In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.
To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].
This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).
To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).
We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).
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Pizza burger taco shake
Answer:
Is there supposed to be a joke in this?
Answer:
bro what
Step-by-step explanation:
The vertex of the parabola below is at the point (5, -3). Which of the equations
below could be the one for this parabola?-ہے
A. y=-3(x-5)^2-3
B. x=3(y-5)^2-3
C. x=3(y+3)^2+5
D. x=-3(y+3)^2+5
None of the available options match the parabola's equation.
Which might be the parabola's equation?To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.
A parabola's vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the parabola's vertex.
[tex]y = a(x-5)^2 - 3[/tex]
These values are substituted into the equation to produce:
[tex]-15 = a(2-5)^2 - 3[/tex]
[tex]-15 = 9a - 3[/tex]
[tex]-12 = 9a[/tex]
[tex]a = -4/3[/tex]
[tex]y = (-4/3)(x-5)^2 - 3[/tex]
This equation is expanded and simplified to produce:
[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]
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-3(-4x + 5) = [?]x - [ ]
(Using the distributive property)
The answer to the distributive property-based problem -3(-4x + 5) = [?]x - [] is 12x - 15.
what is equation ?A mathematical assertion proving the equality of two expressions is known as an equation. Variables, constants, and mathematical processes like addition, subtraction, multiplication, and division are frequently included. Finding the value of the variable that makes an equation correct is the aim of equation solving. Linear equations, quadratic equations, and exponential equations are just a few of the different ways that equations can be expressed.
given
-3(-4x + 5) = [?]x - [ ]
12x - 15
by distributive property
The answer to the distributive property-based problem -3(-4x + 5) = [?]x - [] is 12x - 15.
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PLS HELPPPP
A group of friends go to a basketball game. The function b(x) represents the amount of money spent, where x is the number of friends at the game. Does a possible solution of (4.5, $107.75) make sense for this function? Explain your answer.
• Yes. The input and output are both possible.
• No. The input is not possible.
• No. The output is not possible.
• No. Neither the input nor output is possible.
Part B: During what interval(s) of the domain is the baseball's height staying the same? (2 points)
Your answer
Part C: During what interval(s) of the domain is the baseball's height decreasing the fastest? Use complete sentences to support your answer.
• 6 -x ‹ 8; the slope is the steepest for this interval
• 8-x < 10; the slope is the steepest for this interval
• 6
• 6
Part A: During what interval(s) of the domain is the baseball's height increasing?
Answer:
This is not my own answer it is a copied one.
If h (x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h (x)) Then the pair given is (6.5, $92.25) Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)
you decide to record the hair colors of people leaving a lecture at your school. what is the probability that the next person who leaves the lecture will have gray hair? express your answer as a simplified fraction or a decimal rounded to four decimal places. counting people blonde red brown black gray 50 40 39 33 43
The probability is a fraction of 43/205 which is approximately 0.2098.
What is the probability that the next person who leaves the lecture will have grey hair?To calculate the probability of the next person who leaves the lecture having gray hair, we need to know the total number of people who left the lecture, as well as the number of people who have gray hair.
From the given data, we can see that there were a total of 50+40+39+33+43 = 205 people who left the lecture. We also know that there were 43 people who had gray hair.
Therefore, the probability of the next person who leaves the lecture having gray hair is:
P(gray hair) = (number of people with gray hair) / (total number of people who left the lecture)
P(gray hair) = 43/205
P(gray hair) ≈ 0.2098
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Find the mean, median, mode, and range of the data set after you perform the given operation on each data value.
9, 7, 12, 13, 9, 3; add 5
mean is average =9+7+12+13+9+3+5÷7=8.29
median is middle term =9
mode is frequented data=9
rang is the difference between maximum and minimum data=13_3=10
If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11
True. If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11.
When a two-digit number is reversed, it becomes a new number with the digits swapped, e.g., 12 becomes 21. The difference between the original number and the reversed number is obtained by subtracting one from the other. For example, the difference between 12 and 21 is 9. It can be observed that the difference between any two-digit number and its reverse is always a multiple of 9.
