write the complex number z = 1 in trigonometric form (sometimes called polar form) express the angle in radians, where 0 <= theta < 2pi
Answers
The trigonometric or polar form of a complex number expresses the number in terms of its magnitude and argument. The complex number z = 1 in trigonometric form (polar form) is written as z = 1(cos(0) + i sin(0)), where theta = 0 radians.
The complex number z = 1 can be written in polar form as z = cos(0) + i sin(0), where cos(0) = 1 and sin(0) = 0. Therefore, the magnitude of z is 1, and the argument of z, denoted by theta, is 0 radians since it lies on the positive real axis.
Hence, the trigonometric form of z is z = 1(cos(0) + i sin(0)) = 1(cos(0) + i sin(0)), where 0 <= theta < 2pi. This representation is useful for performing operations on complex numbers, such as multiplication and division, since the operations can be carried out using the magnitude and argument of the numbers.
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Related Questions
-0.931 as a fraction
Answers
Answer:
-0.931
-----------
1000
Step-by-step explanation:
-0.931 = -931/1000
In each of the following situations, a significance test for a population mean µ is called for. State the null hypothesis H0 and the alternative hypothesis Ha in each case. Then, assume p=0.02. State the decision that should be made based upon this p-value. Be sure to justify your decision.
a) Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise as stimulus.
b) The examinations in a large accounting class are scaled after grading so that the mean score is 50. A self-confident teaching assistant thinks that his students have a higher mean score than the class as a whole. His students this semester can be considered a sample from the population of all students he might teach, so he compares their mean score with 50.
c) A university awards credit in French language courses to students who pass a placement test. The language department wants to know if students who get credit in this way differ in their understanding of spoken French from students who actually take the French courses. Some faculty think the students who test out of the courses are better, but others argue that they are weaker in oral comprehension. Experience has shown that the mean score of students in the courses on a standard listening test is 24. The language department gives the same listening test to a sample of 40 students who passed the credit examination to see if their performance is different
(expert answer asks for more information, but this is all that was given. There was no more significance testing information given)
Answers
The null hypothesis (H0) and alternative hypothesis (Ha) for each situation are a) H0: µ = 18 Ha: µ < 18 b) H0: µ = 50 Ha: µ > 50 c) H0: µ = 24 Ha: µ ≠ 24. Based on the given p-value of 0.02, the decision for each situation are a) Since p < 0.05, we reject the null hypothesis b) Since p < 0.05, we reject the null hypothesis c) Since p < 0.05, we reject the null hypothesis.
The null hypothesis (H0) and alternative hypothesis (Ha) for each situation are as follows:
a) H0: µ = 18 (the mean time for mice to complete the maze is equal to 18 seconds)
Ha: µ < 18 (the mean time for mice to complete the maze is less than 18 seconds)
b) H0: µ = 50 (the mean score for the teaching assistant's students is equal to 50)
Ha: µ > 50 (the mean score for the teaching assistant's students is greater than 50)
c) H0: µ = 24 (the mean score for students who passed the credit examination is equal to 24)
Ha: µ ≠ 24 (the mean score for students who passed the credit examination is not equal to 24)
Based on the given p-value of 0.02, the decision for each situation is as follows:
a) Since p < 0.05, we reject the null hypothesis and conclude that the loud noise does cause the mice to complete the maze faster.
b) Since p < 0.05, we reject the null hypothesis and conclude that the teaching assistant's students do have a higher mean score than the class as a whole.
c) Since p < 0.05, we reject the null hypothesis and conclude that the students who passed the credit examination do differ in their understanding of spoken French from students who actually take the French courses.
These decisions are justified because a p-value less than 0.05 indicates that there is a statistically significant difference between the sample mean and the population mean, and therefore we can reject the null hypothesis and accept the alternative hypothesis.
