) A wire made of copper (density 8.5 g/cm') is shaped like a helix that spirals along the r-axis from r = 0 to x = 20. Each cross section of this wire perpendicular to the r-axis is a circular disk of radius 0.25 cm. Find the total mass of the wire.
Answers
The total mass of the copper wire, shaped like a helix with circular cross-sections, can be found by calculating the volume and multiplying it by the density of copper.
To find the total mass of the wire, we need to calculate the volume of the wire and then multiply it by the density of copper.
The wire is shaped like a helix that spirals along the r-axis. Each cross-section perpendicular to the r-axis is a circular disk of radius 0.25 cm. The distance along the r-axis from r = 0 to r = 20 is the length of the wire.
To find the volume of the wire, we can consider it as a collection of small cylindrical segments. Each cylindrical segment has a height equal to the distance between adjacent cross-sections (which is the pitch of the helix) and a circular base with a radius of 0.25 cm.
The pitch of the helix can be calculated using the formula:
pitch = 2πr
The total length of the wire is given as x = 20, so the total number of turns in the helix is:
turns = x / pitch
The volume of each cylindrical segment can be calculated using the formula:
volume = π(radius)^2(height)
Substituting the values, we have:
radius = 0.25 cm
height = pitch
The total volume of the wire is then:
total volume = volume of one segment × number of turns
Finally, we can calculate the total mass of the wire by multiplying the total volume by the density of copper:
total mass = total volume × density
Using the given density of copper (8.5 g/cm³), you can plug in the values and calculate the total mass of the wire.
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Related Questions
FILL IN THE FIRST BOX PLEASE 51 PONTS!
Answers
Answer:
Step-by-step explanation:
The frame -- if it means the box on the outside which has 4 right angles, or the hexagon in the middle which has 0 right angles
In the expression 3x^2+y+-5 which of the following choices is the exponent in the term 3x^2?
A. 3
B. 2
C. X
D. None of these choices
Answers
Answer:
2
Step-by-step explanation:
3x^2
The coefficient is 3
The variable is x
The exponent is 2
can i please get some help with this
Answers
Answer:
The answer is B
Step-by-step explanation:
3x-2 is less than or equal to -20
Answers
Answer:
x \(\leq\) -6
Step-by-step explanation:
3x - 2 \(\leq\) -20
Solve for x:
3x \(\leq\) -18
x \(\leq\) -6
please please please help me ill mark you brainlist last question
Answers
Answer:
B. SF=1/2 (image was reduced)
Step-by-step explanation:
Jayson buys two baseball bats for $300 what is the unit rate per bat
Answers
Answer:
$150
Step-by-step explanation:
$300 divided by 2 = $150
Answer this question based on the number line shown.
A
B
C
The distance from a point to point Cis 1 and the distance from that same point to point Bis 4. The point must be
goint A
Obetween DandA
point D
Obebween CandA
Answers
Since the distance from a point to point C is 1 and the distance from that same point to point B is 4, the point must be: C. point D.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
From the number line shown above, we have:
Distance = 4 + (-1)
Distance = 4 - 1
Distance = 3 (point D).
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What concept does the mean of a discrete random variable generalize? Select the correct answer below. a. Population mean (mean of a variable) b. Expected value c. Sample mean d. Distribution of a discrete random variable
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The correct answer is b. Expected value. The mean of a discrete random variable generalizes the concept of expected value. The expected value of a discrete random variable is the weighted average of all possible outcomes, where the weights are the probabilities associated with each outcome.
It represents the long-term average value that we would expect to observe if we repeated the random experiment multiple times.
In the context of a discrete random variable, the mean (or expected value) is calculated by multiplying each possible value of the variable by its corresponding probability and summing them up. It provides a measure of central tendency and represents the average value we would expect to obtain from the random variable over a large number of trials.
The population mean (mean of a variable) refers to the average value of a variable in the entire population, not specifically related to a random variable. The sample mean is the average value of a variable calculated from a sample of observations. The distribution of a discrete random variable refers to the pattern of probabilities associated with each possible outcome of the variable.
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recall that on the act math section, the scores are graded to follow the normal model with a mean of about 18.5 and a standard deviation of about 5.75. based on this model, what is the cutoff score to be in the bottom 6% of all act math scores?
