For a particle in a 2D box with impenetrable walls, the time-independent Schrödinger equation can be simplified to equation 3, which is a separable differential equation.
Using the Separation of Variables approach, the 2D wavefunction can be expressed as the product of two independent 1D components, given by equation 4.
The resulting differential equations in equations 5 and 6 have the same form as those found for the particle in a 1D box and their solutions are given by equations 8 and 9. The total energy of the particle is given by equation 7.
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Write (182)-3 using positive exponents only. ㅇA¾ 00 00급 O D. -186
Therefore, (18²)⁻³ can be written as 18² - 10^⁻³ using positive exponents only.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. Equations can be used to represent relationships between variables, or to solve problems. Equations use mathematical symbols, such as the equal sign (=), to show the equality between the two expressions. For example, the equation 2x + 3 = 7 represents the relationship between the variable x and the constants 2 and 3. The equation can be solved for x to find its value. In this case, solving for x would give us x = 2.
Using positive exponents only, we can write (182)⁻³ as follows:
(182) can be written as 10²
-3 can be written as 10⁰/ 10³
So, (18²)⁻³ can be written as:
18² - 10⁰ / 10³= 18² - 10⁻³
Therefore, (18²)⁻³ can be written as 18² - 10^⁻³ using positive exponents only.
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Consider the following two loans for P0=$10,000.
Loan A: 3 year loan, monthly installments, annual interest rate of 5%.
Loan B: 5 year loan, monthly installments, annual interest rate of 8%.
On which loan will you pay the least interest?
The Interest (simple interest) will be less on Loan A.
What exactly is simple interest?
Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.
The simple interest formula is as follows:
SI=P*R*T/100
SI stands for simple interest.
P stands for principal.
R is the interest rate (in percentage)
T denotes the length of time (in years)
The following formula is used to compute the total amount:
Amount (A) = Principal (P) x Simple Interest (SI)
Now,
For A Principal=$10000, Time = 3 years, Rate=5%
then interest paid=10000*3*5/100
=300*5=$1500
For B Principal=$10000, Time = 5 years, Rate=8%
Interest=10000*5*8/100
=500*8
=$4000
That means SI(B)>SI(A)
Hence,
The Interest will be less on Loan A.
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Ruby was out at a restaurant for dinner when the bill came. Her dinner came to $27. After adding in a tip, before tax, she paid $34.29. Find the percent tip. Note, please just input the number. NO PERCENTAGE SIGN...remember percent increase/decrease
The percent tip Ruby left was 27%.
What is percent?
A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.
Calculate the tip amount:
The total cost of the meal including the tip is $34.29, and the cost of the meal before the tip is $27. Therefore, the tip amount is:
Tip = Total cost - Cost of meal
Tip = $34.29 - $27
Tip = $7.29
Calculate the percent tip:
The percent tip is the tip amount divided by the cost of the meal, multiplied by 100 to express the result as a percentage:
Percent tip = (Tip / Cost of meal) x 100%
Percent tip = ($7.29 / $27) x 100%
Percent tip = 27%
Therefore, the percent tip Ruby left was 27%.
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on june 1 mario sent out texts offering to sell his 2002 ford f-150 for $10,000 and asking for text acceptances. on june 7, andretti texted mario accepting his offer. however, andretti's text was not received by mario until june 10 due to connection problems. the text from andretti created an enforceable agreement between mario and andretti the moment it was sent.T/F
The statement "the text from andretti created an enforceable agreement between mario and andretti the moment it was sent" is generally true.
In contract law, an agreement is formed when there is an offer from one party and an acceptance of that offer by the other party. An acceptance is typically effective upon communication to the offeror.
In this case, Mario made an offer to sell his 2002 Ford F-150 for $10,000 through a text message. Andretti responded to the offer with a text message accepting it.
The general rule is that an acceptance is effective upon communication to the offeror. Therefore, Andretti's acceptance of the offer was effective as soon as he sent the text message. It doesn't matter if the message was not received by Mario until later due to connection problems.