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2. (15 marks) On September 10 the Moon's phase was full, called a "harvest Moon" because of the time of year, and its distance from Earth was 370,746 km. (a) The Moon's average radius is 1737.4 km. What Kas the Moon's angular diameter on September 10? Express your answer in minutes of are, (b) The Moon's orbit around Earth is elliptical, and its average distance from Earth is 384,400 km. On September 10, what was the percentage difference between the Moon's actual angular diameter and its average angular diameter? (c) The Moon's angular diameter on September 10 found in part (a) was calculated either exactly using trigonometry or using the small angle approximation. What is the percentage error from using the small angle approximation? percent error ≡
θ
exact
(θ
exact
−θ
approx
)
×100
Answers
(a) The Moon's angular diameter on September 10 was approximately 16.92 minutes of arc.
(b) On September 10, the Moon's actual angular diameter was approximately 43.6% smaller than its average angular diameter.
(a) To find the Moon's angular diameter on September 10, we can use the formula:
Angular diameter = 2 * arctan (Moon's radius / Moon-Earth distance)
Moon's average radius (r) = 1737.4 km
Moon-Earth distance (d) = 370,746 km
Substituting these values into the formula, we have:
Angular diameter = 2 * arctan (1737.4 / 370,746)
Using a calculator, we find the angular diameter to be approximately 0.282 degrees.
To express this in minutes of arc, we multiply by 60 (since there are 60 minutes in a degree):
Angular diameter = 0.282 degrees * 60 minutes/degree ≈ 16.92 minutes of arc
Therefore, the Moon's angular diameter on September 10 was approximately 16.92 minutes of arc.
(b) To find the percentage difference between the Moon's actual angular diameter and its average angular diameter, we can use the formula:
Percentage difference = [(Actual angular diameter - Average angular diameter) / Average angular diameter] * 100
Average angular diameter (θ_average) = 0.5 degrees (since the Moon's average diameter is approximately 0.5 degrees)
Actual angular diameter (θ_actual) = 0.282 degrees (as calculated in part a)
Substituting these values into the formula, we have:
Percentage difference = [(0.282 - 0.5) / 0.5] * 100
Calculating this, we find the percentage difference to be approximately -43.6%.
Therefore, on September 10, the Moon's actual angular diameter was approximately 43.6% smaller than its average angular diameter.
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On September 10 the Moon's phase was full, called a "harvest Moon" because of the time of year, and its distance from Earth was 370,746 km. (a) The Moon's average radius is 1737.4 km. What Kas the Moon's angular diameter on September 10? Express your answer in minutes of are, (b) The Moon's orbit around Earth is elliptical, and its average distance from Earth is 384,400 km. On September 10, what was the percentage difference between the Moon's actual angular diameter and its average angular diameter?
Rewrite without parentheses.
(4x²z² − 6x³)(-8xz¹)
-
Simplify your answer as much as possible
Answers
Answer:
Step-by-step explanation:-32x³z³+48x∧4z
Identify the slope of the following equation:
y= 5 - 3x
m=? b=?
Answers
Answer:
y = mx + b
M is slope, b is y intercept
y = -3x + 5
m = -3
b = 5
Anna ran 100 meters in 20 seconds. What was her average speed
Answers
Answer:
5 meters per second
Step-by-step explanation:
Average speed = Total distance covered / Time taken
Answer:
5 meters per second
Step-by-step explanation:
Anna ran 100 meters in 20 seconds. What was her average speed?
