Z= -3 - 8i Find the angle θtheta (in degrees) that z makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express θtheta between -180 180 degrees.
Answers
The angle is negative to indicate a clockwise rotation.
======================================================
Explanation:
Z = -3 - 8i is in the form z = a+bi with a = -3 and b = -8
In the complex plane the point (a,b) represents the location of z = a+bi
Define three points with the locations
P = (a,b) = (-3,8)
Q = (0,0)
R = (10,0)
The angle PQR is the angle theta we're looking for. This is the angle formed between the positive x axis and the terminal point (a,b)
Use the arctan function to find theta
theta = arctan(b/a)
theta = arctan( (-8)/(-3) )
theta = 69.4439547804166
theta = 69.4 degrees approximately
Note how this theta value is in quadrant Q1, but (a,b) = (-3, -8) is in Q3
So we need to add 180 degrees to adjust this error.
69.4+180 = 249.4
and we're now in the proper quadrant. We would stop here if your teacher did not put the restriction that theta must be between -180 and 180.
However, this restriction is in place so we need to find the difference of 360 and 249.4 to get 360-249.4 = 110.6
-----------
The angle 249.4 degrees is coterminal to -110.6 degrees. They both point in the same direction.
angle 249.4 degrees is found by starting pointing directly east and rotating 249.4 degrees counterclockwise
angle -110.6 degrees is found by starting directly east and rotating 110.6 degrees clockwise.
Check out the diagram below. I used GeoGebra to make the diagram.
Related Questions
How many real solutions does this system of equations have?
y=x^2+1
y=x
Answers
Answer:
none
Step-by-step explanation:
y=x²+1
y=x
x²+1=x
x²-x+1=0
Disc.=b²-4ac=(-1)²-4×1×1=1-4=-3<0
so roots are imaginary.
If Jim Roller can paint a room in 3 hours while John Brush would take 5 hours, how long will they take if they work together?
Answers
Answer:
4 hrs
Step-by-step explanation:
half of Jim Rollers time is 1.5 hrs, and half of John Brushs time is 2.5 hrs. The two combined is 4 hrs. Therefore, the answer is four hours.
This is basically finding the average of two numbers, and you can use multiple different equations to find the same answer.
3/2 + 5/2 =4
(3+5)/2 =4
5-3=2, then 2/2=1, 5-1=4
Answer:
1 7/8 hours
Step-by-step explanation:
hi! i need to know the cube root of minus one!! just let me know down there!
Answers
Answer:
[tex]\large \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{-1}[/tex]
Apply radical rule:
[tex]\sqrt[n]{-1}=-1[/tex]
If [tex]n[/tex] is odd.
[tex]\sqrt[3]{-1}=-1[/tex]
The formula for the area of a square is sº, where s is the side length of the square. What is
area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answers
Just multiply the side lengths together to find area
Answer:
36
Step-by-step explanation:
The formula for the area of a square is s², where s is the side length of the square.
If a square with a side length of 6 centimeters then we get,
S = 6
Now, Area of square
= s² = (6)² = 36
8 times the sum of a and b
Answers
Answer:
c
Step-by-step explanation:
i did the quiz
Answer:
8(a + b)
Step-by-step explanation:
Sun of a and b = a + b
8 times of (a + b) = 8(a + b)
cual es el area de un rectangulo
Answers
Answer:
Use this formula:
a = b * h
Where: "a", the area of the rectangle is equal to its "b" (base), multiplied by "h" (height)
Step-by-step explanation:
Usa esta formula:
a = b * h
Donde: "a", el área del rectángulo es igual a su "b" (base), multiplicado por "h" (su altura).
How much water will be in each bottle if the total amount of water is equally divided among the bottles?
Answers
Answer:
D
Step-by-step explanation:
add everything up devide by 3
Answer:
C. 1/2 liter
Step-by-step explanation:
First, find the total amount of water by multiplying the amounts of water by the number of bottles, then adding all 3 values together:
1/4(1) = 1/4 liter
1/2(4) = 2 liters
3/4(1) = 3/4 liter
1/4 + 2 + 3/4 = 3 liters
There are 6 bottles in total, if we count the number of dots.
