As per the expenses, the planning technique that is suitable for Alice is strategic planning
The term expenses in math refers the cost that businesses incur in running their operations.
Here we have given that allice is interested in making deductible charitable contributions, but she does not want to incur the expense of drafting a private trust agreement.
And we need to find planning techniques will meet her needs
While we looking into the given question, we have identified that she does not want to incur the expense of drafting a private trust agreement.
Based on these one, she would prefer strategic planning includes a high-level overview of the entire business and it is the foundational basis of the organization and will dictate long-term decisions.
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(A TEST I NEED IT ASAP)
1. Use each digit from 1 to 5 once to make the following equation true. ■ − ■ ■/■ = 3 ■/6
2. The sum of three mixed numbers is 8 2/5. The difference between the first number and second number is 1. The difference between the first number and third number is 2. What is the least number?
3. Tori plays the tuba. She plays for 4 1/2 measures, rests for 8 3/8 measures, plays for another 16 measures, rests for 2 1/4 measures, and plays for the rest of a 36-measure song. How long was the last section that she played?
Answer:
2
Step-by-step explanation:
g ranking/unranking algorithms to generate a uniform random binary string of length n with exactly k ones.
The solution is written in Python
binary = ""decimal = 13quotient = int (decimal / 2) remainder = decimal % 2binary = str(remainder) + binarywhile(quotient >0):decimal = int(decimal / 2)quotient = int(decimal / 2) remainder = decimal % 2binary = str(remainder) + binaryprint(binary)The given problem can be solved by using the rand() function that generates a random number over the range [0, RAND_MAX] and with the help of the value returned by this function, any number in any range [L, R] can be generated as (rand() % (R – L + 1)) + L. Follow the steps below to solve the problem:
Initialize an empty string, say S.
Iterate over the range [0, N – 1] and perform the following steps:
Store a random number in the range [0, 1] using rand() function.
Append the randomly generated 0 or 1 to the end of the string S.
After completing the above steps, print the string S as the resulting binary string.
This binary is to hold the binary string.
Next, we declare variable decimal, quotient and remainder (Line 2-4). We assign a test value 13 to decimal variable and then get the first quotient by dividing decimal with 2 (Line 3). Then we get the remainder by using modulus operator, % (Line 4). The first remainder will be the first digit joined with the binary string (Line 5).
We need to repeat the process from Line 3-5 to get the following binary digits. Therefore create a while loop (Line 7) and set a condition that if quotient is bigger than 0 we keep dividing decimal by 2 and calculate the quotient and remainder and use the remainder as a binary digit and join it with binary string from the front (Line 9-11).
At last, we print the binary to terminal (Line 13).
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maria is selling chips and candy bars. each box of chips has 20 bags for $13.80 and the candy bars is $6.60 for a box of 12 bars. if maria only has $100 to spend, write an inequality that represents the possible number of boxes of chips (x) and boxes of candy bars (y) maria could buy.
The inequality that represents the possible number of boxes of chips (x) and boxes of candy bars (y) Maria could buy is 13.80x + 6.60y ≤ 100.
How to represent inequality?Maria is selling chips and candy bars. each box of chips has 20 bags for $13.80 and the candy bars is $6.60 for a box of 12 bars.
Maria has only 100 dollars to spend. The inequality that represent the possible number of boxes of chips (x) and boxes of candy bars (y) Maria could buy can be calculated as follows:
Therefore,
x = number of boxes of chipsy = number of boxes of candy barsHence each box of chips is 13.80 dollars and each candy bars is 6.60 dollars.
Therefore, the inequality is 13.80x + 6.60y ≤ 100.
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(Score for Question 1: of 3 points)
1. Represent each situation with an inequality.
(a) The sum of a number and 12 is at most -8.
(b) A number increased by -8 is greater than 12.
(c) -8 less than a number is no more than 12.
Answer:
Inequality for each part be
a) x + 12 ≤ -8
b) x - 8 > 12
c) x + 8 < 12
What do you mean by inequality?
In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size.
The notation a < b means that a is less than b.
The notation a > b means that a is greater than b.
Let the number be x
According to the question:
a) The sum of a number and 12 is at most -8.
inequality become:
x + 12 ≤ -8
b) A number increased by -8 is greater than 12
inequality become:
x + (-8) > 12
⇒ x - 8 > 12
c) -8 less than a number is no more than 12
x - (-8) < 12
⇒ x + 8 < 12
Therefore, inequality for each part be
a) x + 12 ≤ -8
b) x - 8 > 12
c) x + 8 < 12
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A random sample of 75 students at the University of Minnesota spend an average of $614 per month in rent
with a standard deviation of $219. The distribution is moderately skewed to the high end. Which of the
following statements are true?
i. 95% of students at the university spend $564 to $664 on rent.
ii. We are 95% confident that the average rent for students at the university is between $564 and $664.
iii. Because we cannot examine other characteristics of the students in the random sample, it is not
advisable to construct a confidence interval.
Oi only
O ii only
O iii only
Oi and ii
Oi, ii, and iii
Check Answer
The correct option is b) ii only
From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.
What is meant by distribution?
The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.
What are the 3 types of distribution?
The Three Types of Distribution
Intensive Distribution: As many outlets as possible. The goal of intensive distribution is to penetrate as much of the market as possible.Selective Distribution: Select outlets in specific locations. ...Exclusive Distribution: Limited outlets.What are the 5 factors of distribution?
Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.
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Help with this plsssss !!!
Answer:
58
Step-by-step explanation:
There are 5 lines between 50 and 60
60 - 50 = 10
10 / 5 = 2
This means that each increment is 2.
We see the end of the box plot is above the fourth increment above 50.
4 x 2 = 8
50 + 8 = 58
Marco has $16.72. He spends $9.21 on a movie ticket. How much money does Marco have left?
Responses
A $7.68$7.68
B $7.51$7.51
C $7.48$7.48
D $7.61
Answer:
7.51
Step-by-step explanation:
16.72 - 9.21
Helpp!! GIVING BRAINIEST
The value of the c in the function c = 19m - 15 when m=10 is 175.
What is a function?A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.
Given the function;
c = 19m - 15,
where m represents the number of months and c represents the total number of car sent to New York.
To find the value of c:
when m = 10,
Substitute the value of m to the function;
c = 19 (10) - 15
c = 190 - 15
c = 175.
Therefore, the value of c is 175.
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Apply Math Models You have 20 quarters. You
find 40% more quarters in your room. Then you go
shopping and spend 50% of the total number of
quarters.
a. Write an expression that represents the
total number of quarters you take with
you when you go shopping.
b. How much money do you have left?
18. H
F
S
F
t
Answer:
a. Let Q be the total number of quarters you take with you when you go shopping. The total number of quarters you have is 20, and you find 40% more quarters in your room, which is an additional 0.4 * 20 = <<0.420=8>>8 quarters. Therefore, the total number of quarters you have after finding more quarters in your room is 20 + 8 = <<20+8=28>>28 quarters. When you go shopping, you spend 50% of the total number of quarters, which is 0.5 * 28 = <<0.528=14>>14 quarters. Therefore, the total number of quarters you take with you when you go shopping is 28 - 14 = <<28-14=14>>14 quarters. This can be represented by the expression Q = 28 - 0.5 * 28.
b. If you have 14 quarters with you when you go shopping, and you spend 50% of the total number of quarters, then you have 0.5 * 14 = <<0.514=7>>7 quarters left. Since each quarter is worth $0.25, you have 7 * 0.25 = $<<70.25=1.75>>1.75 left. Answer: \boxed{1.75}.
lucy buys a $68 pair of shoes. she receives a 15% employee discount. if the sales tax is 6 1/4 %, how much does she pay for the shoes?
The amount that Lucy pays for the shoes is $61.56.
How to calculate the amount paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this situation, Lucy buys a $68 pair of shoes. she receives a 15% employee discount and the sales tax is 6 1/4. The amount paid will be:
= $68 - (15% × $68)
= $57.80
Addition of the sale tax will be:
= $57.80 + (6.5% × $57.80)
= $57.80 + $3.76
= $61.56.
The price is $61.56.
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Polly borrowed $285 for a new floor lamp. She will make 5 monthly payments of $62 to repay the loan. How much will she pay in interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
How do you calculate interest on a loan?Divide your interest rate by the number of payments you'll make that year. If you have a 6 percent interest rate and you make monthly payments, you would divide 0.06 by 12 to get 0.005. Multiply that number by your remaining loan balance to find out how much you'll pay in interest that month.If the payment plan is $62 per month for 5 months, then the whole payment will be: $310To calculate simple interest on a loan, take the principal (P) times the interest rate (R) times the loan term in years (T), then divide the total by 100. To use this formula, make sure you're expressing your interest rate as a percentage, not a decimal (i.e., a rate of 4% would go into the formula as 4, not 0.04).So, $10$ percent per annum means that $10$ percent interest will be charged yearly or annually over a principal amount or a loan. Note: If the rate of interest is $10$ percent per annum, then the interest calculated will be $10$ percent of the principal amount.To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.
310-285 = 25
So, Polly will pay $25 in interest.
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If the original price of a tv was 1650 before the 17% markup, what is the price of the tv
Which system of linear inequalities is graphe
Answer:
B
Step-by-step explanation:
The vertical dashed line is x = -3. Since the shading is to the right, that is x > -3.