100 / 20 = 5 meters per second
So, her average speed is 5 meters per second
Can y’all please help ASAP
Answers
need the answers step by step for 10-13
Answers
Answer:
Step-by-step explanation:
10) Plugin x = -10 in the equation
h(x) = 0.2x - 4.5
h(-10) = 0.2*(-10) - 4.5
= - 2 - 4.5
= -6.5
11) Plugin a = 8 in the equation
g(a) = (-3/4)a + 2
\(g(8) = \dfrac{-3}{4}*8 + 2 \\\\= -3*2 + 2\\\\= -6 + 2\\\\= -4\)
12) h(x) = 3x +3
h(x) = 0
3x +3 = 0
Subtract (-3) from both sides
3x = - 3
Divide both sides by 3
x = -3/3
x = -1
13) g(x) = - x - 5
g(x) = 4
-x - 5 = 4
Add 5 to both sides
-x = 4 + 5
-x = 9
Multiply both sides by (-1)
x = -9
Determine whether the following possible Random Variables should be classified as Qualitative, Discrete, or Continuous. 1. The score a competitor obtained from a figure skating competition 2. The bearing in which a boat is travelling 3. The condition of a used car you're thinking about purchasing. 4. The capacity of a stapler with respect to staples 5. The time it takes for your car to get an oil change. 6. The amount of dietary fibre in a bag of Psyllium Husk
Answers
1. The score a competitor obtained from a figure skating competition: This random variable is quantitative and discrete. The score is a numerical value that represents a specific outcome in the competition. It is discrete because it takes on specific, distinct values (e.g., 7.5, 8.2, 9.0) and cannot take on any value between those values.
2. The bearing in which a boat is traveling: This random variable is qualitative and discrete. The bearing represents a direction, such as north, south, east, or west. It is discrete because it takes on specific, distinct values from a set of possible directions.
3. The condition of a used car you're thinking about purchasing: This random variable is qualitative. The condition represents different categories or states, such as excellent, good, fair, or poor. It is qualitative because it involves descriptive categories rather than numerical values.
4. The capacity of a stapler with respect to staples: This random variable is quantitative and discrete. The capacity represents the number of staples a stapler can hold, which is a numerical value and can only take on specific, distinct values (e.g., 50, 100, 200).
5. The time it takes for your car to get an oil change: This random variable is quantitative and continuous. The time represents a duration and can take on any real value within a certain range. It is continuous because it can have infinite possible values within that range.
6. The amount of dietary fiber in a bag of Psyllium Husk: This random variable is quantitative and continuous. The amount of dietary fiber represents a measurable quantity, such as grams or milligrams, and can take on any real value within a certain range. It is continuous because it can have infinite possible values within that range.
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x + 4 is prime x2 – 9 can be factored using the formula.
Answers
Answer:
difference-of-squares
Step-by-step explanation:
Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21. At
the same store Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29. Heather bought
1lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23. Write the system of equations to determine how
much a pound of apples costs, a pound of oranges costs and a pound of bananas costs?. Equation 1:
Equation 2:
Equation 3:
0
Answers
The system of equations is:
3a + 2r + 7b = 21
2a + 6r + b = 29
a + 4r + 5b = 23
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
a = price of apples
r = price of oranges (I used r instead of letter o since o can be confused with zero)
b = price of bananas
Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21.
3a + 2r + 7b = 21
Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29.
2a + 6r + b = 29
Heather bought 1 lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23.
a + 4r + 5b = 23
The system of equations is:
3a + 2r + 7b = 21
2a + 6r + b = 29
a + 4r + 5b = 23
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Please help I will give brainliest and a lot of points :)
Answers
The inequality shaded in the graph is given as follows:
y ≥ 5x/2 + 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:
b = 3.
When x increases by 2, y increases by 5, hence the slope m is given as follows:
m = 5/2.
Then the equation of the line is given as follows:
y = 5x/2 + 3.
The line is a solid line, and values above it are plotted, hence the inequality is given as follows:
y ≥ 5x/2 + 3.
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rationalize the denominator !!!
please need help giving brainliest to all recent questions asked on my profile!!
Answers
Answer:
\(\frac{1\cdot \left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}\\\)
\(1\cdot \left(4+\sqrt{3}\right)=4+\sqrt{3}\)
\(\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right) = 13\)
\(= \frac{4+\sqrt{3}}{13}\)
x = 4
y = 3
z = 13
Answer:
x = 4, y = 3, z = 13
Step-by-step explanation:
Multiply the equation by the opposite of the denominator
\(\frac{(1)(4 + \sqrt{3}) }{(4-\sqrt{3})(4+\sqrt{3} ) } \\\\\frac{4 + \sqrt{3} }{16 - 4\sqrt{3} +4\sqrt{3} -3} \\\\= \frac{4+\sqrt{3} }{13}\)
how much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 47 degrees f? (round your answer to 2 decimal places.)
