Find z1z2 if z1 = 3(cos37° + isin37°) and z2 = 2/3(cos53° + isin53°).
Answer:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Step-by-step explanation:
Both variable can be rewritten into polar form:
[tex]z_{1} = 3\cdot e^{i\cdot 0.205\pi}[/tex] and [tex]z_{2} = \frac{2}{3}\cdot e^{i\cdot 0.294\pi}[/tex]
The complex product is equal to:
[tex]z_{1}\cdot z_{2} = (3)\cdot \left(\frac{2}{3}) \cdot e^{i\cdot (0.205\pi+0.294\pi)}[/tex]
[tex]z_{1}\cdot z_{2} = 2 \cdot e^{i\cdot 0.499\pi}}[/tex]
The resultant expression in rectangular form is:
[tex]z_{1}\cdot z_{2} = 2\cdot (\cos 90^{\circ} + i \cdot \sin 90^{\circ})[/tex]
Answer:
The correct question is:
Find [tex]z_{1}.z_{2}[/tex] if [tex]z_{1}= 3(cos37 + isin37)[/tex] and [tex]z_{2}= \frac{2}{3} (cos53 + isin53)[/tex].
(Note: the angles mentioned in the equations above are in degrees)
The answer is [tex]z_{1}.z_{2}= 2i[/tex]
Step-by-step explanation:
[tex]z_{1}.z_{2}= 3(cos37 + isin37)* \frac{2}{3} (cos53 + isin53)[/tex]
[tex]z_{1}.z_{2}= (3cos37 + 3isin37)* (\frac{2}{3} cos53 + \frac{2}{3}isin53)[/tex]
[tex]z_{1}.z_{2}= 3cos37*\frac{2}{3} cos53 + 3cos37*\frac{2}{3}isin53+3isin37*\frac{2}{3} cos53+3isin37*\frac{2}{3}isin53[/tex]
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex] (Because [tex]i*i=i^{2}=-1[/tex] & [tex]i=\sqrt{-1}[/tex])
[tex]z_{1}.z_{2}= 0.961+1.275i+0.724i-0.961[/tex]
[tex]z_{1}.z_{2}= 2i[/tex]
Elliot is simplifying a radical. His work is shown
Which statement best applies to Elliot's mathematical work?
A. The equality V64 = 4.16 is incorrect or invalid.
B. Removing the 4 from under the radial in the second step is incorrect or invalid
C. The work shown above is correct; however, 2V16 can be simplified further.
D. The work shown above is correct; and 2V16 cannot be simplified further
Answer:
C. correct, but can be further simplified
Step-by-step explanation:
Elliot's work is correct, but he apparently failed to recognize that 64 = 8². The radical could be simplified to ...
√64 = 8
Answer:
c
Step-by-step explanation:
got it right
3.
(07.06)
Which of the following graphs shows all the possible values for a number that is less than 7? (3 points)
Number line with closed circle on 7 and shading to the left.
Number line with closed circle on 7 and shading to the right.
Number line with open circle on 7 and shading to the left.
Number line with open circle on 7 and shading to the right.
Answer:
Number line with open circle on 7 and shading to the left
Step-by-step explanation:
Since 7 is not included in "a number less than 7", the circle at 7 is an open circle.
Numbers less than 7 are to the left of 7 on the number line, so the shading will be in that direction.
Number line with open circle on 7 and shading to the left
Answer:
The third one
Number line with open circle on 7 and shading to the left.
Step-by-step explanation:
I took the test, and I got this right
Which is the simplified form of m ^-8 p^0
Answer:
Step-by-step explanation:
m−^8p^0
=1/m^8
The manufacturer of pencils spends $0.05 to make each pencil and sells them for
0.25. The manufacturer also has fixed costs each month of $2000. Find the cost function C when x pencils are manufactured.
Answer: C(x) = 2000+ 0.05 x
Step-by-step explanation:
Hi, to answer this question we simply have to apply the next formula:
Cost (C) = fixed cost + (cost per pencil x number of pencils)
Since:
Fixed cost: $2000
Cost per pencil : $0.05
Replacing with the values given:
C(x) = 2000+ 0.05 x
Where x is the number of pencils manufactured.
Feel free to ask for more if needed or if you did not understand something.
