A. 8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
B. ∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)
C. the mass of the solid 8 enclosed within the sphere is approximately 8.378.
(a) Using the conversion formulas for spherical coordinates, we have:
x = p sin(phi) cos(theta)
y = p sin(phi) sin(theta)
z = p cos(phi)
Substituting these expressions into the given density function, we get:
8(x, y, z) = 8(p sin(phi) cos(theta), p sin(phi) sin(theta), p cos(phi))
= 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
Therefore, the density 8 as a function of spherical coordinates is:
8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)
(b) Since the solid 8 is enclosed within a sphere of radius 1 centred at 2 the origin, we have:
0 ≤ p ≤ 1
0 ≤ theta ≤ 2π
0 ≤ phi ≤ π
Therefore, the bounds of integration in spherical coordinates are:
∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)
(c) Evaluating the triple integral using a computer algebra system or numerical integration, we get:
M = 8π/3
Therefore, the mass of the solid 8 enclosed within the sphere is approximately 8.378.
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Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4). Determine whether or not triangle PQR is a right triangle. Show all calculations for full credit.
Will give Brainliest! No links! Will report
Triangle PQR is not a right triangle.
To determine whether triangle PQR is a right triangle, we need to check if any of its angles is a right angle (90 degrees). We can use the slope formula to find the slopes of the sides of the triangle and check if any of the slopes are negative reciprocals (perpendicular) to each other.
Let's calculate the slopes of the sides PQ, QR, and RP:
Slope of PQ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 1) / (3 - 0)
= 1 / 3
Slope of QR = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 2) / (5 - 3)
= -6 / 2
= -3
Slope of RP = (y₂ - y₁) / (x₂ - x₁)
= (1 - (-4)) / (0 - 5)
= 5 / (-5)
= -1
Now, let's check if any of the slopes are negative reciprocals of each other. We can compare the products of the slopes:
Product of PQ slope and QR slope = (1/3) * (-3) = -1
Product of QR slope and RP slope = (-3) * (-1) = 3
Product of RP slope and PQ slope = (-1) * (1/3) = -1/3
Since the product of the slopes of QR and RP is not equal to -1, triangle PQR is not a right triangle.
Therefore, triangle PQR is not a right triangle.
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TRUE or FALSE:
1. Each exterior angle of a regular hexagon is acute
2. The sum of the interior angles of a polygon is not necessarily a multiple of 180
3. In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle
1. The statement "Each exterior angle of a regular hexagon is acute" is True.
2. The statement "The sum of the interior angles of a polygon is always a multiple of 180" is False.
3. The statement "In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle" is True.
1. TRUE: Each exterior angle of a regular hexagon is acute.
A regular hexagon has six equal sides and six equal interior angles. The sum of the interior angles of a hexagon is (6-2) * 180 = 720 degrees. Since it's a regular hexagon, each interior angle is 720/6 = 120 degrees. The exterior angles are supplementary to the interior angles, so each exterior angle is 180 - 120 = 60 degrees. Since 60 degrees is less than 90 degrees, each exterior angle is acute.
2. FALSE: The sum of the interior angles of a polygon is always a multiple of 180.
The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of vertices (or sides). As you can see, the result is always a multiple of 180.
3. TRUE: In any polygon, the larger the number of vertices, the smaller the measure of an exterior angle.
For a regular polygon, the measure of an exterior angle can be calculated as 360/n, where n is the number of vertices (or sides). As the number of vertices increases, the measure of an exterior angle decreases, since they are inversely proportional.
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30 POINTS!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!
If the measure of arc QR is 40 degrees, what is the measure of angle PQR?
The measure of angle PQR is 20 degrees.
We have,
The measure of angle PQR can be found by using the property that the measure of an inscribed angle is half the measure of its intercepted arc.
Given that the measure of arc QR is 40 degrees, we can conclude that the measure of angle PQR is half of that, which is:
The measure of angle PQR = 1/2 x Measure of arc QR
= 1/2 x 40 degrees
= 20 degrees
Therefore,
The measure of angle PQR is 20 degrees.
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Find the area k of the trianglea = 3, c = 2, b = 135 degrees
The area k of the triangle a = 3, c = 2, b = 135 degrees is approximately 1.06125 square units.
The area k of the triangle, we can use the formula:
k = (1/2) * b * c * sin(A)
where A is the angle opposite side a.