Answers
The amount of natural gas that homeowners can expect to use per month is influenced by various factors, including insulation levels and outdoor temperature.
However, without additional information or an established relationship between these factors, it is not possible to provide a precise estimate.
Insulation levels and outdoor temperature are just a few of the many factors that affect natural gas usage.
Other factors such as the size and efficiency of the heating system, the size and layout of the home, the insulation of walls and windows, and individual usage patterns can significantly impact gas consumption.
To obtain a more accurate estimate, it is recommended to consult energy professionals, utility companies, or use energy consumption calculators specifically designed for estimating natural gas usage based on multiple variables.
These tools take into account various factors to provide a more accurate estimation of monthly natural gas consumption.
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how many are 7 raised to 3 ???
Answers
Answer:
343
Step-by-step explanation:
7^3 =
7*7*7
343
I need help please I dont understand
Answers
Answer:
u can use formula whole root ,( x2-x1)²+(y2-y1)²
hope it helps...
Answer:
7.8 (1.d.p) or √61
Step-by-step explanation:
To solve this question we must use Pythagoras (a²+b²=c²)
Imagine that the line given is the hypotenuse (the longest side of a right-angled triangle) of a right-angled triangle and the other sides as a line from B going to the right, and a line from A going downwards (making the final vertexes for the triangle at coordinates: (3,2), which is B, (9,7), which is A, (9,2), which is the vertex the 2 imaginary lines we added, created) So now we use Pythagoras to find the length of the hypotenuse:
9-3=6 (subtracting the xs of vertexes A and B to find the length of the imaginary line we extended from B) and
7-2=5 (subtracting the ys of vertexes A and B to find the length of the imaginary line we extended from A)
Now to put them into Pythagoras's formula:
6²+5²=c² ⇒ 36+25=c² ⇒ √36+25=c ⇒ √61 = c ⇒ c = 7.8102....
Which can be rounded to 7.8 (as the third digit, the 1, rounds down.
pls help due in an hour if u get it right ill mark you brainliest
Answers
Answer:
The answer is ≈3 to the nearest whole number
Step-by-step explanation:
using SOH CAH TOA
BCA
sin0=opp/hyp
sin0=7.9/11
0=sin‐¹(7.9/11)
0=46 to the nearest degree
<A=<D
so,<EDF=46°
tan0=adj/hyp
tan46=x/3.3
x=tan46×3.3
x=3 to the nearest whole number
What is the sum of areas of the faces on a rectangular prism called
Answers
Answer:
The surface area of the rectangular prism.
Step-by-step explanation:
The formula for the surface area of a rectangular prism is SA = 2 (wl + hl + hw), which actually represents the areas of each of the faces.
SA = 2wl + 2hl + 2hw
We see that the SA is the sum of the areas of the faces on a rectangular prism. Look at a picture of a rectangular prism if you have trouble understanding this.
An Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 was designed to operate between the temperature limits of 86°F at the ocean surface and 41'F at a depth of 2100 ft. About 13,300 gpm of cold seawater was to be pumped from deep ocean through a 40-in-diameter pipe to serve as the cooling medium or heat sink. If the cooling water experiences a temperature rise of 9°F and the thermal efficiency is 2.5 percent, determine the amount of power generated. Take the density of seawater to be 64 Ibm/ft3. Also, take the specific heat of water to be c= 1.0 Btu/lbm-"F. The amount of power generated is 448 99 kW.
Answers
The power generated by the Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 is 448 99 kW.
Given data:
Temperature limits: 86°F at the ocean surface and 41°F at a depth of 2100 ft.