2. Solve 2 tan x + 6 = -tan x + 3 on [0, 2(pie))
Your answer
If one box plot ranges from 25 to 85 and another boxplot ranges from 128 to 188, they will have the same range of what?
Answer:
They have the same range of 60.
Step-by-step explanation:
85-25=60
188-128=60
Put in order from greatest to svllems 12 1/2, 12.09,. 12 2/5,12.8
Answer:
12.8
12 1/2
12 2/5
12.09
[ Cuiu be made.
There are 24 boys for every 36 girls (24:36 ratio)
There are
boys for every
girls
try
Type in an equivalent ratio of boys and girls.
Answer:
24/36 = 12 x 2/12 x 3 = 2/3.
Step-by-step explanation:
In the figure below, which term best describes point T?
Answer:
A
Step-by-step explanation:
Which of the following is the image of C after a rotation of 180° about the origin?
A. (-5,2)
B. (-5, -2)
C. (-2,5)
Answer:
A: (-5,2)
Step-by-step explanation:
algebraically, a 180 rotation about the origin switches the original coordinates of (x,y) to (-x,-y), so the answer would be (-5,2) after plugging the numbers into this formula
Which expression represents a factorization of 32m + 56mp ?
Answer:
8m(4 + 7p)
Step-by-step explanation:
Take out the greatest common factor:
8m(4 + 7p)
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Again taking proportionality between their any two sides as the two triangles as considered separate are similar
AB/AC=AD/AE
4/6=7/AE
cross Multiplying
4×AE =6×7
AE=42/4
AE=10.5
Math Help!!! ASAP!! I will give you brainliest!!
Answer:
Step-by-step explanation:
true true false
HELP PLEASE, 10 points
The diameter of the hemisphere is 16 inches. What is the total surface area of the hemisphere?
Round to the nearest whole number.
Answer:
Step-by-step explanation:
d = 16 cm
r =16/2= 8 cm
Total surface area = 3πr² cubic units
= 3 * 3.14 * 8 * 8
= 602.88
= 603 cm²
The stem-and-leaf plot below shows the number of pages each student in a class read the previous evening.
A stem and leaf plot showing the movie length in minutes shown. The stems from top to bottom are 0, 1, 2, 3, 4, 5. The first column of leaves is 0, 2, 2, 3, 2, 7. The second column of leaves is 0, 3, 4, 5, 4, blank. The third column of leaves is 5, 5, 6, 6, 6, blank, blank. The fourth column of leaves is 8, 8, 7, blank, blank, blank. The fifth column of leaves is blank, 8, 7, blank, blank, blank. The sixth column of leaves is blank, 9, 7, blank, blank, blank.
Which statement is true about the data set?
Its median is greater than its mode.
It has a range of 52 pages.
The value of the first quartile is 13.
The data is symmetric.
Answer:
The value of the first quartile is 13.
Step-by-step explanation:
0 0 0 5 8
1 2 3 5 8 8 9
2 2 4 6 7 7 7
3 3 5 6
4 2 4 6
5 7
Its median is greater than its mode.
median is 12th data point = 24 mode = 27 false
It has a range of 52 pages.
range is largest minus smallest = 57-0 = 57 false
The value of the first quartile is 13.
There are 11 data points 11/2 = 5.5 = 1st quartile is 6th data point = 13
The data is symmetric.
it is not symmetric
Answer:
C) The value of the first quartile is 13.
Step-by-step explanation:
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
x = -3 ±sqrt(27)
Step-by-step explanation:
x^2 +6x = 18
Take the coefficient of x
6
Divide by 2
6/2 =3
Square it
3^2 = 9
Add this to each side
x^2 +6x+9 = 18+9
6/2 or 3 is what is inside the (x+ )^2 on the left
(x+3) ^2 = 27
Take the square root of each side
sqrt((x+3) ^2) = ±sqrt(27)
x+3 = ±sqrt(27)
Subtract 3 from each side
x+3-3 = -3 ±sqrt(27)
x = -3 ±sqrt(27)
how many thousands make 5crore
Answer:
50,000 thousands make a crore.
Step-by-step explanation:
One crore (1,00,00,000) is equal to one hundred lakh (10,000 × 1,000). Thus, 10,000 thousands make a crore.
Let a = 60. What is the value of a ÷ 5? equation
Answer:
12
Step-by-step explanation:
Just substitute 60 for a and divide it by 5
Ta Da!!