As long as Andretti sent the acceptance text message, it created an enforceable agreement between the two parties, assuming that there were no other legal issues that might affect the validity of the agreement.
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Find the cosine of the angle between the plane 4x-5y+z=4 and the plane 5x-4y+3z=-2
Given the planes [tex]4x-5y+z=4[/tex] and [tex]5x-4y+3z=-2[/tex], find the angle between them.
Using the formula,
[tex]\theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]
Where vector, [tex]A= < 4,-5,1 >[/tex] and vector [tex]B= < 5,-4,3 >[/tex].
Plug these values into the formula above...
[tex]\Longrightarrow \theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]
[tex]\Longrightarrow \theta=cos^{-1} (\frac{(4)(5)+(-5)(-4)+(1)(3) }{\sqrt{(4)^2+(-5)^2+(1)^2}\sqrt{(5)^2+(-4)^2+(3)^2} } )[/tex]
[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{\sqrt{42}\sqrt{50} } )[/tex]
[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{10\sqrt{21} } )[/tex]
[tex]\Longrightarrow \theta \approx 20.2\textdegree[/tex]
Graph the equation y=-x+4 intercepts
i need some help on this problem please
Answer:
C
Step-by-step explanation:
180-2x-2=180*7/9
x=19
A barge traveled 24 miles upstream on a river in 8 hours.The return trip took the barge 3 hours.What is the rate of the current,in miles per hour?
The rate of the current is 5/11 of the speed of the barge in still water.
Rate of the Miles per HourLet's call the speed of the barge in still water "s" (in miles per hour) and the speed of the current "c" (also in miles per hour).
When the barge travels upstream (against the current), its effective speed is reduced by the speed of the current, so the speed of the barge relative to the riverbank is (s - c). On the return trip, the current is going in the same direction as the barge, so the effective speed of the barge relative to the riverbank is (s + c).
We can use the formula distance = rate x time to set up two equations based on the information given:distance upstream = (s - c) x 8 miles
distance downstream = (s + c) x 3 miles
We also know that the two distances are equal, since the barge ends up back where it started. So we can set these two expressions equal to each other and solve for the unknown variable, c:(s - c) x 8 = (s + c) x 3
Expanding and simplifying, we get:8s - 8c = 3s + 3c
5s = 11c
c = 5s/11
Therefore, the rate of the current is 5/11 of the speed of the barge in still water.
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Which statements are true about the graph of f(x)=cot(x)? Select each correct answer. Responses The graph will have a vertical asymptote at x=π2. The graph will have a vertical asymptote at , x equals pi over 2, . The graph will have a vertical asymptote at x=π. The graph will have a vertical asymptote at , x equals pi, . The graph will have a vertical asymptote at x=3π2. The graph will have a vertical asymptote at , x equals fraction numerator 3 pi over denominator 2 end fraction, . The graph will have a vertical asymptote at x=2π. The graph will have a vertical asymptote at , x equals 2 pi, . The graph will go through the point (π4, 1). The graph will go through the point , left parenthesis pi over 4 comma 1 right parenthesis, .
Answer:
the correct responses are:
The graph will have a vertical asymptote at x = π/2.
The graph will have a vertical asymptote at x = 3π/2.
The graph will have a vertical asymptote at x = 2π.
The graph will not go through the point (π/4, 1).
Step-by-step explanation:
The statements that are true about the graph of f(x) = cot(x) are:
The graph will have a vertical asymptote at x = π/2.
The graph will have a vertical asymptote at x = 3π/2.
The graph will have a vertical asymptote at x = 2π.
These are true because the cotangent function has vertical asymptotes at every odd multiple of π/2, which includes π/2, 3π/2, and 5π/2, and so on.
The statement that the graph will go through the point (π/4, 1) is false. The cotangent function does not pass through this point, although it does have a vertical asymptote at x = π/4.
Therefore, the correct responses are:
The graph will have a vertical asymptote at x = π/2.
The graph will have a vertical asymptote at x = 3π/2.
The graph will have a vertical asymptote at x = 2π.
The graph will not go through the point (π/4, 1).
Answer:
Step-by-step explanation:
The table shows the population of a city decreases over time. Calculate the average rate of
change of the population per year from year 20 to year 50.
Year
Population
1972
1,090,000
1982
1,060,000
1992
2002
940,000 860,000
2012
800,000
2022
770,000
The average rate of change of the population per year is -5666.66
How to determine the average rate of change of the population per yearFrom the question, we have the following parameters that can be used in our computation:
Year Population
1972 1,090,000
1982 1,060,000
1992 940,000
2002 860,000
2012 800,000
2022 770,000
Given that the year is from 1972, we have
year 20 = 1992 940,000
year 50 = 2022 770,000
So, we have
Average rate = Difference in values/Difference in years
This gives
Average rate = (770,000 - 940,000)/30
Evaluate
Average rate = -5666.66
Hence, the rate is -5666.66
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What portion of shared $6000 security costs should be apportioned to store B?
Answer:#
Step-by-step explanation:
Part B
Question
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the
average number of customers per hour. Create : inequality in standard form that represents the restaurant owner's
desired revenue.
Type the correct answer in each box. Use numerals instead of words.
The inequality in standard form that represents the restaurant owner's
desired revenue is x² + 2x - 80 ≤ -65.
What are Inequalities?Inequalities are defined as the expressions consisting of both variables and constants connected by inequality signs like ≠, >, <, ≤ and ≥.
Part A :
Cost : 10 + x
Customers : 16 - 2x
Part B :
Given that,
Hourly revenue = Price paid by each customer × average number of customers per hour.
Price paid by each customer = 10 + x
Average customers per hour = 16 - 2x
Given that the restaurant owner wants a minimum revenue of $130 per hour.
(10 + x) (16 - 2x) ≥ 130
(10 × 16) + (16x) - (10 × 2x) - 2x² ≥ 130
160 + 16x - 20x - 2x² ≥ 130
-2x² - 4x + 160 ≥ 130
Dividing the equation throughout by -2,
x² + 2x - 80 ≤ -65
The inequality sign changes as we multiply or divide with a negative number.
Hence the required inequality is x² + 2x - 80 ≤ -65.
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The complete question is given below.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Part A
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that the x represents the number of $1 increases in the cost of buffet.
Part B
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create inequality in standard form that represents the restaurant owner's desired revenue.
need help asap 25 pointd
Answer:
x= 7 ;
y+x=18
y=18-x
y=18-7
y=11
*-*-*-*
บ
y=x
E(3.-3) F(5,-3)
H(2-5) G(4-5)
What are the coordinates of the image of vertex G after
a reflection across the line y = x?
O(-4,-5)
O (4, 5)
O(-5, 4)
(5,-4)
The coordinates of the image of vertex G after a reflection across the line y = x will be (-5, 4). Then the correct option is C.
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection given will be given as,
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
The coordinates are given below.
E(3, -3), F(5, -3), H(2, -5), G(4, -5)
The coordinates of the image of vertex G after a reflection across the line y = x are given as,
G(4, -5) ⇒ G'(-5, 4)
The coordinates of the image of vertex G after a reflection across the line y = x will be (-5, 4). Then the correct option is C.
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A real estate investor buys a house and lot for $50,000. He pays $1,400 to have it painted, $2,500 to fix the plumbing, and $1,600 for grading a driveway. At what price must he sell the property in order to make a 20% profit?
A) $66,600
B) $49,760
C) $52,000
D) $52,800
E) $44,480
Help
Answer:
$66,600
Step-by-step explanation:
First you add everything up.
50,000 + 1,400 = 51,400
51,400 + 2,500 = 53,900
53,900 + 1,600 = 55,500
Now you need to get 20% of 55,500
20% of 55,500 is 11,100
Now you add them
55,500 + 11,100 = 66,600
Suppose you randomly select a group of American adults and ask them how many hours of TV they watched this past Saturday. The average of their answers is 4 hours. Which is most likely to be the distribution of their answers? PLS, I need the answer ASAP.
A. distribution A
B. distribution B
C. distribution C
D. distribution D
The most likely to watch TV for 4 hours is distribution B. Therefore, option B is the correct answer.
What is random sampling?In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
Given that, average number of hours American adults watch TV is 4 hours.
In distribution A, B, C and D, the most likely to watch TV for 4 hours is distribution B and less likely to watch TV for 4 hours is distribution A.
Therefore, option B is the correct answer.
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Question 3 of 10
A circle has an area of 36 m². What is the area of a 40°
sector of this circle?
A. 3 m²
B. 2m²
C. 6m²
O D. 4 m²
SUBMIT
The area of a 40° sector of this circle is 4m², the correct option is D.
How to find the area of a circle?Suppose the circle has radius of 'r' units, then, its area is given as:
[tex]A = \pi \times r^2[/tex]
sq. units
Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:
[tex]A = \pi \times r^2[/tex]
sq. units
Given;
A circle has an area of 36 m².
Now,
40° of circle= 360/40=9
Area of circel;
=36/9
=4
Therefore, the area of 40° of circle will be 4m^2
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In a school, 35% of the students are girls and the number of boys are 910, find the number of girls in the school. Also, find the total enrolment in the school
Answer:
Step-by-step explanation:
Percentage of girls = 35%
Percentage of boys = 100 - 35 = 65%
There are 910 boys:
65% = 910
Find the number of students in the school:
1% = 910 ÷ 65 = 14
100% = 14 x 100 = 1400
Answer: There are 1400 students in the school
if (xy)/2=7 and x^2+y^2 = 28 find (x+y)^2
Answer:
Step-by-step explanation:
Expanding (x + y)^2, we get:
(x + y)^2 = x^2 + 2xy + y^2
We are given that xy/2 = 7, so 2xy = 14. We are also given that x^2 + y^2 = 28. Substituting these values, we get:
(x + y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 14 = 42
Therefore, (x + y)^2 = 42.
Let p = "x > 7," q = "x = 7," and r = "11 > x."Select the symbol form for each of the following statement.(a). x ≥ 7p v qp ~ qp v rq ~ rp ^ q(b) 11 > x > 7p ~ qr ~ pr ^ pr v pp ^ q(c) 11 > x ≥ 7r ~ (p v q)r ^ (p ~ q)p ^ (q v r)r ^ (p v q)r v (p ^ q)
The correct symbol forms are:
a) x ≥ 7 is equivalent to p v q
b) 11 > x > 7 is equivalent to p ∧ r
c) 11 > x ≥ 7 is equivalent to ( p v q) ∧ r
We have the following definitions:
p = "x > 7"
q = "x = 7"
r = "11 > x"
a) The statement "x ≥ 7" is true if x is greater than 7 or if x is equal to 7. In other words, "x > 7 or x = 7" must be true. Using the given definitions, we can see that this is equivalent to p v q.
b) 11 > x > 7. The statement "7 < x < 11" means that x is greater than 7 and less than 11. In other words, both "x > 7" and "x < 11" must be true. hence, it can be expressed as the conjunction of "x > 7" and "x < 11," which is equivalent to p ∧ r.
c) 11 > x ≥ 7. Combining answer from part a and b, this is equivalent to:
( p v q) ∧ r
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If JK=x+8,kL=10, and JL=7x, what is JL
The value of JL is 21
What is line segment?
A line segment is defined as the part of a straight line that is bounded by two distinct end points.
It is known to contain all the points on the line that is between its endpoints.
From the information given, we have that the point K is found between J and L and the line segment, JL
Then, we have;
JK + KL = JL
substitute the values, we have;
x + 8 + 10 = 7x
collect the like terms
x - 7x = -10 - 8
subtract the like terms
-6x = -18
x = 3
So. JL = 7(3) = 21
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Let A be a random variable the represents the money you earn from Job A and let B be a random variable that represents the money you earn from Job B. The mean amount earned from Job A is $220 with a standard deviation of $30. The mean amount you earn from Job B is $180 with a standard deviation of $35.
a) On average how much more do you make from Job A?
b) What is the standard deviation of the difference in the amount you make (A – B)
c) Your mom really doesn’t want you working two jobs. She offers you the following deal. If you quit Job B, in addition to what you make in Job A, she will give you half of your average Job A salary plus $100. Would you take the deal if making the most money was most important to you? Explain.
The given statement indicates that (a) Your average pay is $40 (b) The standard deviation is 45.12 (c) If you retain both positions, your anticipated income is $400.
The significance of standard deviation?Because it aids in comprehending observations when the data is dispersed, standard deviation is significant. The standard error of the data will be higher the more evenly spread the data is.
a) On average, you make $220 - $180 = $40 more from Job A.
b) The standard deviation of the difference in the amount you make from Job A and Job B is given by:
σ(A - B) = √[σ(A)² + σ(B)²]
= √[(30)² + (35)²]
≈ 45.12
c) To determine whether to take the deal, we need to compare the expected earnings from the two scenarios. If you quit Job B and accept your mom's offer, your total earnings would be:
Earnings = (1/2) × $220 + $100 = $210
On the other hand, if you keep both jobs, your expected earnings would be:
Earnings = $220 + $180 = $400
Since $400 is greater than $210, you would not take the deal if making the most money is the most important thing to you.
It is important to remember that this choice may also be influenced by aspects like the amount of time and effort needed for each work, the chance for professional advancement, job security, and other non-financial considerations.
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I Need help now please
In the congruent triangles; ΔABC and ΔBDE, ∠ABC = ∠DBE by CPCT that is Corresponding parts of Congruent Triangle.
Explain about the ASA congruence?The triangles are congruent if their including sides are congruent and two of their angles match two of the other triangle's angles called Angle - Side -Angle congruenceThe term "CPCT" stands for "Corresponding parts of Congruent Triangle," meaning that if two triangles are congruent, they are precisely mirror images of one another and their corresponding parts, such as side lengths and angles, can be assumed to be equal.So,
ΔABC and ΔBDE, are congruent triangles
Thus,
∠ABC = ∠DBE (Corresponding parts of Congruent Triangle) CPCT.
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two dice (one red and one green) are to be rolled. the sample space consists of the 36 outcomes listed below. the first number is what is rolled on the red die and the second number is what is rolled on the green. determine: [ 1,1 1,2 1,3 1,4 1,5 1,6 ][ 2,1 2,2 2,3 2,4 2,5 2,6 ]S = [ 3,1 3,2 3,3 3,4 3,5 3,6 ][ 4,1 4,2 4,3 4,4 4,5 4,6 ][ 5,1 5,2 5,3 5,4 5,5 5,6 ][ 6,1 6,2 6,3 6,4 6,5 6,6 ]a) p(at least one of the dice is a 5) b) p(sum of the dice is equal to 7) c) p(sum of the dice is 11 or more) d) p(both are less than 3) e) p(red is larger than green) f) p(sum is greater than 9) g) p(red = 6)h) P(largest number is a 5)i) P(smallest number is a 5)
a) To find the probability that at least one of the dice is a 5, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 11 outcomes where at least one die is a 5: (1,5), (2,5), (3,5), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,5). Therefore, the probability is:
P(at least one 5) = 11/36
b) To find the probability that the sum of the dice is equal to 7, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 6 outcomes where the sum is 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Therefore, the probability is:
P(sum is 7) = 6/36 = 1/6
c) To find the probability that the sum of the dice is 11 or more, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 2 outcomes where the sum is 11 or more: (5,6), (6,5). Therefore, the probability is:
P(sum is 11 or more) = 2/36 = 1/18
d) To find the probability that both dice are less than 3, we can count the number of outcomes where this is true and divide by the total number of outcomes. There is only 1 outcome where both dice are less than 3: (1,1). Therefore, the probability is:
P(both less than 3) = 1/36
e) To find the probability that the red die is larger than the green die, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 15 outcomes where the red die is larger than the green die: (2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5). Therefore, the probability is:
P(red is larger) = 15/36 = 5/12
f) To find the probability that the sum of the dice is greater than 9, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 4 outcomes where the sum is greater than 9: (4,6), (5,5), (5,6), (6,4), (6,5), (6,6). Therefore, the probability is:
P(sum is greater than 9) = 6/36 = 1/6
g) To find the probability that the red die is 6, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 6 outcomes where the red die is 6: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). Therefore, the probability is:
P(red = 6) = 6/36 = 1/6
h) To find the probability that the largest number rolled is 5, we can count
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The deck of a bridge is suspended 225 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 225 – 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 3 and lasting the following amount of time. (i) 0.1 seconds ______ ft/s (ii) 0.05 seconds ______ft/s (iii) 0.01 seconds _______ ft/s (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 3 seconds._______ ft/s
a) (i) Average velocity = -96.8 ft/s
(ii) Average velocity = -95.2 ft/s
(iii) Average velocity = -92.8 ft/s
b) The instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.
What is average velocity?
The change in position or displacement (x) divided by the time intervals (t) in which the displacement happens yields the average velocity. Depending on the sign of the displacement, the average velocity can be positive or negative.
(a)
(i) The time period from t = 3 to t = 3.1 is 0.1 seconds. The average velocity of the pebble during this time period can be found by taking the difference in position (y) divided by the difference in time (t).
Average velocity = (y(3.1) - y(3)) / (3.1 - 3)
Substituting [tex]y = 225 - 16t^2[/tex], we get:
[tex]Average\ velocity = [(225 - 16(3.1)^2) - (225 - 16(3)^2)] / (0.1)[/tex]
Average velocity = -96.8 ft/s (rounded to one decimal place)
(ii) The time period from t = 3 to t = 3.05 is 0.05 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:
[tex]Average\ velocity = (y(3.05) - y(3)) / (3.05 - 3)[/tex]
Substituting [tex]y = 225 - 16t^2[/tex], we get:
[tex]Average\ velocity = [(225 - 16(3.05)^2) - (225 - 16(3)^2)] / (0.05)[/tex]
Average velocity = -95.2 ft/s (rounded to one decimal place)
(iii) The time period from t = 3 to t = 3.01 is 0.01 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:
Average velocity = (y(3.01) - y(3)) / (3.01 - 3)
Substituting [tex]y = 225 - 16t^2[/tex], we get:
[tex]Average \ velocity = [(225 - 16(3.01)^2) - (225 - 16(3)^2)] / (0.01)[/tex]
Average velocity = -92.8 ft/s (rounded to one decimal place)
(b)
The instantaneous velocity of the pebble at any given time t can be found by taking the derivative of the position function y(t) with respect to time:
[tex]\frac{dy}{dt} =-32t\\[/tex]
Substituting t = 3, we get:
[tex]\frac{dy}{dt} =-96ft/s\\[/tex]
Therefore, the instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.
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Exhibit 2-1 Production possibilities curve data Consumption Goods Capital Goods
10 0
9 1
7 2
4 3 0 4
In Exhibit 2-1, according to the information, the opportunity cost of producing 3 units of capital is: A) 3 units of consumption goods B) 4 units of consumption goods C) 6 units of consumption goods D) 7 units of consumption goods.
The answer is C) 6 units of consumption goods.
What is Cost of producing?
The overall cost incurred by a business to manufacture a product or provide services is referred to as the cost of production. Supplies and raw materials consumed during production, as well as labor costs, are often included in production costs.
The opportunity cost of producing 3 units of capital is 6 units of consumption goods, as we can see from the data in the production possibilities curve.
Moving from producing 4 units of capital to producing 3 units of capital involves giving up 3 units of consumption goods (from 7 to 4), and moving from producing 3 units of capital to producing 2 units of capital involves giving up another 3 units of consumption goods (from 4 to 1).
Therefore, the opportunity cost of producing 3 units of capital is 6 units of consumption goods.
So, the answer is C) 6 units of consumption goods.
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3) Flying with the wind a plane went 359 km/h. Flying into the same wind the plane only went 337
km/h. Find the speed of the plane in still air and the speed of the wind.
Answer: Let's call the speed of the plane in still air "p" and the speed of the wind "w".
When flying with the wind, the plane's speed is increased by the wind speed, so the equation is:
359 = p + w
When flying against the wind, the plane's speed is decreased by the wind speed, so the equation is:
337 = p - w
We can add these two equations to eliminate "p":
696 = 2p
So,
p = 348
Now that we know the speed of the plane in still air, we can use either equation to find the speed of the wind:
w = 359 - p = 359 - 348 = 11 km/h.
So, the speed of the plane in still air is 348 km/h and the speed of the wind is 11 km/h.
Step-by-step explanation:
Find the exact value of the following expression for the given value of 0. Do not use a calculator tan (0/2) if 0x/2 If 0 x/2, then tan (0/2) (Simplify your answer. Type an exact answer, using radicals as needed.)
The exact value of the expression tan(0/2) for the given value of 0 is 0.
In mathematics, it is important to understand how to simplify expressions and solve for their exact values. One such expression is tan(0/2), where 0 is a given value. In this explanation, we will break down the steps to simplify this expression and find its exact value without using a calculator.
The expression we are given is tan(0/2), which can be simplified using the formula for the tangent of half an angle. This formula states that tan(x/2) = sin(x) / (1 + cos(x)).
In our given expression, we have x = 0, so we can substitute it into the formula and get:
tan(0/2) = sin(0) / (1 + cos(0))
Now, we know that sin(0) = 0 and cos(0) = 1, so we can simplify further:
tan(0/2) = 0 / (1 + 1) = 0/2 = 0
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PLEASE HELP ASAP! DUE SOON!
The domain of the function g(x) = √x - 4 as an inequality is x ≥ 0.
What is the domain of the given function?The domain of a function is simply the set of all possible inputs for the function.
Given the function in the question;
g(x) = √x - 4
Domain: ?
To determine the domain of the function, set the radicand in √x to greater than or equal to 0 and find where the expression is defined,
x ≥ 0
Hence, the domain is all values of x that makes the expression defined.
Interval notation: [0,∞)
Set-Builder notation or inequality : { x|x ≥ 0 }.
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There are only Year 7 pupils, Year 8 pupils and Year 9 pupils in a group The ratio of Year 7 to Year 8 is The ratio of Year 8 to Year 9 is Find the ratio Year 7 : Year 8 : Year 9 Give your ratio in its simplest form with integer parts.
Given the ratio of Year 7 pupils to Year 8 pupils as 9:5 and the ratio of Year 8 pupils to Year 9 pupils as 1:11, the ratio of Year 7, Year 8, and Year 9 pupils together is 9:5:55.
What is the ratio?The ratio refers to the relative size of values.
Ratios are fractional values, depicted as fractions, decimals, or percentages. Ratios can also be denoted in ratio form (:).
Ratios are computed as the comparative values that each quantity has in relation to other quantities or values.
The ratio of Year 7 pupils to Year 8 pupils = 9:5
The ratio of Year 8 pupils to Year 9 pupils = 1: 11
The ratio of Year 7, Year 8, and Year 9 = 9:5:55 (11 x 5)
The sum of ratios = 69 (9 + 5 + 55)
Thus, the ratio of Year 7, Year 8, and Year 9 is 9:5:55.
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Complete Question:There are only Year 7 pupils, Year 8 pup,ils, and Year 9 pupils in a group The ratio of Year 7 to Year 8 is 9:5. The ratio of Year 8 to Year 9 is 1: 11.
Find the ratio Year 7: Year 8: Year 9. Give your ratio in its simplest form with integer parts.