Answers
The cutoff score to be in the bottom 6% of all ACT math scores is about 27.71. To find the cutoff score to be in the bottom 6% of all ACT math scores, we need to use the normal distribution table.
First, we need to convert the score to a z-score using the formula: z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation.
For the bottom 6% of scores, we need to find the z-score that corresponds to a cumulative probability of 0.06. Looking at the normal distribution table, we find that the closest value is 1.55.
So, we can solve for the score by rearranging the formula as x = z * σ + μ. Plugging in the values, we get:
x = 1.55 * 5.75 + 18.5 = 27.7125
It's important to note that this calculation is based on the assumption that the distribution of ACT math scores follows the normal model with a mean of about 18.5 and a standard deviation of about 5.75. In reality, the distribution may not be exactly normal, and the mean and standard deviation may vary depending on the sample of test takers.
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What is the y-intercept of the line represented by -2x + y = 4?
Answers
the t value for a 98% confidence level with a sample standard deviation and 52 degrees of freedom is -
Answers
The t-value for a 98% confidence level with a sample standard deviation and 52 degrees of freedom is 2.03.
To calculate the t value for a 98% confidence level with a sample standard deviation and 52 degrees of freedom, we used the t-distribution table. The t-distribution table has two variables: degree of freedom and confidence level.
The first step was to locate the row in the table that corresponds to the given degrees of freedom (df=52). The next step was to locate the column in the table that corresponds to the given confidence level (98%). the t -value for the given df and CL was located at the intersection of the row and column, which is -2.03. essentially the t-distribution table provides a range of values for the amount of variability that is expected within a given sample.
The t-value is the point within the range that will represent the 98% confidence level for the sample with 52 degrees of freedom. the t-value of -2.03 indicates that the sample has a 9.8% chance of falling within a range of values that is two standard deviations away from the mean.
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The measure θ of an angle in standard position is given. -45°
b. Find the exact values of cos θ and sin θ for each angle measure.
Answers
The exact values of cos(-45°) and sin(-45°) are √2/2 and -√2/2 respectively. To find the exact values of cosine (cos θ) and sine (sin θ) for an angle measure θ in standard position, we can use the unit circle.
The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane.
For an angle of -45°, we can determine its position on the unit circle and find the corresponding values of cos θ and sin θ.
To start, let's convert -45° to radians. Since 1 revolution is equal to 360°, we can calculate the equivalent angle in radians by multiplying -45° by (π/180) to get:
θ = -45° × (π/180) = -45π/180 = -π/4 radians
Now, let's determine the position of the angle -π/4 radians on the unit circle:
1. The angle -π/4 radians is located in the fourth quadrant, as it has a negative angle measure.
2. The reference angle for -π/4 radians is π/4 radians, which is the positive acute angle between the terminal side of the angle and the x-axis.
3. The point on the unit circle corresponding to π/4 radians is (√2/2, -√2/2). This means that the x-coordinate is √2/2, and the y-coordinate is -√2/2.
Therefore, for θ = -45° (or -π/4 radians), the exact values of cos θ and sin θ are:
cos θ = √2/2
sin θ = -√2/2
So, cos(-45°) = √2/2 and sin(-45°) = -√2/2.
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What is the output of the following command, given that value1 = 2.0 and value2 = 12
Answers
if value1 = 2.0 and value2 = 12, then the output of a following command = 24.0
The correct option is A.
Briefing:The output of the given document is issued is 24.0 (2.0 * 12=24, i.e., it is simply the multiplication operation) if both values, i.e., value 1 and value 2, are taken into consideration as decimal data type values.
A simple data type is what, exactly?There is only one value represented by simple data types. Integer: a basic data type used in the creation of policies. A positive or negative whole number is represented by the integer data type. 0, 1, 2, 3, and 4 are examples of integers.
Why do we employ data types?An attribute of data that instructs a computer system how to interpret its value is called the data type. Knowing the different types of data makes it possible to collect information in the desired format and ensure that the values of each property are as expected.
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I understand that the question you are looking for is:
What is the output of the following command, given that value1 = 2.0 and value2 = 12? print (value+ value2)
A) 24.0
B) value + value2
C) 24
D) 2.0 + 12
7.1 divided by 312.755
Answers
answer 0.0227014756
Step-by-step explanation:
or if you meant 312.775/7.1 it's 44.0528169
The Dallas Cowboys have a season ticket membership deal. If you join the club for $300 then tickets cost $50 each. If you aren't in the
club tickets are $100 each. How many tickets must be purchased for the cost of club members and non-members to be equal?