Find A, we can use the fact that the angles in a triangle add up to 180 degrees:
A + B + C = 180
Substituting in the given values, we get:
A + 135 + 180 = 360
A = 45 degrees
Now we can plug in all the values into the area formula:
k = (1/2) * 2 * 3 * sin(45)
k = 1.5 * 0.707
k = 1.06125
Therefore, the area k of the triangle is approximately 1.06125 square units.
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What is one more solution to the following. i already have the first solution which is x=9 but there is one more.
let f (x) = log3(x) + 3 and g(x) = log3(x3) – 1.
part a: if h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points)
part b: determine the solution to the system of nonlinear equations.
( i already have the answer to part a as well it should be log3(x^4)+2) i just need the last solution to part b) also im using all my points for this so ya:) have a nice day!
The solutions to the system of nonlinear equations are
x = 9 and x =[tex]3^2[/tex]= 9.
What is the solution to the system of nonlinear equations:f(x) = g(x), where f(x) = log3(x) + 3 and g(x) = log3(x^3) – 1?
To determine the solution to the system of nonlinear equations:
f(x) = g(x)
We can substitute the given expressions for f(x) and g(x) and simplify:
log3(x) + 3 =[tex]log3(x^3) - 1[/tex]
Using the properties of logarithms, we can simplify this equation as follows:
log3(x) + 3 = 3*log3(x) - 1
4 = 2*log3(x)
2 = log3(x)
x =[tex]3^2[/tex]
Therefore, the solutions to the system of nonlinear equations are x = 9 and [tex]x = 3^2 = 9.[/tex]
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Jenny and Kera are playing a game. Jenny has -10 points and loses 5 more points. How many points does Jenny have now? Kera has 22 points and loses 14 points. How many points does Kera have now? Make sure that you type each name with her current score
The current scores of both Jenna and Kera in the game they were playing are
Jenny's current score is -15.
Kera's current score is 8.
How many points does Jenny have now?In the given problem, we are given two players, Jenny and Kera, playing the game.
Jenny has -10 points, which means she already has negative points. He has since lost 5 more points. So his current score would be:
-10 - 5 = -15
So now Jenny has a score of -15.
Kera, meanwhile, has 22 points and 14 points to lose. So his current score would be:
22 - 14 = 8
So now Kera has 8 points.
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How do I do this step by step
Answer:
Step-by-step explanation:
Let's call the total volume of the container "V".
We know that the container was originally 15% full, so the amount of water in the container was 0.15V.
When 48 litres of water was added, the new volume of water in the container became 0.15V + 48.
We also know that the container is now 75% full, so the new volume of water in the container must be 0.75V.
We can set up an equation to solve for V:
0.15V + 48 = 0.75V
Subtracting 0.15V from both sides:
48 = 0.6V
Dividing both sides by 0.6:
V = 80
So the container can hold 80 litres of water when it is full.
In a certain triangle, one angle has a measure of 42° and another angle has a measure of 96°. If the triangle is isosceles, then which of the following could be the measure of the third angle?
A.
60°
B.
42°
C.
96°
D.
69°
If the triangle is isosceles, then the measure of the third angle could be 42 degrees
Which could be the measure of the third angle?From the question, we have the following parameters that can be used in our computation:
One angle has a measure of 42° Another angle has a measure of 96°.The sum of angles in a triangle is 180 degrees
If the triangle is isosceles, then we have the following possible sum of angles
Sum 1 = 42 + 96 + 96 = 234 -- false
Sum 1 = 42 + 96 + 42 = 180 -- true
Hence, if the triangle is isosceles, then the measure of the third angle could be 42 degrees
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The following graph shows a proportional relationship.
What is the constant of proportionality between
�
yy and
�
xx in the graph?
The constant of proportionality between y and x in the graph is 3
What is the constant of proportionality between y and x in the graph?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings
(x, y) = (1, 3)
Using the above as a guide, we have the following:
The constant of proportionality between y and x in the graph is
k = y/x
substitute the known values in the above equation, so, we have the following representation
k = 3/1
Evaluate
k = 3
Hence, the constant of proportionality between y and x in the graph is 3
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In 2010, Little Elm had 3646 residents. Five years later, they had 17,150 residents. If the population grows at this rate, about how many residents will the town have in 2020? Include explanation.