Now, let's consider the three-digit number ABC. When this number is reversed, it becomes CBA. The difference between the two is
(100C + 10B + A) - (100A + 10B + C) = 99(C - A),which is a multiple of 11.
Therefore, if a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11.
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Complete Question:
If a counting number with two or more digits remains the same with its digits reversed, then the counting number is a multiple of 11. True/ False.
suppose that 6 j of work is needed to stretch a spring from its natural length of 26 cm to a length of 36 cm. (a) how much work is needed to stretch the spring from 30 cm to 32 cm? (round your answer to two decimal places.) 0.6 incorrect: your answer is incorrect. j (b) how far beyond its natural length will a force of 20 n keep the spring stretched? (round your answer one decimal place.)
(a)The amount of work needed to stretch the spring from 30 cm to 32 cm is 0.6 J. (b) The distance the spring will be stretched by a 20 N force is 0.03 m.
The formula for the force needed to keep a spring stretched beyond its natural length is F = kx where F is the force, k is the spring constant, and x is the distance from the spring's natural length. The spring constant k is given by the formula: k = (Wd)/x² where W is the work done, d is the distance the spring is stretched from its natural length, and x is the distance from the spring's natural length.
Substituting the values for W, d, and x gives: k = (6 J)/(0.10 m)²
k = 600 N/m
Using the formula F = kx and substituting the values for F and k gives: 20 N = (600 N/m)x
Solving for x gives: x = (20 N)/(600 N/m)
x = 0.0333 m.
Hence, the correct answer is 0.03 m.
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Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 12. What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?
A. -3
B. -1.5
C. 1.5
D. 3
change the denominator of the fraction a+3/6-2a to 2(a^2-9)
The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
What is Formula?In mathematics, formula is mathematical expression or equation that describes relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.
Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.
To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.
First, we can factor the denominator of the original fraction as follows:
6 - 2a = 2(3 - a)
Next, we can rewrite the denominator using the difference of squares formula:
2(a² - 9) = 2(a + 3)(a - 3)
Now, we can use the factored form of the denominator to rewrite the original fraction:
(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))
Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
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Here is the question please help
1) With regard to the statistical diagram given:
The total number of women in the group = 180130 women intend to vote for party A.2)
24 Adults chose EnglishYes, an equal number of Adults and children chose Math because the portion of the pie chart that represents the choice of Children and adults are both identical and equal to 1/4 or 25%.What is a statistical diagram?A statistical diagram is a visual representation of data using graphs or charts, typically used to summarize and communicate information about the distribution, relationship, or comparison of variables.
1)
a) To derive the total number of women in the group, we must remove 200 from 380.
That is:
Total women in the group = 380 - 200
= 180 Women.
b) To get women who intend to vote for party A.
We must first derive the total who intend to vote for Party A.
the total who intend to vote for Party A = 380 - 130
= 250
Women who intend to vote for party A = Total who want to vote for Party A - Men who want to vote for Party A.
Women who intend to vote for party A = 250 - 120
= 130
2)
a) Given that 48 adults were evaluated, the the portion of the pie chart that shows their choice of English reads 50%, it means that
Adults who Chose English = 48 * 50%
= 24
b) an equal number of Adults and children chose Math because the portion of the pie chart that represents the choice of Children and adults are both identical and equal to 1/4 or 25%.
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Can someone help me with this
Solving a system of equations we can see that he cost of a corn dog is $1.25 and the cost of the fries is $3.50
How to find the cost of each item?We can define two variables here:
x = cost of a corn dog.
y = cost of the fries.
With the information in the question we can write two equations, these two equations form a system of equations that we can solve, the system of equations is the one below:
2x + 3y = 13
4x + y = 8.50
We can isolate y in the second equation to get:
y = 8.50 - 4x
Replace it in the other one:
2x + 3*(8.5 - 4x) = 13
2x + 25.5 - 12x = 13
-10x = 13 - 25.5
x = -12.5/-10 = 1.25
Then:
y = 8.5 - 4*1.25 = 3.5
The cost of a corn dog is 1.25 dollars and the cost of the fries is 3.50 dollars.