To find how much water would be in each bottle if the water was equally divided, divide the total amount of water by the number of bottles:
3 / 6 = 1/2
= 1/2 liter
What is the ratio DE of the length of to the length of BC?
Answers
Answer:
1:4
Step-by-step explanation:
so we are comparing the arc lengths to get the ratio of DE:BC
[tex] \beta \div 360 \times 2 \times \pi \times r[/tex]
to get arc length BC as
[tex] \beta \times \pi \times r \div 90[/tex]
and for DE as
[tex] \beta \times \pi \times r \div 360[/tex]
so divide DE by BC where beta pi r will cancel out. and you remain with 1/4 Wich will translate to 1:4
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 4 centimeters long, and the height of the equilateral triangle is 3.5 centimeters. The pyramid's slant height is 8 centimeters. What is its surface area?
Answers
Answer:
The surface area is 55 cm².
Step-by-step explanation:
The formula to compute the surface area of the triangular pyramid is:
[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]
Here h is the slant height.
Compute the Base perimeter as follows:
Perimeter of the equilateral triangle = 3 × side
= 3 × 4
= 12 cm
Compute the Base area as follows:
Area of the equilateral triangle = 0.50 × side × height
= 0.50 × 4 × 3.50
= 7 cm²
Compute the surface area as follows:
[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]
[tex]=(0.50\times 12\times 8)+7\\=48+7\\=55\ \text{cm}^{2}[/tex]
Thus, the surface area is 55 cm².
When a boy pulls his sled with a rope, the rope makes an angle of 70° with the horizontal. If a pull of 20 pounds on the rope is needed to move the sled, what is the horizontal component force?
7 lb
19 lb
20 lb
24 lb
Answers
Answer:
The answer to your question is 7 lbs.
Step-by-step explanation:
Data
angle = 70°
force = 20 lb
horizontal component
Process
To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.
1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.
cos Ф = adjacent side / hypotenuse
- Solve for the adjacent side
adjacent side = hypotenuse x cosФ
- Substitution
adjacent side = 20 x cos 70
- Simplification
adjacent side = 20 x 0.342
- Result
adjacent side = 6.84 ≈ 7 lb
Xian and his cousin Kai both collected stamps. Xian has 56 stamps, and Kai has 80 stamps. They boys recently joined different stamp-collecting clubs. Xian’s club will send him 12 new stamps per month. Kai’s club will send him 8 new stamps per month. after how many months will Xian and Kai have the same number of stamps? How many stamps will each have?
Answers
Answer:
After 4 months Xian will have 104 stamps,
But after three months Kai will also have 104 stamps
Step-by-step explanation:
To celebrate the first day of a leap year, I taught my dog to jump through a hoop. It was a Sunday. When he taught me the same trick the first day of the next year, it was a ?
Answers
Answer:
Tuesday
Step-by-step explanation:
364/7 = 52, meaning that 364 days later will also be a Sunday. 2 days after that (366 as it is a leap year) would be a Tuesday.
There will be Tuesday when the dog jumps the next year.
What is the reasoning?the process of applying logical reasoning to examine a situation in order to identify the optimal strategy for solving a specific problem, then using this approach to develop and justify a solution.
Reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.
Since when the dog jumped it was Sunday
Next Sunday will be at
364/7 = 52
So, after 52 weeks or 364 days, there will be next Sunday.
Since leap year is 366 days years
366 - 364 = 2
So, two days after Sunday is Tuesday.
Hence the day after next year when the dog jump will be Tuesday.
For more about reasoning,
https://brainly.com/question/2923977
#SPJ2
Verify the identity. cos quanity x plus pi divided by two = -sin x
Answers
Answer:
see below
Step-by-step explanation:
cos ( x+pi/2) = -sinx
We know that
cos(A + B) = cos A cos B - sin A sin B
Let x = A and pi/2 = B
cos x cos pi/2 - sin x sin pi/2 = -sin x
We know cos pi/2 = 0 and sin pi/2 = 1
cos x * 0 - sin x *1 = -sin x
- sin x = - sin x
After taking off from the landing pad, a helicopter flies 3 miles west, then 2 miles southeast. How far is the helicopter from the landing pad? If someone could explain to that would be very helpful
Answers
Answer:
When the plane makes its turn to fly southeast, it makes a 45º angle at point a, making angle abc also equal to 45º.
