The first four nonzero terms are 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8
To find the first 4 nonzero terms of the Taylor series for the function f(t) = e^(t)cos(t) about 0,
we can use the known Taylor series for e^(t) and cos(t).
Taylor series:
The Taylor series for e^(t) is:
e^(t) = 1 + t + (t^2)/2! + (t^3)/3! + ...
And the Taylor series for cos(t) is:
cos(t) = 1 - (t^2)/2! + (t^4)/4! - (t^6)/6! + ...
To find the Taylor series for f(t) = e^(t)cos(t), we can multiply these two series together using the distributive property of multiplication. We get:
f(t) = (1 + t + (t^2)/2! + (t^3)/3! + ...) * (1 - (t^2)/2! + (t^4)/4! - (t^6)/6! + ...)
Expanding this out, we get:
f(t) = 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8 + (t^5)/15 - (t^6)/72 - ...
The first 4 nonzero terms of this series are:
f(t) = 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8 + ...
So, the first 4 nonzero terms of the Taylor series for f(t) = e^(t)cos(t) about 0 are:
1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8
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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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30 % of a number is 14.99 . Set up an equation and solve to find the original number
Answer:
The original number is approximately 49.97.--------------------
Let the original number be n.
We are given that 30% of n is 14.99.
Set up an equation to reflect this relation:
30% of n = 14.99Solve it for n:
0.3*n = 14.99n = 14.99/0.3n = 49.97 (rounded)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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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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Chris buys 19 raffle tickets. A total of 250 tickets were sold. Find the probability that Chris does not win the prize
Answer:For 19 to 250 odds against winning;
Probability of:
Winning = (0.9294) or 92.9368%
Losing = (0.0706) or 7.0632%
"Odds for" winning: 250:19
"Odds against" winning: 19:250
Step-by-step explanation:
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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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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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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You can use the formula V = lwh to find the volume of a box.
a. Write a quadratic equation in standard form that represents the volume of the box.
b. The volume of the box is 6 ft3. Solve the quadratic equation for x.
c. Use the solution from part (b) to find the length and width of the box.
Describe any extraneous solutions
Write the quadratic equation in standard form that represents the volume of the box:[tex]w^2 - 6w = 0[/tex]
Find the length, width, height a box with volume of 6 [tex]ft^3[/tex], given the formula V = lwh.Solve the quadratic equation for x and find the length and width of the box:
w(w - 6) = 0 (factor the quadratic)
w = 0 or w = 6 (apply the zero product property)
Since a box can't have a width of 0, we reject the solution w = 0.
So, the only solution is w = 6.
To find the length, we use the formula l = V/wh:
l = 6/(6h) = 1/h
The length depends on the value of h, but we can choose h = 1/6 ft to get a reasonable set of dimensions:
length = 1 ft
width = 6 ft
height = 1/6 ft
Therefore, the quadratic equation that represents the volume of the box is[tex]w^2 - 6w = 0[/tex], and the dimensions of the box are length = 1 ft, width = 6 ft, and height = 1/6 ft.
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Gabriella decides to estimate the volume of an orange by modeling it as a sphere. She measures its circumference as 50.2 cm. Find the orange's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The answer is 2143.6.
(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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The dean of students at a large college is interested in learning about their opinions regarding the percentage of
first-year students who should be given parking privileges in the main lot. He sends out an email survey to all
students about this issue. A large number of first-year students reply but very few sophomores, juniors, and seniors
reply. Based on the responses he receives, he constructs a 90% confidence interval for the true proportion of
students who believe first-year students should be given parking privileges in the main lot to be (0. 71, 0. 79). Which
of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
O response bias
O nonresponse bias
O sampling variation
O undercoverage bias
Mark this and retum
Save and Exit
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The dean of students at a large college is interested in learning about their opinions regarding the percentage of students who are satisfied with their academic experience. This is an important question for the dean to consider, as it can help them identify areas for improvement and ensure that they are meeting the needs of their students.