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owen already has 3 plants in his backyard, and he can also grow 2 plants with every seed packet he uses. how many seed packets does owen need to have a total of 9 plants in his backyard? write and solve an equation to find the answer.
Answer:
3 seed packets
Step-by-step explanation:
So first, we know that for every 1 seed packet Owen uses, he can grow 2 plants. The ratio is 1:2 (1 = # of seed packets, 2 = # of plants). So now, we need to figure out how many seed packets he needs to have a total of 9 plants. Before we calculate anything, we need to subtract 3 from 9 because it is the total number of plants, and we get 6 plants. To calculate the amount of seed packets Owen needs, we need to get the ration (1:2) and multiply it by 3 on both sides because we need 6 plants. 2 × 3 = 6, and 1 × 3 = 3. The ratio is 3:6. So now we know that Owen needs 3 more seed packets in order to have a total of 9 plants in his backyard. :)
You ate 4/12 of the pizza your family bought for dinner. Your brother ate 3/12 of the pizza. Which equation represents the fraction of pizza both you and your brother ate?
Answer:
7/12 pizzas have been eaten
Step-by-step explanation:
3 + 4= 7
7/12
7-12=5
5 pizzas left
commuting times for employees of a local company have a mean of 63.6 minutes and astandard deviation of 2.5 minutes. what does chebyshev's theorem say about thepercentage of employees with commuting times between 58.6 minutes and 68.6 minutes?
According to Chebyshev's theorem, at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.
Chebyshev's theorem states that for any set of data, regardless of its distribution, a certain percentage of the data lies within a certain number of standard deviations from the mean. Specifically, Chebyshev's theorem states that for any data set, at least 1 – 1/k² of the data values will lie within k standard deviations of the mean, where k is any number greater than 1. If k=2, at least 75% of the data values lie within 2 standard deviations of the mean. If k=3, at least 89% of the data values lie within 3 standard deviations of the mean.
Therefore, for a data set with a mean of 63.6 minutes and a standard deviation of 2.5 minutes, we can use Chebyshev's theorem to determine that at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.
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expand and simplify 4(2x-1)+3(2x+5)
Answer:
Step-by-step explanation: 4(2x-1)+3(2x+5)
Expand the expression to eliminate the brackets
8x-4+6x+15.....Expansion
Now simplify by grouping like terms
8x+6x-4+15
8x+6x=14x
-4+15=11
Therefore simplification=14x+11
Suppose a product's revenue function is given by R(q) = - 7q + 600qr. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q) =
The expression for the marginal revenue function is MR(q) = 600r - 7.
The given product's revenue function is R(q) = - 7q + 600qr.
To find an expression for the marginal revenue function, we can use the following steps:
Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).
Step 2: Simplify the expression for MR(q) to record the final result.
In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.
So, we have to differentiate R(q) with respect to q to get MR(q).
The derivative of - 7q with respect to q is - 7.
The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.
MR(q) = dR(q) / dq
= (d/dq)(- 7q + 600r)
= (- 7) + (600r)
= 600r - 7
The equation that represents the marginal revenue function is MR(q) = 600r - 7.
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Please help, due very soon !!
A love expert carried out a study to quantify the effect of love songs on emotion. To do so, he used 30 volunteers. He random
Publishers
assigned the 30 volunteers to listen to either a love song or classical music. Then he asked them to draw a heart on a piece of paper. He measured the size of the heart drawn from bottom to top, in inches, for each person. The results are displayed in the stem and leaf plots.
The analysis of the data to obtain the confidence interval of the difference in the means indicates;
99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
The correct options are;
Name of Procedure
Two sample interval for [tex]\bar{x}[/tex]₁ - [tex]\bar{x}[/tex]₂Random
The volunteers are randomly selectedWe have a random sample of 15 subjects who listen to love songsWe have a random sample of 15 subjects who listen to classical music10%
The 10% condition is metNormal/Large Sample
The stemplot of the classical music sample data shows no strong skewness or outliersThe stemplot of the love song music sample data shows no strong skewness or outliers99% CI = (-0.302, 2.301)
Conclude;
We are 99% confident that the interval give in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.