A. 20,800
B. 27,000
C. 30,700
D. 35,400
PLS DON'T PUT LINKS AND WRITE ANSWER, THX! I WILL MARK BRAINLIEST IF YOU WRITE THE ANSWER!
The answer is option C) 30,700
Why the answer is option C?The problem involves using linear interpolation to estimate the population of Little Elm in 2020 based on the given data from 2010 and 2015.
To start, we need to calculate the annual growth rate of the population between 2010 and 2015. This can be done by taking the difference between the population in 2015 and the population in 2010, and then dividing that difference by the number of years in that time period:
Annual growth rate = (17,150 - 3,646) / 5 = 2,700
This means that, on average, the population of Little Elm grew by 2,700 people per year between 2010 and 2015.
Next, we can use this annual growth rate to estimate the population of Little Elm in 2020. To do this, we need to add 10 years of growth to the initial population of 3,646 (since we want to estimate the population in 2020, which is 10 years after 2010):
Estimated population in 2020 = 3,646 + (2,700 x 10) = 30,646
Therefore, the estimated population of Little Elm in 2020 is approximately 30,700, which corresponds to answer choice C.
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A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test.
Change: Final Blood Pressure - Initial Blood Pressure
The researcher wants to know if there is evidence that the drug affects blood pressure. At the end of 4 weeks, 36 subjects in the study had an average change in blood pressure of 2. 4 with a standard deviation of 4. 5.
Find the
p
-value for the hypothesis test
The p-value for the hypothesis test is 0.04. This means that if the null hypothesis is true
To find the p-value, we need to conduct a hypothesis test.
The null hypothesis is that there is no difference in blood pressure before and after taking the medication:
H0: μd = 0
The alternative hypothesis is that there is a difference in blood pressure before and after taking the medication:
Ha: μd ≠ 0
where μd is the population mean difference in blood pressure before and after taking the medication.
We are given that the sample size is n = 36, the sample mean difference is ¯d = 2.4, and the sample standard deviation is s = 4.5.
We can calculate the t-statistic as:
t = (¯d - 0) / (s / sqrt(n)) = (2.4 - 0) / (4.5 / sqrt(36)) = 2.13
Using a t-distribution table with 35 degrees of freedom (df = n - 1), we find that the two-tailed p-value for t = 2.13 is approximately 0.04.
Therefore, the p-value for the hypothesis test is 0.04. This means that if the null hypothesis is true (i.e., if there is really no difference in blood pressure before and after taking the medication), there is a 4% chance of observing a sample mean difference as extreme or more extreme than 2.4. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence that the drug affects blood pressure.
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Please help!
An airplane is approaching Seattle International Airport. The pilot begins a 13 degree angle of d scent starting from a height of 500 feet. How far from the airport is the plane? Round to the nearest tenth.
We get that the plane is about 2193.0 feet from the airport, Rounding to the nearest tenth
To solve the problem, we will use trigonometry and the tangent function, which relates the other facet of a right triangle to the adjoining aspect:
tan(theta) = opposite / adjacent
wherein theta is the angle of descent, opposite is the change in height, and adjacent is the space from the airplane to the airport.
Rearranging the formula, we get:
adjacent = contrary / tan(theta)
because the angle of descent is 13 ranges and the alternate in height is from 500 ft, we've got:
contrary = 500 ft
theta = 13 stages
Substituting these values into the formula, we get:
adjacent = 500 ft / tan(13 ranges)
using a calculator, we find that tan(13 stages) is about 0.228, so:
adjacent = 500 feet / 0.228 = 2192.98 feet
Therefore, we get that the plane is about 2193.0 feet from the airport.
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How to get 51 by using all four numbers 8 5 6 7 once.
To get 51 using the numbers 8, 5, 6, and 7 exactly once each, you can use the following mathematical expression:
(8 x 6) - 7 + 5 = 51
How it works:
1. Multiply 8 by 6 to get 48: (8 x 6) = 48
2. Subtract 7 from 48 to get 41: 48 - 7 = 41
3. Add 5 to 41 to get 51: 41 + 5 = 51
Therefore, (8 x 6) - 7 + 5 = 51.
Answer:
Step-by-step explanation:
8 x (7 - 5) + 6 = 51
A magic square is shown below. Every row, column and long diagonal adds to the same total. Each number can only be used once. Copy the magic square into your book and complete it using the numbers provided. 2 Numbers to use 3 -1 0 3 X 2 4 Magic square -3 2 1 -4 -2
Answer:
Here is the complete magic square:
-3 4 -1
2 0 -2
1 -4 3
Every row, column, and long diagonal adds to 0.
6(5-4x) < 54
solve the inequality
i hope this helps you.
Kika and Mato each took out a loan for $5,000 from the bank. Kika has an interest rate of 5. 2%, and he plans to repay the loan in 5 years. Mato has an interest rate of 7. 5%, and he plans to repay the loan in 24 months. Who will pay more in interest, and about how much more will he pay?
A:Kika; $300
B:Kika; $700
C:Mato; $700
D:Mato; $300
Mato will pay about $700 more in interest than Kika ($625 - $1,300 = $675, which rounds to $700). The answer is C: Mato; $700
Mato will pay more in interest because he has a higher interest rate and a shorter repayment period. To calculate the amount of interest each will pay, we can use the formula:
Interest = (Loan amount) x (Interest rate) x (Time in years)
For Kika:
Interest = $5,000 x 0.052 x 5
Interest = $1,300
For Mato:
Interest = $5,000 x 0.075 x (2/12)
Interest = $625
Therefore, Mato will pay about $700 more in interest than Kika ($625 - $1,300 = $675, which rounds to $700). The answer is C: Mato; $700.
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Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet.
n/360=115/225
n=162. 35
Round to the nearest tenth.
The area should equal ______ft2.
It appears to be setting up a proportion between the central angle of the sector and the ratio of arc length to the circumference of the circle, rather than the ratio of the central angle to the full angle of the circle. Then the area should equal to 126.9 [tex]ft^2.[/tex]
To find the area of sector XZY, we need to know the measure of angle XYZ. However, the given equation n/360 = 115/225 is incorrect, as it appears to be setting up a proportion between the central angle of the sector and the ratio of arc length to the circumference of the circle, rather than the ratio of the central angle to the full angle of the circle.
To find the correct measure of angle XYZ, we need to use the formula:
Area of sector XZY = (n/360) x π[tex]r^2[/tex]
where r is the radius of circle Z.
We know that the area of circle Z is 255 square feet, so we can find the radius as follows:
Area of circle Z = π[tex]r^2[/tex]
255 = π[tex]r^2[/tex]
[tex]r^2[/tex] = 81
r = 9
Now we can solve for n using the given ratio of 115/225:
n/360 = 115/225
n = (115/225) x 360
n = 184.32
Rounding to the nearest tenth, we get:
n ≈ 184.3
Finally, we can find the area of sector XZY as:
Area of sector XZY = (n/360) x π[tex]r^2[/tex]
Area of sector XZY = (184.3/360) x π[tex](9)^2[/tex]
Area of sector XZY ≈ 126.9 [tex]ft^2[/tex]
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(4,7);y=3x+6
Write an equation passing through the point and parallel to the given line.
The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".
In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.
The given line ""y = 3x + 6" has a slope of 3,
So, the "parallel-line" we want to find must also have a slope of 3.
Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),
where m is slope and (x₁, y₁) is a point on the line,
So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:
⇒ y - 7 = 3(x - 4),
⇒ y - 7 = 3x - 12,
⇒ y = 3x - 5
Therefore, the equation of the required line is y = 3x - 5.
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How to find the area of this whole figure? Please help me
The area of the whole figure is 31.5 sq. units.
What is the area of a figure?The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.
From the given question, the figure given can be likened to a rhombus. So that;
area of a rhombus = (diagonal 1 * diagonal 2)/ 2
Then,
area of the figure = (diagonal 1 * diagonal 2)/ 2
where: diagonal 1 = 7.5, and diagonal 2 = 8.4
So that;
area of the figure = (7.5*8.4)/ 2
= 63/ 2
= 31.5
The area of the whole figure is 31.5 sq. units.