Cooling water temperature rise = 9°F
Thermal efficiency = 2.5%
Amount of cold seawater pumped = 13,300 gpm
Density of seawater = 64 Ibm/ft³
Specific heat of water = c = 1.0 Btu/lbm-°F
Solution: We have to find the amount of power generated by the Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987. Power is given by the following equation:
Power = Q × ρ × c × (T₂ - T₁) × η
Here, Q = Mass flow rate of cold seawater
= 13,300 gpm
= 13,300 × 60 × 24
= 19,152,000 lb/day
ρ = Density of seawater
= 64 Ibm/ft³
c = Specific heat of water
= 1.0 Btu/lbm-°F
T₁ = Temperature of seawater at depth
= 41°F
T₂ = Rise in temperature of seawater
= 9°F,
T₂ = T₁ + 9
= 41 + 9
= 50°F
Temperature difference (T₂ - T₁) = 50 - 41
= 9°F
Efficiency of the power plant,
η = 2.5%
= 0.025
Substitute all the values in the equation:
Power = 19,152,000 × 64 × 1.0 × 9 × 0.025
= 448,992 kW (approx)
Therefore, the amount of power generated by the Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 is 448 99 kW.
Conclusion: Thus, the power generated by the Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 is 448 99 kW.
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answer for brainilest and 30 points.
Answers
Answer:
Top Right
Step-by-step explanation:
231/pi(3)^2 =8.17
Round down to 8
Answer:
The height is 8 inches
Step-by-step explanation:
Well to find the volume of a cylinde like this, he formula is Base * height.
To find the base we need to find the area of the circle.
a=πr^2
The radius is 3 inches, 3^2=9
Since π is suppose to be 3.14 multiply
9*3.14= 28.26
We know that the cylinder can hold 231 cubic inches. So technically it can fill (x) 28.26 inches.
solve the equation
28.26x=231
Divide
231/28.26
The answer would be about 8 inches
let ax = a2x-1, a1 = 2 find a3 =
Answers
The value of a₃ is equal to 8.
To find a₃ using the given terms, aₓ = a₂x-1 and a₁ = 2, follow these steps:
Step 1: Identify the value of x when finding a₃.
Since you want to find a₃, the value of x will be 3.
Step 2: Use the given formula to find a₃.
The formula provided is aₓ = a₂x-1.
Plug in the value of x as 3:
a₃ = a₂(3)-1.
Step 3: Simplify the formula.
Simplify the formula as follows:
a₃ = a₁(4).
Step 4: Substitute the given value of a₁ into the formula.
You're given that a₁ = 2, so substitute it into the simplified formula:
a₃ = 2(4).
Step 5: Solve for a₃.
To find a₃, multiply the values:
a₃ = 8.
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Show work. Will mark branliest
Answers
Answer:10
Step-by-step explanation:
12 x 30 to see how many bottles per hour
360 x 8 to see how many it makes in a day
Divide 28,000 by 2,800 to see how many days it would take.
Step-by-step explanation:
first u will find how much bottles in 8 hours so that will be 60/2minutes =30so 30*12ottles=to 360 bottles per hour so 8*360=2,880 so u will do 28,000/2,880 it will be. 10 days of work.
Consider a continuous random variable x, which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________. 0.50 0.075 0.75 1.00
Answers
The probability of x taking on a value between 75 to 90 is 0.25.
Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.
The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.
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Ms. Cohen is buying supplies for her kindergarten class room. she can spend at most $30. she wants to buy boxes of crayons that cost $2 per box. she also buys a poster for $5. mrs.Cohen wants to know how many boxes of crayons she can buy.
Answers
Answer:
Ms. Cohen can buy 12 poxes of crayons.
Step-by-step explanation:
Ms. Cohen can buy 12 boxes of crayons with the rest of her money. In the question it states she only wants to buy 1 poster not more than one so if she buys 1 poster that's
30-5-25
and than you can just count up by 2 till you get the closest to 25
25-24=1$
24/2 = 12
Hope this helps.