Tickets =
Answers
Answer:
7 tickets?
Step-by-step explanation:
srry if its wrong. i suck at math
Besides being simple for its own sake, what other advantage do simple models usually have?
a) Higher accuracy
b) Greater complexity
c) Easier interpretation
d) More detailed predictions
Answers
The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.
This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.
Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.
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When is it most appropriate to use completing the square method to solve a quadratic equation?
Answers
Answer:
It's best to use the completing the square method to solve a quadratic when the coefficient of the squared term is 1 and the coefficient of the linear term is even.
a light is on the ground 30 \text{ m} from a building. a man 1.85 \text{ m} tall walks from the light directly toward the building at 1.5\text{ m/s.} what is the rate of change of the length of his shadow on the building when he is 10 \text{ m} from the building? please enter your answer in decimal format with three significant digits after the decimal point.
Answers
The rate of change of the length of the man's shadow on the building when he is 10 m from the building is approximately -0.278 m/s
How to determine rate of change of the length?The rate of change of the length of the man's shadow on the building when he is 10 m from the building can be found by first setting up a proportion using similar triangles.
Here are the steps:
Set up a proportion using similar triangles:
(height of man) / (distance from light to man) = (length of shadow) / (distance from light to building)
Plug in the given values:
(1.85 m) / (10 m) = (length of shadow) / (30 m)
Solve for the length of shadow:
Length of shadow = 1.85 m x 30 m / 10 m = 5.55 m
Differentiate the proportion equation with respect to time (t) to find the rate of change of the shadow length (dS/dt):
d(height of man) / d(time) / d(distance from light to man) / d(time)
= d(length of shadow) / d(time) / d(distance from light to building) / d(time)
Since the height of the man and the distance from the light to the building are constants, their derivatives with respect to time are 0.
The rate of change of the distance from the light to the man is -1.5 m/s (negative because the man is walking toward the light).
Plug in the values:
0 / (-1.5 m/s) = (dS/dt) / 0
Solve for the rate of change of the shadow length (dS/dt):
dS/dt = -1.5 m/s x (5.55 m / 30 m) = -0.2775 m/s
So, the rate of change of the length of the man's shadow on the building when he is 10 m from the building is approximately -0.278 m/s (rounded to three significant digits after the decimal point).
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The value of a car, V, in dollars, t years after it is purchased is given by V = -1800t + 20,000.Your entry must contain the following:What is the y-intercept and what does it represent?What is the slope? What does it mean in the context of the problem?When will the car be worth $11,000?Using complete sentences, explain why this is important information for you to know.
Answers
Step-by-step explanation:
Given the equation, V = -1800t + 20,000, where:
V = the value of a car in dollars
t = the number of years after the car's purchase
The y-intercept in the given equation is 20,000, which represents the initial value of the car. It is at this point where t = 0, representing the same time as the car was purchased.
The slope is -1800, which represents the amount for which the car depreciates in value.
In order to determine the time, t, will be worth $11,000, we must substitute its value into the variable, V.
V = -1800t + 20,000
$11,000 = -1800t + 20,000
Subtract 20,000 from both sides:
$11,000 - 20,000 = -1800t + 20,000 - 20,000
- $9,000 = -1,800t
Divide both sides by -1,800 to solve for t:
\(\frac{-9,000}{-1800} = \frac{-1800t}{-1800}\)
t = 5
Therefore, the car will be worth $11,000 in 5 years. Understanding these types of information allows us to evaluate our finances and make informed purchase decisions. Certain types of assets such as cars and equipment tend to depreciate (or decrease) in value over time, while investing in a Certificate of Deposits (CDs) tends to appreciate (or increase) in value over time.
Help! I'm not doing so well in my math class. :(
Answers
Answer:
one solution, x= -4
Step-by-step explanation:
Answer:
One solution, x = -4
Step-by-step explanation:
6x + 32 = -2x -- Minus 6x from both sides
32 = -8x -- Divide -8 on both sides
-4 = x
What is the product of 3500 and 5.6 x 10^4 expressed in scientific notation?
PLSSSS HELP
Answers
Answer:
Your answer is 196000000
Step-by-step explanation:
The product of 3500 and 5.6 x 10⁴ in scientific notation will be;
⇒ 19.6 × 10⁷
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
⇒ 3500 × 5.6 × 10⁴
Now,
Since, The expression is,
⇒ 3500 × 5.6 × 10⁴
After multiply, we get;
⇒ 19,600 × 10⁴
⇒ 19.6 × 10³ × 10⁴
⇒ 19.6 × 10⁷
Thus, The product of 3500 and 5.6 x 10⁴ in scientific notation = 19.6 × 10⁷
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Mr. Davis rented a car for $29 per day plus $0.15 per mile. If he kept the car for 3 days and drove 180 miles, what was his total rental cost?
Answers
Answer:
87 || 2,700 || 2,787
Step-by-step explanation:
29x3=87
180x15=2,700
2,700+87=2,787
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer:
looking at the screenshot! it can be a or b
Step-by-step explanation:
Pls help! Will give brainliest
Answers
Answer:
a = 1, b = -9, c = 14; Solutions = 2,7
Step-by-step explanation:
x² has a coefficient of 1
-9x has a coefficient of -9
14 has a coefficient of 14 (Pretty obvious)
Factor the equation:
(x-2)(x-7) = 0
x = 2,7
17 points please help
Answers
Answer:
3% of the figure is shaded
Fraction: 3/10
Decimal: 0.3
Hope this helped
The diameter of the wheel of a unicycle is 0.6m. lisa tries to ride the unicycle and manages to go in a straight line for 30 full revolutions before falling off. how far did lisa manage to cycle in metres? give your answer rounded to 1 dp.
Answers
Total distance travelled by lisa before falling off is 56.52 m
What is circumference of circle?The circumference of a circle is the straight-line distance around it. In other words, if you open a circle and draw a straight line, the length of that line will be the perimeter. The perimeter is the total distance around the circle. Then find the perimeter using the formula C = 2πr.
Given,
Unicycle wheel diameter = 0.6 m
Unicycle wheel radius = 0.3 m
Number of revolutions before falling = 32
Circumference (C) = 2 x Pi x Radius
= 2 × π × r
= 2 × 3.14 × 0.3
= 1.884 m
Distance travelled by lisa = 30 × 1.884
= 56.52 m
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Sooo my math teacher who’s a pain in the behind was the only one gave us homework while we’re out for and extended 1 day so if you would please help me bc I have to go back and turn this in tomorrow, please and thank you :/ (just 8-16)
Answers
Answer:ok??/????????
Step-by-step explanation:Whaaaaat?????
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of inequalities.
yx2 , z0
xz2 , -5y0
Answers
The set of points in space that satisfy the given pairs of inequalities can be described geometrically as follows: The inequality y ≤ x^2 represents a parabolic region in the x-y plane where the y-coordinate is less than or equal to the square of the x-coordinate. This corresponds to a downward-opening parabola that opens towards the negative y-axis.
The inequality z ≥ 0 represents the region above the xy-plane, including the xy-plane itself. This is a half-space extending upwards from the xy-plane.
The inequality x ≥ z^2 represents a region in the x-z plane where the x-coordinate is greater than or equal to the square of the z-coordinate. This corresponds to a sideways-opening parabola that opens towards the positive x-axis.
The inequality -5 ≤ y ≤ 0 represents a vertical range of values for the y-coordinate between -5 and 0, inclusive. This corresponds to a segment on the negative y-axis between y = -5 and y = 0.
By combining these geometric descriptions, the set of points in space satisfying both pairs of inequalities is the region that lies below the parabolic surface, above or on the xy-plane, and to the right of the sideways-opening parabola, within the specified range on the negative y-axis. It is a three-dimensional region that can be visualized as a solid bounded by these surfaces.
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Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of inequalities.
yx2 , z0
xz2 , -5y0
one angle of a triangle measures 35°. A second angle measures (3x)°, and the third angle measures 2x - 20)°. what is the value of x?
Answers
Answer:
x = 33
Step-by-step explanation:
Sum of the angles in a triangle is 180 so,
35 + 3x + 2x - 20 = 180
35 + 5x - 20 = 180
15 + 5x = 180
5x = 180 - 15
x = 165/5
x = 33
urgente porfa 50 PUNTOS POR LAS 3 FICHAS
Answers
You dont deserve answers if ur gonna do that to other people.