Line ab is the 2 miles southeast the plane flies.
Line ac = line cb
sine (45º) = opposite / hypotenuse = cb / 2
.70711 = cb / 2
cb = 1.41422 miles = line ac
Line cs = 3 - 1.41422 = 1.58578
Line x^2 = cs^2 + cb^2
Line x^2 = 2.5146982084 + 2.0000182084
Line x^2 = 4.5147
Line x = 2.1248
Step-by-step explanation:
Use the Law of Sines to find the missing angle of the triangle.
Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40
Answers
Answer:
66.9 degrees
Step-by-step explanation:
The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:
71/sin40 = 102/sinC
Cross multiplying, we get:
102(sin40deg) = 71(sinC)
Now, we simplify the left side and get:
65.56 = 71(sinC)
Next, we divide 65.56 by 71 to get:
0.92 = sinC
Taking the inverse sign we get:
C = 66.9 degrees
find the positive square root of 26.77
Answers
Answer:5.173973328
Step-by-step explanation:
Thus: 5.1739733 x 5.1739733 = 26.77
a pizza shop offers 30% of the price of a large pizza every tuesday night. if the regular price is 25, what is the discount price?
Answers
Answer:
17.50
Step-by-step explanation:
First find the discount
25 * .3
7.5
Subtract this from the original price
25-7.5
17.50
multiplying polinomiyal(5x+2)(3x+4)
Answers
Answer:
(5x+2) (3x+4)
= 15x²+20x+6x+8
= 15 x²+ 26x+8
Hope this helps ^_^
Answer:
Step-by-step explanation:
Use FOIL method
(5x + 2)(3x + 4) = 5x * 3x + 5x *4 + 2*3x +2*4
= 15x² + 20x + 6x + 8 { now add like terms}
= 15x² + 26x + 8
which phrase matches the algebraic expression bellow? 2(x+7)+10
Answers
Answer:
i think your answer is two times the sum of x and seven plus ten
if i am wrong than tell me
Step-by-step explanation:
hope this will help :)
A card is chosen at random from a standard deck of 52 cards. What is the probability that the card is a Queen or a $\diamondsuit$ (or both)?
Answers
Answer:
probability that the card is a Queen or a diamond= 0.3269
Step-by-step explanation:
There are 4 queen in a deck of cards and 13 diamond in a deck of cards.
And a deck of cards contains 52 cards total.
Probability of the card selected to be a queen = number of queen/total number of cards
Probability of the card selected to be a queen =4/52
Probability of the card selected to be a queen= 1/13
Probability of the card selected to be a diamond= number of diamond/ total number of cards
Probability of the card selected to be a diamond=13/52
Probability of the card selected to be a diamond=1/4
probability that the card is a Queen or a diamond= Probability of the card selected to be a queen + Probability of the card selected to be a diamond
probability that the card is a Queen or a diamond= 1/13+1/4
probability that the card is a Queen or a diamond= 0.3269
How many equations are thereof: 70 divided by h equals 10?
What are those equations?
Answers
Answer:
We have:
"70 divided by h equals 10"
We can write it in only one equation:
70/h = 10.
This is a rational equation because our variable is in the denominator of a quotient.
To solve it we can multiply by h on both sides of the equation and get:
(70/h)*h = 10*h
70 = 10*h
now we divide both sides by 10.
70/10 = (10*h)/10
7 = h.
Help pleasee!!! Tyyyyy
Answers
Answer:
G. 7
Explanation:
The longest side must be less than the sum of the two shorter sides.
The difference between the longest and shortest sides must be less than the middle side.
l+a = 11
l < (a + 4) ... l < (11 - l + 4)
... 2 l < 15 ... l < 7.5
--Variables
l = 7 (Longest Side/Answer)
a = 4 (Other Missing Length)
m = 4 (Side Given)
5 of 17Questions Question 5 Safiya needs to find a number that can be multiplied by 18−−√3 to result in a rational product. Which values could she use? Select all that apply.