The number of boxes of crayons that can be bought is needed.
The number of boxes that can be bought at most is 12.
Linear inequalitiesLet \(x\) be the number of boxes of crayons
Total amount of money = $30
Cost of one box = $2
Cost of poster = $5
The linear inequality will be
\(2x+5\leq 30\\\Rightarrow x\leq\dfrac{30-5}{2}\\\Rightarrow x\leq 12.5\)
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Please assist, no links
Answers
Answer:
\(\frac{1}{a^{7} }\)
Step-by-step explanation:
Use this rule:
\(\frac{x^a}{x^b}=x^{a-b}\)
So, this gives you
\(a^{-13+6}\)
This equates to:
\(a^{-7}\)
However, we cant leave the exponent negative, so we use this formula:
\(a^{-b}=\frac{1}{a^b}\)
So, the answer is:
\(\frac{1}{a^{7} }\)
Answer:
There is no denominator a^-7
The power is positive 1/a^7
Step-by-step explanation:
Remark
We are not told what the restrictions on the power are. Here are the possibilities.
There is no denominator.The power must be positive.So I will give the answer to both conditions. You will have to choose.
There is no denominator
That means that The powers are subtracted
Multiply numerator and denominator by a+6
a^- 13 * a^6
=========
a^-6 * a^6
To start a^(-6 + 6) = a^0 which = 1. That is not written, so you are left with a^ (-13 + 6) = a ^ -7
The answer must have a positive power.
Multiply the numerator and denominator by a^13.
numerator
a^-13 * a^13
a^(-13 + 13)
a^0
1
So we are left with 1 in the numerator.
a^-6 * a^13
a^(-6 + 13)
a^7
Answer: what is left is 1/a^7
Can someone help me with this pleaseee…….
Answers
The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.
We have,
To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:
Distance Formula:
If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:
AB = √((4 - (-5))² + (5 - 5)²) = 9
BC = √((2 - 4)² + (0 - 5)²) = √(29)
CD = √((-5 - 2)² + (-2 - 0)²) = √(74)
DA = √((-5 - (-5))² + (5 - (-2))²) = 7
Therefore,
The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.
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The difference between the park and house of a student is 1Km 575m. Every day he walks both ways between the park and his house. Find the total distance covered by him in a week's time?
Answers
The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.
To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.
Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.
In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.
Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.
Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.
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the prescriber orders medication f 150 mcg po q.12h. the pharmacy sends a bottle labeled: medication f 0.05 mg/ml. how many milliliters will the nurse administer with each dose?
Answers
The nurse will have to administer 3 milliliters with each dose.
When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:
medication f 0.05 mg/ml.
Milliliters will the nurse administer with each dose :
The conversion factor from mcg to mg is 1/1000.
Therefore, 150 mcg = 150/1000 = 0.15 mg.
The nurse has to administer 0.15 mg of medication f per dose.
The medication f available with the pharmacy is 0.05 mg/ml.
So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).
Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.
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what is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x3, the y-axis, and the horizontal line y=1 is revolved about the y-axis?
Answers
The volume of the solid is 4/5π.
The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.
In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by
V = ∫0 1 π(y)2dy
= ∫0 1 πx6dx
= π/7
= 4/5π
The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.
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Triangle def contains right angle e. if angle d measures 40° and its adjacent side measures 7.6 units, what is the measure of side ef? round your answer to the nearest hundredth. 4.89 units 5.34 units 6.38 units 9.06 units
Answers
The measure of side EF in triangle DEF is 5.34 units when angle D measures 40° and its adjacent side measures 7.6 units.
To get this answer, use the Pythagorean Theorem:
a2 + b2 = c2,
where a and b are the lengths of the sides adjacent to the right angle, and c is the length of the hypotenuse.
In this case, a = 7.6 and b = 5.34, so c = 8.93. Round this to the nearest hundredth and you get 5.34.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides adjacent to the right angle is equal to the square of the hypotenuse.
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