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what two double inequalities define shaded region
The calculated two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2
Determining the two double inequalities that define shaded regionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following properties
Shaded region is between y = 1 and y = 5 (exclusive of y = 5)Shaded region is between x = -3 and x = 2 (exclusive of y = 5)Using the above as a guide, we have the following:
1 ≤ y < 5
-3 < x ≤ 2
Hence, the two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2
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The function R = 73. 3*/M3, known as Kielber's law, relates the basal metabolic rate R In Calories per day
burned and the body mass M of a mammal In kilograms.
a. Find the basal metabolic rate for a 180 kilogram lion. Then find the formula's prediction for a 80
kilogram human. If necessary round down to the nearest 50 Calories.
b. Use your metabolic rate result for the lion to find what the basal metabolic rate for a 80 kllogram
human would be if metabolic rate and mass were directly proportional. Compare the result to the result
from part a.
a. Kleiber's law for lion
Calories
Kleiber's law for humans
Calories
b. If metabolic rate and mass were directly proportional
Calories
If the metabolic rate were directly proportional to mass, then the rate for a human would be
(select)
than the actual prediction from Kleiber's law. Kleiber's law Indicates that smaller
organisms have a (select) v metabolic rate per kilogram of mass than do larger organisms.
The estimate from direct proportionality is higher than the prediction from KLEIBER's law.
a. For a 180 kilogram lion, we can use KLEIBER's law: R = 73.3*(180^0.75) = 6136.5 Calories per day. For an 80 kilogram human, we can use the same formula: R = 73.3*(80^0.75) = 1537.6 Calories per day.
b. If metabolic rate and mass were directly proportional, we could use the ratio of the masses to find the basal metabolic rate for an 80 kilogram human.
The ratio of the masses is 80/180 = 0.44. We can multiply this by the basal metabolic rate for the lion to get an estimate for the human: 0.44*6136.5 = 2701.26 Calories per day.
This estimate is higher than the prediction from Kleiber's law for an 80 kilogram human (1537.6 Calories per day). KLEIBER's law indicates that smaller organisms have a higher metabolic rate per kilogram of mass than do larger organisms.
Therefore, the estimate from direct proportionality is higher than the prediction from KLEIBER's law.
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First one gets brainlist
the average january surface water temperatures (°c) of lake michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34.
the mean value of these temperatures is 4.312.
what is the variance of this data set?
The variance of the data set is 0.318652.
To find the variance of this data set, we need to use the formula:
variance = Σ(x - μ)² / n
Where Σ represents the sum, x is the value of each data point, μ is the mean value, and n is the number of data points.
Using this formula, we can calculate the variance as follows:
Variance = [(5.07 - 4.312)² + (3.57 - 4.312)² + (5.32 - 4.312)² + (3.19 - 4.312)² + (3.49 - 4.312)² + (4.25 - 4.312)² + (4.76 - 4.312)² + (5.19 - 4.312)² + (3.94 - 4.312)² + (4.34 - 4.312)²] / 10
Variance = [0.225769 + 0.449769 + 0.370656 + 1.323856 + 0.716164 + 0.006544 + 0.175684 + 0.382884 + 0.135556 + 0.000484] / 10
Variance = 3.18652 / 10
Variance = 0.318652
Therefore, the variance of the data set is 0.318652.
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In circle K with \text{m} \angle JKL= 90m∠JKL=90, find the \text{m} \angle JMLm∠JML
The measure of angle JML is 180 degrees because in a circle, an angle formed by two chords intersecting inside the circle.
How to find the measurement of angle?In a circle, the measurement of angle formed by two chords intersecting inside the circle is half the sum of the arcs intercepted by the angle. Using this property, we can find the measure of angle JML.
Since angle JKL is a right angle, its intercepted arc is the diameter of the circle. Therefore, its measure is 180 degrees.
By the same property, we know that angle JML is half the sum of the arcs intercepted by it. The arcs intercepted by angle JML are arcs JL and KM.
Since angle JKL is a right angle, arc JL is also 180 degrees.
Since J, K, L, and M are concyclic, we know that angle JKM is supplementary to angle JLM. Therefore, arc KM is the supplement of arc JL and has measure 360 - 180 = 180 degrees.
Thus, the sum of the intercepted arcs is 180 + 180 = 360 degrees, and angle JML is half of this, so its measure is 180 degrees.
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How many sides does a regular n-gon have if one interior angle measures 150°? Show all work!
Answer:
A regular n-gon with one interior angle of 150° has 12 sides.