Answers
Answer:
18 + √3
Step-by-step explanation:
The product of a surd and its conjugate gives a rational number. Hence;
(18 - √3) (18 + √3)
=324 + 18√3 - 18√3 - 3
=321
A rational number does not contain any surd, hence the answer.
Answer: cube root 1/18 & cube root 12
what is the common number to be subtracted from each term of the ratio 11:8 to get the new ratio 2:1.?
Answers
Answer:
5 should be subtracted from each term
Step-by-step explanation:
[tex]\frac{11-x}{8-x}=\frac{2}{1}[/tex]
Cross multiply,
1 * (11 - x) = 2*(8-x)
11 -x = 2*8 - 2*x
11 - x = 16 - 2x
Subtract 11 from both sides,
-x = 16 - 2x - 11
-x = 5 - 2x
Add 2x to both sides
-x +2x = 5 - 2 + 2x
x = 5
(3-1) (4+2) + 9 - 3 I need help
Answers
Answer:
18
Step-by-step explanation:
(3-1) (4+2) + 9-3 =
2 • 6 + 6 = 12 + 6
= 18
Answer:
[tex]\displaystyle 18[/tex]
Step-by-step explanation:
[tex]\displaystyle (3 - 1)(4 + 2) + 9 - 3 = [(2)(6)] + 9 - 3 = 12 + 9 - 3 = 12 + 6 = 18\:[OR\:21 - 3 = 18][/tex]
G - Grouping Symbols
E - Exponents
M\D - Division & Multiplication [left to right]
A - Subtraction & Addition [right to left OR vice versa]
I am joyous to assist you at any time.
An online company wants to establish ratings for the products they provide. To do so, they ask visitors to their website to evaluate the products and leave a "thumbs up" or a "thumbs down." What type of sample is this? Explain why.
Answers
Answer:
This is a group specific influence sample, it only shows a demographic sample of those that are influenced by the reviews in the first place.
Step-by-step explanation:
6p- 2q for p = 3 and q = -7
Answers
Answer:
32
Step-by-step explanation:
plug in the values of the variables then simplify
Answer:
[tex]\boxed{32}[/tex]
Step-by-step explanation:
Hey there!
Well given the expression,
6p - 2q
and p and q we need to plug them in.
6(3) - 2(-7)
Simplify
18 - -14
18 + 14
= 32
Hope this helps :)
Determine the measure of the interior angle at vertex D. A. 27 B. 162 C. 20 D. 36
Answers
Answer:
162°
Step-by-step explanation:
The shape is a hexagon, so the interior angles equal 720. (N-2)*180=720
9x+9x+9x+2x+9x+2x=720
40x=720
x=720/40
x=18
D=9x=9(18)=162°
The sum of interior angles of a polygon with n sides is [tex](n-2)\cdot180[/tex]
In this case [tex]n=6[/tex]
Therefore
[tex]4\cdot9x+2\cdot2x=(6-2)\cdot180\\36x+4x=4\cdot180\\40x=720\\x=18[/tex]
[tex]9x=9\cdot18=162[/tex]
So B
Area of a trapeziod with a top base length of 6 cm a bottom base length of 12 cm and a height of 5 cm
Answers
Answer:
A=45cm^2
Step-by-step explanation:
A= h/2(b1 + b2) for trapezoid
A=(5/2(6+12))cm^2
A=(2.5(18))cm^2
A=45cm^2
There are (43)2⋅ 40 strawberries on a farm. What is the total number of strawberries on the farm?
Answers
Answer:
3,440 strawberries
Step-by-step explanation:
Because of PEMDAS you want to start with the parentheses, and want to treat them like the distributive property.
So,
43 x 2 = 86
Then,
86 x 40 = 3440.
I hope that helps!!
Answer: 3440 strawberries on the farm.
Step-by-step explanation: (43)(2)⋅40 (86)(40) 3440