To gather this information, the dean may choose to conduct a survey or hold focus groups with students to hear their feedback. They may also review data on student retention rates and academic performance to get a sense of how satisfied students are with their experience at the college.
Once the dean has gathered this information, they can use it to make informed decisions about how to improve the academic experience for their students. This may involve investing in new programs or resources to better support students, or making changes to existing programs based on feedback from students.
Ultimately, by taking the time to gather and listen to student opinions about their academic experience, the dean can create a more student-centered learning environment that meets the needs and expectations of their diverse student population.
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WILL MARK BRAINLIEST QUESTION IS IN THE PHOTO
Based on the inscribed angle theorem, the measure of angle JKL in the circle is: m<JKL = 121°.
What is the Inscribed Angle Theorem?Where an inscribed angle is subtended by an arc it intercepts, the measure of the inscribed angle is equal to half of the the measure of the intercepted arc in the circle, based on the inscribed angle theorem.
Angle JKL is the inscribed angle that is subtended by arc JML. Find the measure of arc JML.
Measure of arc JML = 360 - 53 - 65
Measure of arc JML = 242°
m<JKL = 1/2(measure of arc JML) [inscribed angle theorem]
Substitute:
m<JKL = 1/2(242)
m<JKL = 121°
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5-|p+6|=-8
2 answers
NOT 19
In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water T (in °F) can be approximated by the model T = -1. 83a + 212, where a is the altitude in thousands of feet. Two campers hiking in Colorado boil water for tea. If the water boils at 196°F, approximate the altitude of the campers. Give the result to the nearest hundred feet
The Colorado hikers are at an altitude of 8753.1694 feet.
Here we have been given the equation T = -1. 83a + 212.
Here, T is the boiling point in Fahrenheit of water, while a is the altitude of the place.
We know that the campers in hiing in Colorado boil water for ea. The water boils at a temperature of 196°F, we need to find the altitude.
Here we are going to clearly take T = 196°F
Substituting the value in the above equation will give us
196 = - 1.83a + 212
Taking the variable to the Right Hand Side will give us
196 + 1.83a = 212
Taking 196 to LHS to separate the constant and variable will give us
1.83a = 212 - 196
Solving LHS gives us
1.83a = 16
Taking 1.83 to the other side will give us
a = 16/1.83
or, a = 8.7431694 thousands feet
= 8753.1694 feet
Hence, the Colorado hikers are at an altitude of 8753.1694 feet.
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An insulated collar is made to cover a pipe. Find the volume of the material used to make the collar. Let r = 3 inches, R = 5 inches, and h = 21 inches. Use 3. 14 for p, and round to the nearest hundredth
The volume of the material used to make the insulated collar is 1060.56 cubic inches.
The volume of the material used to make the insulated collar can be determined as follows.
1. Identify the given dimensions:
inner radius (r) = 3 inches,
outer radius (R) = 5 inches, and
height (h) = 21 inches.
2. Use the formula for the volume of a cylinder:
V = πr^2h.
3. Calculate the volume of the outer cylinder with radius R:
V_outer = πR^2h = 3.14 * (5^2) * 21 ≈ 1653.3 cubic inches.
4. Calculate the volume of the inner cylinder with radius r:
V_inner = πr^2h = 3.14 * (3^2) * 21 ≈ 592.74 cubic inches.
5. Subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of the material used:
V_material = V_outer - V_inner ≈ 1653.3 - 592.74 ≈ 1060.56 cubic inches.
The volume of the material is approximately 1060.56 cubic inches, rounded to the nearest hundredth.
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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.
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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To answer questions 4 - 6.
A new school opened with 225 students in 2021 and plans to increase by 13. 3% per year
until they reach full capacity.
Is this situation exponential growth or decay?
4.
5.
Write an equation that models the population of the school, P, after x years since
the opening of the school in 2021
The situation provided is exponential growth and the equation is
p = 225 * 1.133ˣ
How to determine the situationThis scenario represents a significant improvement as the number of students increases each year.
The basic approach to incremental growth is:
[tex]P = P_{0} * (1 + r)^t[/tex]
where:
P. = initial population
r = increase in decimal form
t = time in years
Here
P₀ = 225 (initial population in 2021).
r = 13.3% = 0.133 (growth rate as decimal) .
t = x (time in years from the opening of the school in 2021)
Substituting these values in the formula we get:
[tex]p = 225 * (1 + 0.133)^x[/tex]
Simplifying further, we get:
p = 225 * 1.133ˣ
This is the equation that predicts school population x years after the school opens in 2021
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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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Consider the quadratic relation y=2(x-2)^2-18
write the relation in a standard form
what do u know about this relation
please quick
The standard form of the quadratic relation y=2(x-2)^2-18 is y=2x^2-8x-14.
The standard form of a quadratic relation is y=ax^2+bx+c, where a, b, and c are constants. To convert y=2(x-2)^2-18 to standard form, we need to expand the squared term and simplify the expression.
First, we expand the squared term to get y=2(x^2-4x+4)-18. Then, we distribute the 2 to get y=2x^2-8x+8-18. Finally, we simplify by combining like terms to get the standard form y=2x^2-8x-14.
This quadratic relation is a parabola with a vertex at (2,-18) and it opens upwards since the coefficient of x^2 is positive. The axis of symmetry is a vertical line passing through the vertex, and the y-intercept is -14.
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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
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 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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Assume that Jocoro Provincial Park occupies an area modeled by the domain D. This domain is bordered by the coordinate axes and the lines y = 60 and y = 180 - 2x (where units are in kilometers). Futhermore, assume that snow depth measurements (in meters) were taken over the park on April 15 and that the depth measurements are modeled by the function d(x, y) = -0.024x + 0,012y + 1.2. Estimate the volume of the snowpack in the park in cubic meters. (Give your answer as a whole or exact number.) V= ____billion m
The estimated volume of the snowpack in the park is approximately 1.94 billion cubic meters.
To estimate the volume of the snowpack in the park, we need to calculate a double integral of the function d(x, y) over the domain D:
V = ∬_D d(x, y) dA
We can evaluate this integral by using iterated integrals. First, we integrate with respect to x over the interval [0, 30] (since the line y = 180 - 2x intersects the x-axis at x = 90):
V = ∫_0^30 (∫_0^(180-2x) (-0.024x + 0.012y + 1.2) dy) dx
Simplifying the inner integral:
V = ∫_0^30 [-0.024xy + 0.006y^2 + 1.2y]_0^(180-2x) dx
V = ∫_0^30 (-0.432x^2 + 21.6x - 5832) dx
Simplifying the integral:
V = [-0.144x^3 + 10.8x^2 - 5832x]_0^30
V = -0.144(30)^3 + 10.8(30)^2 - 5832(30)
V = 1.942592 billion cubic meters (rounded to nine decimal places)
Therefore, the estimated volume of the snowpack in the park is approximately 1.94 billion cubic meters.
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The base of a prism is a right triangle with legs measuring 3 feet and 4 feet. If the height of the prism is 13 feet, determine its volume
The volume of the prism is 78 cubic feet.The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism.
In this case, the base of the prism is a right triangle with legs measuring 3 feet and 4 feet, so its area is (1/2)(3)(4) = 6 square feet. The height of the prism is 13 feet. Therefore, the volume of the prism is V = Bh = (6)(13) = 78 cubic feet.To understand this calculation, think of the prism as a stack of identical, parallel cross sections. Each cross section is a copy of the base, with an area of 6 square feet.
The height of each cross section is the same, and equal to the height of the prism, which is 13 feet. To find the total volume of the prism, we add up the volumes of all these cross sections, which is equal to the area of the base times the height of the prism.