I will make you the brainliest if you can help me with my geometry homework.
Answer:
SAS
Step-by-step explanation:
Sides WV and XV on either side of angle WVX have been shown to be congruent to their corresponding parts. When you're concerned with a Side, Angle, and Side in that geometrical sequence, the SAS theorem is applicable.
Jenny has saved $600 from her summer job. During the school year, she withdraws $20 from her account every week for her daily expenses. She
wants to keep more than $300 in the account for college. The number of weeks, w, that Jenny can withdraw money from her account is
represented by the inequality 600 – 20w> 300. How many weeks can Jenny continue to withdraw $20 from her account?
A.
14
B.
17
O C.
20
D.
22
Answer:
A
Step-by-step explanation:
since she wants to keep 300 in her account first you would subtract 300 from 600 to get 300. Then you would divide it by 20 to get 15 so your answer would be a because she want's to keep at least 300 in her account.
What is the circumference of a circle when it has a radius of 3cm
Answer:
18.85
Step-by-step explanation:
Circumference = 2πr
=2*3.142*3
=18.85
Which is one way to find 2/3 of a number?
A. Divide by 2 and divide by 3.
B. Multiply by 3/2
C. Divide by 3 and multiply by 2.
D. Divide by 2 and multiply by 3.
Answer:
C. Divide by 3 and multiply by 2.
Step-by-step explanation:
To find 2/3 of a number, we multiply by 2 and divide by 3
2/3 * x
This is the same as dividing by 3 and multiplying by 2
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
B and E
Step-by-step explanation:
2x²-7x+3=0
2x²-x-6x-3=0
x(2x-1)-3(2x-1)=0
(x-3)(2x-1)=0
x=3 or x=1/2
I need help if you answer it ill make you the brainliest!!!
2x+5= 17
what is the value of X?
What is the slope for the linear function y=3x-4
Answer:
3
Step-by-step explanation:
This is written in the form
y= mx+b
where m is the slope and b is the y intercept
3 is the slope and -4 is the y intercept
In a certain Algebra 2 class of 25 students, 5 of them play basketball and 10 of them play baseball. There are 12 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
Probability of students who plays both baseball and basketball is [tex]\frac{2}{25}[/tex]
Step-by-step explanation:
We have given total number of students = 25
5 of them play basket ball 10 of them plays base ball
there are 12 students who neither play baseball nor basket ball
So the number of students who play either baseball or basketball is
[tex]n(A\cup B)=25-12=13[/tex], here A is for basketball and B is for baseball.
From set theory we know that
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
[tex]13=5+10-n(A\cap B)[/tex]
[tex]n(A\cap B)=2[/tex]
Therefore there are two students who play both baseball and basketball
Probability is equal to [tex]=\frac{2}{25}[/tex]
16. The local hiking club went on a 7-day hiking trip to Denali National
Park. The group started with 98 pounds and returned with no food.
If the decreasing amount of food each day is modeled by a linear
function, what is the slope of the line?
Answer:
The slope of the line is 14 pounds per day
Step-by-step explanation:
We are given that The local hiking club went on a 7-day hiking trip to Denali National Park.
The group started with 98 pounds
We are also given that the decreasing amount of food each day is modeled by a linear function
On Day 1 amount of food = 98 pounds
Since day 7 was the last day
So, On Day 8 amount of food = 0
So,[tex](x_1,y_1)=(1,98)[/tex]
[tex](x_2,y_2)=(8,0)[/tex]
Slope = Constant Rate of change per unit
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{0-98}{8-1}[/tex]
So, Slope =[tex]\frac{-98}{7}[/tex]
Slope = - 14
Negative sign shows decreasing amount of food each day
Hence the slope of the line is 14 pounds per day
Two math students were asked to write an exeponential growth equations that had a starting value of 300 and a growth rate of 2%. Pierre thinks the answer is y=300(1.02)^x and Scott thinks that the answer is y=300(1.2)^x. Are either of them right and why?
Answer:
Pierre is right.
Step-by-step explanation:
A growth rate of 2% means that the values is increasing by 0.02 each year so the multiplying factor is 1.02.
Pierre is correct y = 300(1.02)^x.
Scotts answer 1.2 = a growth rate of 20%.
The diameter of a golf ball is about four centimeters which of these is closest to the volume of a golf ball?
Answer:
33.51
Step-by-step explanation:
