of $18,200.
- A commission of 2.3% for all ticket sales, which average $15,500 per week. Hence 52 x 15,500 per year, as a year has 52 weeks.
- Another commission of $0.03 per visitor to the website, which averages 12,400 per month, hence 12 x 12,400 per year, as a year has 12 months.
Then, the total commissions are given by:
T = 0.023x52x15500 + 0.03x12x12400 = 23002
Tonio will earn a total of $23,002 in commissions this year.
Total amount Tonio earns from visits to the website: 0.03x12x12400 = $4464
Tonio’s total earnings: $18,200 + $23,002 = $41202
When attacked by a giant hornet, Japanese honeybees cluster together to form a ball around the hornet and then generate heat by buzzing. The honeybees can endure temperatures of up to 48C, which is 3C greater than the hornet can tolerate. Find the maximum temperature tolerated by a Japanese giant hornet.
_______ degrees Celsius
Answers
The required temperature that can be tolerated by Japanese hornets is 45°C.
Given that,
The honeybees can endure temperatures of up to 48C, which is 3C greater than the hornet can tolerate.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
honeybees temperature = 48
According to the question temperature endure by hornet,
= honeybees temperature - 3
= 48 - 3
= 45°C
Thus, the required temperature that can be tolerated by Japanese hornets is 45°C.
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The distance around a circle is called the
OA. volume
OB. area
OC. circumference
Marina
TAPOR
Hea
OD. diameter
Answers
The distance around the circle is called circumference.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry.
Also, it has rotational symmetry around the Centre for every angle.
The circumference of a circle is defined as the
distance around the circle. The word ‘perimeter’
is also sometimes used, although this usually
refers to the distance around polygons, figures made up of the straight line segment.
A circle circumference formula is given by
C = πd = 2 π r
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8. Jase earns $5.00 per lawn mowed and $5.00 per car washed. Let m be the number of lawns mowed and let c be the number of cars washed. Select all the expressions that could represent the total earned, in dollars, by Jase. A 5(m + c) (B) 5m + c C 5+mc D 5c + m E 5m+5c
Answers
The expressions that can be used to represent the total earned amount is 5(m + c) and 5m + 5c (option A and D).
What are the expressions that represent the total amount earned?In mathematics, an expression is a statement that is made up variables and numbers that are linked together by a mathematical operation.
The total amount earned by Jase is the sum of the total amount earned from mowing the lawn and from washing cars.
Total amount earned = total amount earned from washing cars + total amount earned from mowing lawns
Total amount earned = (cost per lawn mowed x total lawns mowed) + (cost per car washed x number of cars washed)
Total amount earned = ($5 x c) + ($5 x m)
Total amount earned = $5c + 5m
Total amount earned = $5( c + m)
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
Find the parallel line for (2,0) y=-5x+3
Answers
The linear equation parallel to y=-5x+3 is:
y = -5*x + 10
How to find the parallel line?Two lines are parallel if and only if both lines have the same slope.
Remember that the general line is:
y = m*x + b
Where m is the slope and b is the y-intercept.
So a line parallel to:
y = -5x + 3
Must have a slope equal to -5, so our line is:
y = -5*x + b
To find the value of b we use the fact that the line passes through (2, 0), then:
0 = -5*2 + b
0 = -10 + b
10 = b
Then the line is:
y = -5*x + 10
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