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The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined. true or false
True. In a continuous uniform distribution, all values within a specified interval are equally likely to occur. The mean or expected value of this distribution can be found by taking the average of the upper and lower limits of the interval.
This can be represented mathematically as (a+b)/2, where a and b are the lower and upper limits of the interval. For example, if we have a continuous uniform distribution on the interval [0,10], the mean value would be (0+10)/2 = 5.
This means that on average, we would expect a randomly selected value from this distribution to be around 5. It's important to note that the mean of a continuous uniform distribution is not affected by the shape or spread of the distribution, as all values have an equal chance of occurring.
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A 10 ft ladder is used to scale 9 ft wall. at what angle of elevation must the ladder be situated in order to reach the top of the wall?
ps. please include an illustration/drawing of the problem. thank you!
The ladder must be situated at an angle of approximately 63.43° to reach the top of the 9 ft wall.
How to find the angle of elevation at which the ladder must be situated?
Certainly, here's an illustration of the problem:
|\
| \
| \ 9 ft
| \
ladder | \
(10 ft)|_____\
wall
To find the angle of elevation at which the ladder must be situated, we can use the trigonometric function of sine. Let θ be the angle of elevation. Then:
sin θ = opposite / hypotenuse
In this case, the opposite side is the height of the wall (9 ft), and the hypotenuse is the length of the ladder (10 ft). So:
sin θ = 9/10
Using a calculator or a trigonometric table, we can find the angle whose sine is 9/10:
θ ≈ 63.43°
Therefore, the ladder must be situated at an angle of approximately 63.43° to reach the top of the 9 ft wall.
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Susan is a college student with two part-time jobs. She earns $10 per hour tutoring
elementary students in math. She earns $15 per hour cleaning in the library. Her goal is
to earn at least $240 per week, but because of college, she does not work more than
20 hours each week.
Which combinations allow Susan to work no more than 20 hours in one week and earn
at least $2402
Select the three correct combinations.
The required inequalities are h + l ≤ 20, 10h + 15l ≥ 240 and 20h + 25l ≥ 440
Given, for tutoring elementary students in math Susan earns $10 per hour. She earns $15 per hour for cleaning in the library.
Let h be the number of hours Susan works in one week tutoring elementary students.
Let l be the number of hours Susan works in one week cleaning the library.
Given that each week Susan cannot work more than 20 hours.
So, h + l ≤ 20 ....(1)
Susan's total earnings must be at least $240 per week.
10h + 15l ≥ 240 ...(2)
Multiplying equation (1) by 10
10h + 10l ≤ 200 ...(3)
Adding equations (2) and (3)
20h + 25l ≥ 440
Thus, the three required inequalities are h + l ≤ 20, 10h + 15l ≥ 240 and 20h + 25l ≥ 440
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Two sisters, working together can clean the house in 3 hours. The older sister works 3 times faster than the younger sister when cleaning the house. How long will it take the younger sister to finish the same job by herself? Type just the number don't include words
The time taken by the younger sister to finish the same work by herself is 12 hours.
To solve the problem of how long it will take the younger sister to finish the job by herself, let's use the following terms:
1. Older sister's work rate = O
2. Younger sister's work rate = Y
3. Time taken by the younger sister alone = T
Given that the older sister works 3 times faster than the younger sister, we have: O = 3Y.
Also, the sisters together can finish the job in 3 hours. Therefore, their combined work rate is equal to completing 1/3 of the job per hour. So,
O+Y=1/3.
Now, we can substitute O with 3Y: 3Y+Y=1/3. Combine the terms and simplify:
4Y=1/3
Now, solve for Y:
Y=1/12
Since Y is the work rate of the younger sister, to find the time it takes for her to complete the job alone (T), we can use the following formula:
Work rate × Time = 1 job.
So, Y × T = 1.
Substitute Y with 1/12:
[tex]\frac{1}{12} \times T=1[/tex]
Now, solve for T:
T = 12.
Therefore, it will take the younger sister 12 hours to finish the job by herself.
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