Final answer:
The complex number 4i in polar form is 4(cos 90° + i sin 90°), which matches choice (c). The magnitude is 4, and the argument is 90° since 4i lies on the positive imaginary axis.
Explanation:
To convert the complex number 4i to polar form and express the argument in degrees, we should consider the general polar form of a complex number which is r(cos θ + i sin θ), where r is the magnitude (modulus) and θ is the argument of the complex number. The complex number 4i has a real part of 0 and an imaginary part of 4. Therefore, its magnitude is 4 and it lies on the positive imaginary axis. In the complex plane, this corresponds to an angle of 90° or 270° from the positive real axis. Since it is on the positive imaginary axis, the correct angle is 90°.
The correct polar form of the complex number 4i is 4(cos 90° + i sin 90°), which corresponds to choice (c).
Write an equation for the line perpendicular to 2x−3y = 5 and containing (−2, 1).
Hello:
the equation is : y = ax+b
the slope is a : a×(2/3) = -1......(
perpendicular to a line : 2x-3y =7 with a slope of 2/3 because : y = (2/3)x-7/3)
a = -3/2 y=(-3/2)x+b
the line that passes through (-2, 1) : 1 =
(-3/2)(-2)+b
b = -2
the equation is : y = (-3/2)x-2
Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).
Answer:
Volume of the cone = 7 unit³
Step-by-step explanation:
Soda can has the shape of a cylinder.
Volume of soda can = πr²h
where r = [tex]\frac{6}{2}=3[/tex] units
and volume = 21 unit³
We put the values in the formula to get the value of h.
21 = πr²h
[tex]h=\frac{21}{\pi r^{2} }[/tex]
Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.
By the formula of volume of cone
Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]
= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]
= [tex]\frac{21}{3}=7[/tex] units³
Volume of the cone is 7 unit³
The box plot shows the total amount of time, in minutes, the students of a class spend reading each day
What information is provided by the box plot? 10 Points
1. The mean for the data
2. The median for that data
3. The number of students who provided information
4. The number of students who read for more than 21.15 minutes
In a zoo, there are 3 male penguins for every 4 female penguins. What is the ratio of females to the total number of penguins at the zoo? 4 to 7 3 to 7 4 to 3 4 to 1
Final answer:
The correct answer is a ratio of 4 to 7, representing the ratio of female penguins to the total number of penguins in the zoo.
Explanation:
We're given that there are 3 male penguins for every 4 female penguins in a zoo.
To find the ratio of females to the total number of penguins, we first have to add up the total number of penguins, which is 3 males + 4 females = 7 penguins in total.
Now, we can express the ratio of females to the total number of penguins. There are 4 females out of 7 total penguins, so the ratio is 4 females to 7 penguins in total.
Therefore, the correct answer to the student's question is 4 to 7.
Select the assumption necessary to start an indirect proof of the statement. If 3a+7 < 28, then a<7.
At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased. Maria spends $83.00 on CDs. How many CDs has Maria purchased
Answer:
Maria purchased total 8 CDs.
Step-by-step explanation:
At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased.
Maria spends = $83.00
She purchased her first CD for = $13.00
Now balance of her charge = 83.00 - 13.00 = $70.00
other CDs are purchased for $10.00
Therefore, 70.00 ÷ 10.00 = 7 CDs
Total CDs = 7 + 1 = 8 CDs
Maria purchased total 8 CDs.
Simplify completely quantity 6 x minus 12 over 10.
Answer:
3(x+12)
-----------
10
(three times x plus twelve OVER ten)
Step-by-step explanation:
Find the missing terms in the following geometric sequence.
a.48, 162c.96, 192b.116, 220d.36, 108
We flip three coins and obtain more tails than heads. Write the event as a set of outcomes.
The set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
All outcomes in flipping 3 coins then the number of samples will be:-
Sample space of all outcomes
Sample space = {HHH,THH, HTH, HHT, TTT, HTT, THT, TTH} = 8 =All possible outcomes.
Sample space of all favorable outcomes (more tails than heads)
Favourable outcomes= {TTT, HTT, THT, TTH} = 4 = All favorable outcome.
Therefore, the set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.
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the volume of pyramid shown above is 147.97units and the height is is 9.6 units find the length of one edge of the square base
Are the lines parallel, perpendicular, or neither?
5x + 2y = 10
15x + 4y = -4
A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 51°. she rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 34°. how tall is the building across the street? (round to the nearest foot.)
Using trigonometric functions, specifically the tangent function, we create two equations corresponding to two right triangles formed by the lines of sight from the ground floor and from 60 feet high in the elevator. Solving those equations simultaneously, we can calculate that the height of the building across the street is approximately 149 feet.
Explanation:This is a trigonometry problem where we're going to establish two right triangles with the elevator as one side, the building across the street as another (the one we're trying to find), and the line of sight as the hypotenuse. From the ground, we form a triangle with the angle of elevation of 51 degrees. Then from 60 feet above the ground, we form another triangle with an angle of elevation of 34 degrees.
Here, we apply tangent of an angle which equals the opposite over adjacent sides in a right triangle. So, we get tan(51) = h/x and tan(34) = (h-60)/x. We have two unknowns here: 'h' which is the height of the building and 'x' the distance from the elevator to the building. Solving these equations simultaneously, we can find 'h'.
If we solve these equations, we'll get 'h' equals approximately 149 feet (rounding to the nearest foot). So, the building across the street is around 149 feet tall.
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Solve the equation.
12 + 0.35x = 20.05
A. 91.5
B. 57.3
C. 2.8175
D. 23
What is sum of the area under the standard normal curve to the left of z = -1 and to the right og z = 1.25?
