Correct Answer:
z1= 2(cos 56 deg + i sin 56 deg)
z2= 2(cos 128 deg + i sin 128 deg)
z3 = 2(cos 200 deg + i sin 200 deg)
z4 = 2(cos 272 deg+ i sin 272 deg)
z5 = 2(cos 344 deg+ i sin 344 deg)
Step-by-step explanation:
De Moivre's Theorem--> e^i theta = cos theta + i sin theta
The fifth root of 32 is 2 and 280/5 is 56
z1= 2(cos 56 deg + i sin 56 deg)
360deg/ 5 = 72 deg
(If it was asking for cubed root u would do 360/3. whatever the root is you divide that by 360)
z2= 2(cos 56 + 72) + (i sin 56 + 72)
z2= 2(cos 128 deg + i sin 128 deg)
z3 = 2(cos 128 + 72) + ( i sin 128 + 72)
z3 = 2(cos 200 deg + i sin 200 deg)
z4 = 2(cos 200 + 72) + (i sin 200 + 72)
z4 = 2(cos 272 deg + i sin 272 deg)
z5 = 2(cos 272 + 72) + (i sin 272 + 72)
z5 = 2(cos 344 deg + i sin 344 deg)
deg means degrees
Determine whether quantities vary directly or inversely and find the constant of variation. It takes four identical water pumps 6 hours to fill a pool. How long would it take three of these same pumps to fill the pool, assuming they all pump at the same rate?
Let the number of water pumps be n and the time taken to fill the pool is t.
Now, we can see that higher the number of water pumps, lesser the time to fill the pool.
It means quantities vary indirectly.
Thus, [tex]n=\frac{k}{t} , \text{ where k is the constant of variation}[/tex]
Now, we have been given that It takes four identical water pumps 6 hours to fill a pool.
Thus, we have
[tex]4=\frac{k}{6} \\ \\ k=24[/tex]
Hence, constant of variation is 24.
Now, we have to find the time that three pumps will take to fill the same pool.
[tex]3=\frac{24}{t} \\ \\ 3y=24\\ \\ y=\frac{24}{3} \\ \\ y=8[/tex]
Hence, it will take 8 hours to fill the pool by three identical pumps.
Solve for m -20+14m=10m+16
Please help with geometry
!!!!!!!!!!!!!which answe
Answer:
I think it's D
Step-by-step explanation:
The perimeter of the rectangle below is 90 units. find the length of side vy . write your answer without variables.
the length of side VY is equal to the height, which is 19.4 units. The formula for the perimeter of a rectangle is given as `2 * (base + height)`.
It's correctly stated that the base of the rectangle is `3y + 1`, and the height is `2y + 3`. The perimeter is given as `90 units`.
To find the dimensions, we set up an equation using the formula for the perimeter:
90 = 2 * [(3y + 1) + (2y + 3)]
This equation represents that the perimeter is equal to twice the sum of the base and height.
The equation is then simplified:
90 = 2 * [5y + 4]
By dividing both sides by 2, it becomes:
5y + 4 = 45
Solving for y:
5y = 45 - 4
5y = 41
y = 41 / 5
y = 8.2 units
So, the value of y is correctly determined as 8.2 units.
With the value of y known, the base and height expressions are evaluated:
Base: `3y + 1 = 3 * 8.2 + 1 = 24.6 + 1 = 25.6 units`
Height: `2y + 3 = 2 * 8.2 + 3 = 16.4 + 3 = 19.4 units`
The dimensions of the rectangle are correctly calculated as follows:
Base: 25.6 units
Height: 19.4 units
It's also mentioned that the length of side VY is equal to the height, which is 19.4 units.
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In the figure above, Angle FEB is a central angle. True or False?
A. True
B. False
We know that the central angle is an angle subtended at the center of the circle by any two points on the circle.
In the given figure of the circle, the center of the circle is C. Hence, the central angle must be subtended at the center C.
Since, angle FEB is not subtended at the center of the circle.
Hence, angle FEB is not a central angle.
Therefore, the given statement is FALSE.
Find the volume of a cube that is 7 cm on each edge.
Final answer:
The volume of a cube with each edge measuring 7 cm is calculated using the formula V = s^3, which results in a volume of 343 cubic centimeters (cm3).
Explanation:
To find the volume of a cube that is 7 cm on each edge, we use the formula for the volume of a cube, which is V = s3, where s is the length of one side of the cube. In this case, s is 7 cm. Therefore, the volume can be calculated as follows:
V = 7 cm imes 7 cm imes 7 cm = 343 cm3
So the volume of the cube is 343 cubic centimeters (cm3).
how do you evaluate 71 - b, if b is 27
A triangle has sides with lengths: 6, 9, and 5. How do you find the area of the triangle using Heron's formula?
Rebecca is planting an orange grove that covers 32 acres she uses the same amount of ground space for each tree Rebecca plants 15 trees in a section of the grove that measures 250 feet by 25 feet what is the population density of this section of the grove use 1 acre= 43,560 square feet
If you take 5 quizzes and get scores of 95%, 95%, 80%, 85%, and 75%, how would you find your mean quiz score?
The mean of the quiz scores is given by the equation M = 86 %
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the mean of the quizzes be represented as M
Now , the equation will be
Let the number of quizzes be n = 5
Let the scores of each quizzes be represented by set A
Set A = { 95% , 95%, 80%, 85%, 75% }
So , the mean of the quizzes M = sum of the quizzes / number of quizzes
Substituting the values in the equation , we get
The mean of the quizzes M = ( 95% + 95% + 80% + 85% + 75% ) / 5
The mean of the quizzes M = ( 430/5 )
The mean of the quizzes M = 86 %
Therefore , the value of M is 86 %
Hence , the mean of the quizzes is 86 %
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divide (x^3-20x+16)divide (x-4)
Aaron took three times as many pictures as jennifer.jennifer has 16 fewer pictures than aaron.which system of equations can be used to find the number of oictures each person took?
Can derivatives be used to measure the the slope of the tangent line at x=a
Write an equation in intercept form of the parabola that passes through the point (1,32) and has x-intercepts −7 and 3?
The correct equation of the parabola in intercept form is [tex]2 (x+2)^2 -50[/tex].
To derive this equation, we will use the fact that the parabola passes through the given point (1,32) and has x-intercepts at -7 and 3.
[tex]y = k*(x+7)(x-3)[/tex]
[tex]y = k *(x^2 + 4x - 21)[/tex]
[tex]32 = k ( 8 * -2)32 = -16* kk = 32/-16 = -2[/tex]
[tex]y = -2(x+7)(x-3)[/tex]
[tex]= -2(x^2 + 4x - 21)[/tex]
[tex]= -2(x^2 +4x ) -42[/tex]
[tex]= 2(x^2 + 4x + 4) - 42 - 8[/tex]
[tex]= 2 (x+2)^2 -50[/tex]
The base of a triangular prism is a right triangle with hypotenuse 10 m long and one leg 6 M. If the height of the prism is 12 M, what is the volume of the prism
Find the missing values given that cos(theta) = 1.
Sin(Theta):
Csc(Theta)
Sec(Theta):
Cot(Theta):
I NEED HELP ON THIS EQUATION PLEASE (:
Anyone know this geometry question?
Solve 5x = 10x - 5(2x-3) for x. Show your work.
Eliminate parentheses using the distributive property.
... 5x = 10x -10x +15
Collect terms, then divide by the coefficient of x.
... 5x = 15
... x = 3
What are the period and amplitude of the function?
A) period 3, amplitude 1.5
B) period 3, amplitude 3
C) period 4, amplitude 1.5
D) period 4, amplitude 3
Answer:
Option: A is the correct answer.
A) Period: 3 , amplitude : 1.5
Step-by-step explanation:
We know that Period of a function is the smallest value such that the function repeats after a fixed time.
and also the amplitude of the function is the height above or below the mid-line.
After looking at the graph we see that the period of the function is: 3
Since the function is repeating itself after every x=3.
Also, the mid-line of the function is: y= -0.5.
Hence, the height above the mid-line is: 1+0.5 = 1.5
Hence, amplitude= 1.5
A cylinder has a radius of 10m and a 8m. What is the exact volume of the cylinder?
160 TT m3
80 TT m3
800 TT m3
18 TT m3
9) If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?
Which one is it? Will give brainiest
The coach attempts to determine an association between shirt size and hat size. Which is most likely true?
Answer:
There is likely an association because 0.8 is not similar to ≈ 0.33.
Mrs. rifkin had 84 oranges. 24 of her oranges were rotten; the rest were either ripe or unripe. there were 18 more ripe oranges than unripe oranges. find the ratio of the number of ripe oranges to the number of rotten oranges to the number of unripe oranges.
The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.
What is the vertex of the absolute value function defined by f (x) = |x - 7| + 1?
A. (7,1)
B. (-7, -1)
C. (-7, 1)
D. (7, -1)
PLEASE HELP ME FIND THE VALUE OF X
25 POINTS
Answer:
the answer is x = 9 cm
Step-by-step explanation:
A gas station sells regular gas for $2.20 per gallon and premium gas for $3.00 a gallon. at the end of a business day 300 gallons of gas has been sold, and receipts totaled $700. how many gallons of each type of gas had been sold