What is a confidence interval?A confidence interval is a range of value that is likely to contain the true value of a population parameter with a certain degree of confidence.
The two-sample t-test can be used to construct the 99% confidence interval as follows;
([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)
Where;
[tex]\bar x[/tex]₂ and [tex]\bar x[/tex]₁ = The sample means of the love song and classical music groups
s₁, and s₂ = The sample standard deviations
n₁ and n₂ = The sample sizes
df = The degrees of freedom
t(α/2, df) = The value from the t-distribution table with a significance level of 0.01 and df = n₁ + n₂ - 2
The data indicates;
n₁ = n₂ = 15
[tex]\bar x[/tex]₁ = 5.07, s₁ = 1.63
[tex]\bar x[/tex]₂ = 4.07, s₂ = 1.13
Therefore, we get;
([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)
= (5.07 - 4.07) ± t(0.005, 28) × √(1.62²/15 + 1.13²/15)
= 1 ± 2.763 × 0.469
= 1 ± 1.301
The 99% confidence interval for the difference in the true mean heart for subjects who listen to a love song versus classical music is; (-0.301, 2.301).
The correct statement is; 99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
The correct statements, placed in the box are;
Name of Procedure;
Two sample interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
Random
The volunteers are randomly selected
The random condition is met
We have a random sample of 15 subjects who listen to a love song
We have a random sample of 15 subjects who listen to classical music
10%
The 10% condition is met
15 < 10% of all subjects like these who listen to love songs
15 < 10% of all subjects like these who listen to classical music
Normal/Large Sample
The Normal/Large condition is met
The stemplot of the classical music sample data shows no strong skewness or outliers
The stemplot of the love song music sample data shows no strong skewness or outliers
Therefore;
99% CI = (-0.301, 2.301)
Conclude;
We are 99% confident that the interval given in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.
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could someone help me with 7 and 8 i don’t really understand this..
By answering the presented question, we may conclude that from the given graph we can say that zeros are = (-3,-1 ) and (--5,-9) ; y - intercept is, y = -2x/3 + 15 and vertex are = (-0-1)
What exactly are graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
from the given graph we can say that
zeros are = (-3,-1 ) and (--5,-9)
y - intercept is, y = -2x/3 + 15
vertex are = (-0-1)
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Select all numbers that are solutions to the inequality w < 1
In the case of the inequality w < 1, we found that the set of solutions is (-∞, 1), which represents all real numbers less than 1.
The inequality w < 1 means that w is less than 1. To identify all the numbers that satisfy this inequality, we need to look for values of w that are less than 1.
We can continue this process and substitute different values of w in the inequality w < 1 to find more solutions. For instance, if we substitute w = -1, we get -1 < 1, which is also true.
Therefore, -1 is a solution to the inequality w < 1. However, if we substitute w = 2, we get 2 < 1, which is false. This means that 2 is not a solution to the inequality w < 1.
Therefore, the set of all numbers that are solutions to the inequality w < 1 is the set of all real numbers that are less than 1. We can represent this set using interval notation as (-∞, 1), where (-∞) represents all numbers less than negative infinity and 1 represents the upper bound of the interval.
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Solve for x to the nearest tenth.
2
X
4
10
Answer:
x ≈ 8.9
Step-by-step explanation:
using Pythagoras' identity.
the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.
consider the right triangle on the left with hypotenuse h , then
h² = 2² + 4² = 4 + 16 = 20 ( take square root of both sides )
h = [tex]\sqrt{20}[/tex]
consider the right triangle on the right , then
x² + h² = 10²
x² + ( [tex]\sqrt{20}[/tex] )² = 10²
x² + 20 = 100 ( subtract 20 from both sides )
x² = 80 ( take square root of both sides )
x = [tex]\sqrt{80}[/tex] ≈ 8.9 ( to the nearest tenth )
What is the exact value of the trigonometric expression? State your answer in simplified radical form and include all work.
*Please reference included picture for problem. Thank you!
Answer:
The exact value of the given trigonometric expression is undefined.
Step-by-step explanation:
Given trigonometric expression:
[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]
To find the exact value of the given trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression
The exact value of cos(2π/3) is:
[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]
The exact value of tan(-7π/4) is:
[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]
Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:
[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]
listed are 29 ages for academy award winning best actors in order from smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. (5pts) find the score at the 20th percentile
The score at the 20th percentile is 27.
To find the score at the 20th percentile of the 29 ages for Academy Award winning best actors, follow the steps below:
Arrange the given ages from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77
Determine the total number of data points
n = 29
Find the rank of the percentile
20th percentile = (20/100) * 29 = 5.8 = 6 (rounded to the nearest whole number).The rank of the percentile is 6.
Use the rank to determine the corresponding data value. The corresponding data value is the value at the 6th position when the data is arranged in ascending order. The score at the 20th percentile is 27.
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Translate Into a equation!
The sum of 7 times a number and 6 is 3
Step-by-step explanation:
x is the number.
the equation is
7x + 6 = 3
The velocity of a particle. P. moving along the x-axis is given by the differentiable function v, where (t) is measured in meters per hour and r is measured in hours. V() is a continuous and decreasing function Selected values of v(f) are shown in the table above. Particle P is at the t= 30 at time t = 0. T(hours) 0 2 4 7 10 V(t) (meters/hour) 20.3 14.4 10 7.3 5 (a) Use a Right Riemann sum with the four subintervals indicated by the data in the table to approximate the displacement of the particle between 0 hr to 10 hr. What is the estimated position of particle Pat t=10? Indicate units of measure. (b) Does the approximation in part (a) overestimate or underestimate the displacement? Explain your reasoning (c) A second particle, Q. also moves along the x-axis so that its velocity for O<=T<= 10 is given by VQ(t) = 35✓t cos( 0.06t^2) meters per hour. Find the time interval during which the velocity of particle vo(t) is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is at least 40 meters per hour. (d) At time t = 0, particle Q is at position x = -90. Using the result from part (a) and the function vo(t) from part (c), approximate the distance between particles P and Q at time t = 10.
The velocity of a particle. P. moving along the x-axis is given by the differentiable function v, where (t) is measured is given by:
A differential function v gives the velocity of a particle P travelling down the x-axis, where v(t) is measured in metres per hour and t is measured in hours. v(t) is a declining function that is continuous. The table below shows several examples of v(t) values.
T [hours] 0 2 4 7 10
v(t) [meters/hour] 20.3 14.4 10 7.3 5
a) We know that the particle's displacement is the area under the curve v(t). We can calculate the particle's displacement by integrating v(t). Because v(t) is a monotonous (constantly declining) differentiable function, it is also Riemann Integrable. There are now five non-uniform subdivisions:
Partition t0 t1 t2 t3 t4
T [hours] 0 2 4 7 10
v(t) [meters/hour] 20.3 14.4 10 7.3 5
Using Right Riemann sum to approximate the displacement of particle between 0 hr and 10 hr is given by:
[tex]\sum_{n=1}^{4}v(t_n)\Delta t_n=v(t_1)(t_1-t_0)+v(t_2)(t_2-t_1)+v(t_3)(t_3-t_2)+v(t_4)(t_4-t_3) \\=(14.4)(2)+(10)(2)+(7.3)(3)+(5)(3) \\=28.8+20+21.9+15 \\=85.7[/tex]
Therefore, the total displacement between 0 hr and 10 hr is is 85.7 meters.
The estimated position of particle P at time t = 10 hour is 115.7 (= 30 +85.7) meters.
b) Because the function v(t) is decreasing and we are estimating the integral using the Right Riemann sum, the approximation in part(a) underestimates the displacement.
c) A second particle Q also moves along the x-axis so that its velocity is given by :
[tex]V_Q(t)=35\sqrt{t}\cos(0.06t^2)\text{ meters per hour for }0\leq t\leq 10.[/tex]
Hence, the time interval during which the velocity of a particle is atleast 60 meters per hour is [9.404, 10].
Now, the time periods during which a particle's velocity is at least 40 metres per hour are [1.321,4.006] and [9.218, 10]. The distance travelled by the particle Q when its velocity is at least 40 metres per hour is then calculated. :
[tex]\int_{1.321}^{4.006}v_Q(t)dt+\int_{9.218}^{10}v_Q(t)dt\\\\=\int_{1.321}^{4.006}35\sqrt{t}\cos(0.06t^2)dt+\int_{9.218}^{10}35\sqrt{t}\cos(0.06t^2)dt[/tex]
d) At time t = 0, particle Q is is at position x = -90.
We know that P is at xp = 115.7 meters.
Now, The position of Q at t = 10 hr is xq:
[tex]x_q=-90+\int_{0}^{10}v_Q(t)dt=-90+\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt[/tex]
And the distance between Q and P is given by :
[tex]|x_p-x_q|=|115.7-(-90+\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt)|[/tex]
[tex]\\=|205.7-\int_{0}^{10}35\sqrt{t}\cos(0.06t^2)dt|[/tex]
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A shadow 9 feet long is cast by a plum tree that is 12 feet tall. What is the height of a nearby lemon tree that casts a shadow 6 feet long?
The height of the nearby lemon tree is 8 feet using the property of similar triangles.
What are similar triangles?Triangles that are similar to one another in shape but differ in size are called similar triangles. Their respective sides are proportional to one another, and their corresponding angles are equal. The ratio of the corresponding sides of two triangles that are comparable is constant across all pairs of corresponding sides. Problems involving unknown lengths or heights in comparable forms can be resolved using this attribute.
The given situation represent two proportional triangles.
We know that the ratio of lengths of similar triangles are equal thus,
height of plum tree / length of plum tree's shadow = height of lemon tree / length of lemon tree's shadow
Substituting the values we have:
12 / 9 = height of lemon tree / 6
Using cross multiplication:
height of lemon tree = 12 * 6 / 9 = 8 feet
Hence, the height of the nearby lemon tree is 8 feet using the property of similar triangles.
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Which of the following statements is about CD and CE is true? A. CD is longer than CE B. CE is longer than CD C. CD and CE are the same length D. CE is 5 units long
From the given graph, CE is longer than CD.
What is the distance between two coordinates?The length of the line segment bridging two locations in a plane is known as the distance between the points. d=√((x₂ - x₁)²+ (y₂ - y₁)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Coordinates of E(8,6)
Coordinates of C(6,1)
Coordinates of D(3,-3)
x=8, y=6
x=6, y=1
x=3, y=-3
Distance CE=√{(8-6)² +(6-1)²} = √29
Distance CD=√{(6-3)² +(1+3)²}= √25=5
Therefore, CE is longer than CD.
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Please help me with my math!!
Answer:
The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.
Since a = -3 < 0, the parabola opens downwards and has a maximum point.
To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:
x = -3
y = -3(-3+3)^2 + 4 = 4
Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.
Hence, the answer is option C
Answer:
C) Maximum point; 4
Step-by-step explanation:
Given parabola:
[tex]y=-3(x+3)^2+4[/tex]
The given parabola is in vertex form:
[tex]\boxed{y = a(x - h)^2 + k}[/tex]
where:
(h, k) is the vertex of the parabola.a is the leading coefficient.By comparing the given equation with the vertex form, we can see that:
a = -3h = -3k = 4As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.
The vertex of the parabola is (h, k) = (-3, 4).
Therefore, the maximum value of y is 4, which occurs at x = -3.
Express the following in exponential notation: 16384
The exponential notation of 16384 is 2^14
16384 can be expressed in exponential notation as 2^14, where 2 is the base and 14 is the exponent.
In exponential notation, a number is expressed as a base raised to an exponent, where the base is the number being multiplied repeatedly and the exponent represents the number of times the base is multiplied.
In this case, 2 is being multiplied 14 times to arrive at the value of 16384. Exponential notation is a useful way to represent very large or very small numbers in a concise and standardized format, making it easier to work with and compare values across different scales. It is commonly used in scientific and mathematical contexts.
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