Given the declaration, where is the value 97 stored in the numbers array? int numbers[]={83, 62, 77, 97, 88};
Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statement is:
there are two angles.
the sum of two angles is 90°.
the angles are complementary.
Angles are complementary if their sum is 90°.
A room measures 12 feet by 12 feet. A couch is 10 feet and 6 inches long. If you center the couch in the middle of the room, how far will each end of the couch be from the nearest wall?
Final answer:
To determine the distance from the ends of the couch to the nearest wall, convert all measurements to inches, find the difference between the room and couch lengths, and divide by two. The ends of the couch will be 0.75 feet or 9 inches from the nearest wall.
Explanation:
The question involves determining the distance from the ends of a couch to the nearest wall when the couch is centered in a 12 feet by 12 feet room. The couch is 10 feet and 6 inches long.
To solve this, first convert the couch length to inches. 10 feet is 120 inches, and adding 6 inches gives us a total of 126 inches for the couch length. Since 1 foot equals 12 inches, the room's length in inches is 12 feet times 12 inches per foot, which equals 144 inches.
Now, to find the distance from each end of the couch to the nearest wall, we subtract the couch length from the room's length:
Room's length in inches: 144 inchesCouch length in inches: 126 inchesDifference: 144 inches - 126 inches = 18 inchesDivide the difference by 2 to get the distance from each end of the couch to the wall:
Distance from each end to the wall: 18 inches / 2 = 9 inchesFinally, convert this distance back to feet:
9 inches / 12 inches per foot = 0.75 feet, or 9 inchesTherefore, each end of the couch will be 0.75 feet, or 9 inches, from the nearest wall when the couch is centered in the room.
how to express -8+4-2+1 in sigma notation
The area of the rectangular playground enclosure at Happy Times Nursery School is 600 meters. The length of the playground is 25 meters longer than the width. Find the dimensions of the playground. Use an algebraic solution.
The solution would be like this for this specific problem:
Area = L * W = 600
Length = W + 25
Substitute and solve for "W":
(W + 25)W = 600
w^2 + 25w - 500 = 0
(w - 15) (w + 40) = 0
Positive solution:
Width = 15 meters
Length = 15 + 25 = 40 meters
So, the dimensions of the playground using an algebraic solution is 15 meters by 40 meters.
To add, the minimum number of coordinates needed to specify any point within it is the informal definition of the dimension of a mathematical space.
I NEED THIS ANSWER
Which linear inequality is represented by the graph?
y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3
What is the frequency of the function y = cos5x?
Final answer:
The frequency of the function y = cos5x is 5/2π.
Explanation:
The given function is y = cos5x. To find the frequency of this function, we need to determine the coefficient of x in the argument of the cosine function. In this case, the coefficient is 5, which means the argument of the cosine function will complete 5 full cycles in an interval of 2π.
The frequency of a function is the reciprocal of the period. The period is found by dividing 2π by the coefficient of x. So, the period of the given function is 2π/5, and the frequency is the reciprocal of the period, which is 5/2π.
Therefore, the frequency of the function y = cos5x is 5/2π.
Three consecutive integers have a sum of 234. What are the three integers?
What is the cost of constructing a fence 6 and a half feet (6'6") high around a lot measuring 90 ft by 175 ft; if the cost of erecting the fence is $1.25 per linear ft and the cost of materials is $.825 per square ft?
Final answer:
To construct a fence around a 90 ft by 175 ft lot at $1.25 per linear foot and $.825 per square foot for materials, it would cost a total of $13,656.25.
Explanation:
To calculate the cost of constructing a fence for a lot that measures 90 ft by 175 ft with a fence height of 6'6" (6.5 ft), we need to determine both the perimeter of the lot for the linear feet cost and the total area for the material cost per square foot.
The perimeter of the lot is 2*(90 + 175) = 2*265 = 530 feet. So, the cost of erecting the fence at $1.25 per linear ft is 530 ft * $1.25/ft = $662.50.
The total area that needs to be fenced is 90 ft * 175 ft = 15,750 square feet. Thus, the cost of materials at $.825 per square ft is 15,750 sq ft * $0.825/sq ft = $12,993.75.
The total cost of constructing the fence is the sum of the cost of erecting the fence and the cost of materials, which adds up to $662.50 + $12,993.75 = $13,656.25.
Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work
Betty has 10 more dimes than quarters. If she has $3.45, how many coins does she have?
d = dimes
q = quarters
d=10+q
0.25q +0.10d = 3.45
0.25q + 0.10(10+q) = 3.45
0.25q + 1 +0.10q =3.45
0.35q=2.45
q = 2.45/0.35 = 7
d = 10+7 =17
0.25*7=1.75, 17*0.10 = 1.70, 1.75+1.70 = 3.45
she has 7 quarters and 17 dimes for a total of 24 coins
you spend $124.00 shopping, but the store is offering a 30% discount. what is the total cost after the discount? round to the nearest cent
What is the length of side PQ?
Answer: The length of PQ = 64
Step-by-step explanation:
We are given that ΔPQR and ΔABC are similar right triangles .
Since, we know that the corresponding sides of similar triangles are proportional.
Therefore, we get
[tex]\dfrac{PQ}{AB}=\dfrac{QR}{BC}\\\\\Rightarrow\dfrac{PQ}{16}=\dfrac{80}{20}\\\\\Rightarrow\ PQ=4\times16\\\\\Rightarrow\ PQ=64[/tex]
Hence, the length of side PQ = 64 units
7+2[3(x+1) -2 (3x-1)]
Write log(x^2-9)-log(x+3) as a single logarithm.
Answer:
b edge
Step-by-step explanation:
Solve for x: 15x2 = x+2
x2 is x to the second power