Step-by-step explanation:
The formula for the measure of each interior angle of a regular n-gon is:
180(n-2)/nwhere:
n is the number of sidesWe are given that one interior angle measures 150°, so we can set up the equation:
180(n-2)/n = 150Multiplying both sides by n, we get:
180(n-2) = 150nDistributing, we get:
180n - 360 = 150nSubtracting 150n from both sides, we get:
30n - 360 = 0Adding 360 to both sides, we get:
30n = 360Dividing both sides by 30, we get:
n = 12Therefore, a regular n-gon with one interior angle of 150° has 12 sides.
A company operates two plants which manufacture the same item and whose total cost functions areC1=6.7+0.03(q1)² and C2=7.9+0.04(q2)²,where q1 and q2 are the quantities produced by each plant. The company is a monopoly. The total quantity demanded, q=q1+q2, is related to the price, p, byp=40−0.04q.How much should each plant produce in order to maximize the company's profit? Q1= Q2=
Each plant should produce 576.92 units and 384.61 units respectively to maximize the company's profit.
To maximize the company's profit, we need to find the quantity that maximizes the difference between the total revenue and the total cost. The total revenue is given by:
TR = pq
= (40 - 0.04q)(q1 + q2)
= 40q1 + 40q2 - 0.04[tex]q1^2[/tex]- 0.04[tex]q2^2[/tex] - 0.04q1q2
The total cost is given by:
TC = C1 + C2
[tex]= 6.7 + 0.03q1^2 + 7.9 + 0.04q2^2= 14.6 + 0.03q1^2 + 0.04q2^2[/tex]
The profit is given by:
π = TR - TC
= [tex]40q1 + 40q2 - 0.04q1^2 - 0.04q2^2 - 0.04q1q2 - 14.6 - 0.03q1^2 - 0.04q2^2[/tex]
Simplifying, we get:
π = [tex]40q1 + 40q2 - 0.04q1^2 - 0.04q2^2 - 0.04q1q2 - 14.6 - 0.03q1^2 - 0.04q2^2[/tex]
= [tex]-0.03q1^2 - 0.04q2^2 - 0.04q1q2 + 40q1 + 40q2 - 14.6[/tex]
To maximize profit, we need to take the partial derivatives of the profit function with respect to q1 and q2 and set them equal to zero:
∂π/∂q1 = -0.06q1 - 0.04q2 + 40 = 0
∂π/∂q2 = -0.08q2 - 0.04q1 + 40 = 0
Solving these equations simultaneously, we get:
q1 = 576.92
q2 = 384.61
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Construct angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm ii, Construct M the midpoint of XZ where XYZ= 60o
Holly cuts 6 ribbons into fifths for a craft project.
1
how many --size ribbons does she have?
5
holly has
one-fifth-size ribbons.
If Holly cuts 6 ribbons into fifths for her craft project, after cutting, she has a total of 30 one-fifth-size ribbons (6 ribbons x 5 cuts each).
Holly has cut 6 ribbons into fifths for her craft project. This means that she has a total of 30 ribbons, each with a size of one-fifth. To understand this better, we can break it down into fractions. Each ribbon is one-fifth of a whole ribbon, and since Holly has cut 6 ribbons, she has 6 times one-fifth, which equals 30. So, to answer the question, Holly has 30 ribbons, each with a size of one-fifth. These ribbons can be used for various crafts, such as creating bows, wrapping presents, or decorating cards. The possibilities are endless, and with 30 ribbons, Holly can get creative and make a lot of beautiful crafts.
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if an airplane travels around the world, flying just above the equator it would travel 1.25 x 10^4 miles. How many miles would a plane travel if it flew around the world just above the equator 3 1/2 times?
(in standard form)
A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.
If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:
1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles
To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.
We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.
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Solve for 2x+y=10
3x=y
Answer:
x=2
Step-by-step explanation:
2x+y=10
3x=y
2x+3x=10
5x=10
x=2
Buy-Rite Pharmacy has purchased a small auto for delivering prescriptions. The auto was purchased for $26,000 and will have a 6-year useful life and a $5,500 salvage value. Delivering prescriptions (which the pharmacy has never done before) should increase gross revenues by at least $33,500 per year. The cost of these prescriptions to the pharmacy will be about $28,000 per year. The pharmacy depreciates all assets using the straight-line method. The payback period for the auto is closest to (Ignore income taxes. ): (Round your answer to 1 decimal place. )
The payback period for the auto is approximately 8 years.
Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.
Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.
To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.
The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.
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