The solid line has slope -4/5 and y-intercept -2. It's shaded above, so it is y ≥ -x - 2.
Answer: B
-2x + 13 = -7x + 28
Answer:
x=3
Step-by-step explanation:
step one: first, you want to make it so that the variable x is only on one side. to do this, you use inverse operations. this means adding 7x to both sides.
-2x+7x=5x -7x+7x cancels itself out
the equation is now 5x+13=28
step two: next, you want to isolate the variable x. to do this you are going to use inverse operations yet again, this time subtracting 13 from both sides.
13-13=0 28-13=15
the equation is now 5x=15
step three: lastly, you want get x by itself without the 5 in front of it. using inverse operations for the last time, you are going to divide both sides by 5 because 5x means "5 times x" and division is the opposite of multiplication.
5x/5=x 15/5=3
the answer is now x=3
x= 3.
Step-by-step explanation:1. Write the equation.[tex]-2x + 13 = -7x + 28[/tex]
2. Add "7x" to both sides of the equation.[tex]-2x + 13 +7x= -7x + 28+7x\\ \\13+5x=28[/tex]
3. Subtract "13" from both sides of the equation.[tex]-13+13+5x=28-13\\ \\5x=15[/tex]
4. Divide both sides by "5".[tex]\frac{5x}{5}=\frac{15}{5} \\ \\x=\frac{15}{5}\\ \\x=3[/tex]
5. Verify.If the result is correct, when we substitute the value of x in the original equation, it should return the same value on both sides of the equal (=) symbol. Let's test it!
[tex]-2(3 ) + 13 = -7(3) + 28\\ \\-6+13=-21+28\\ \\7=7[/tex]
That's correct! Therefore, the correct answer is x=3.
8x + 2 = 26
can someone please help?..
Answer:
x = 3
Step-by-step explanation:
8x + 2 = 26
8x = 26 - 2
8x = 24
x = 24/8
x = 3
Check:
8*3 + 2 = 26
24 + 2 = 26
The function below has at least one rational zero. Use this fact to find all zeros of the function. f(x)=7x^4 +27x^3 -40x^2 +x +5
The rational zeros of the function can be found using the Rational Zero Theorem. The possible rational zeros of the function are ±1, ±5, ±1/7, ±5/7.
Zeros:
x=-5, -1/7, 0, 1, 5
The Rational Zero Theorem states that if a polynomial function of degree n has integer coefficients, then the possible rational zeros of the function will be of the form ±p/q, where q is a factor of the leading coefficient and p is a factor of the constant term.
In this case, the degree of the polynomial is 4, which means that the leading coefficient is 7 and the constant term is 5. Thus, the possible rational zeros of the function will be of the form ±p/q, where p is a factor of 5 and q is a factor of 7. The factors of 5 are ±1 and ±5, and the factors of 7 are ±1 and ±7. This means that the possible rational zeros of the function are ±1, ±5, ±1/7, and ±5/7.
To find the zeros of the function, we can use the rational zeros we found and plug them into the original equation. We can then solve for the zeros and find that the zeros of the function are x=-5, -1/7, 0, 1, 5.
x=-5: 7(-5)^4 +27(-5)^3 -40(-5)^2 +(-5) +5= 0
x=-1/7: 7(-1/7)^4 +27(-1/7)^3 -40(-1/7)^2 +(-1/7) +5= 0
x=0: 7(0)^4 +27(0)^3 -40(0)^2 +(0) +5= 0
x=1: 7(1)^4 +27(1)^3 -40(1)^2 +(1) +5= 0
x=5: 7(5)^4 +27(5)^3 -40(5)^2 +(5) +5= 0
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57. Center: (0, 0); Radius: 3
Solve the equation 6x² + 1 = 10x to the nearest tenth.
Suppose that a high school marching band has 112 members. Of these 112 band members, 35 are seniors, 21 play the trumpet, and 8 are seniors who play the trumpet. What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? Give your answer as a percentage, rounded to one decimal place. What is the probability that a randomly selected band member plays the trumpet given that he or she is a senior?
Answer:
Part A: 38.1% of the members are seniors that play the trumpet
Part B: 22.9% of the members who are seniors play trumpet
Step-by-step explanation:
Part A:
8 of the 21 members play trumpet that are seniors
8/21 = .381 or %38.1 of the members
Part B:
8 of the 35 seniors in the marching band play trumpet
8/35 = .229 or %22.9 of the members
Please Help!!!
Marshall wants to buy a car in five years worth $20,000. He finds a savings account with a simple interest rate of 4%. How much money must he put in the account now so he has $20,000 to buy the car in five years (round to the nearest dollar). SHOW ALL WORK
The amount of money he must put in the account is $16666.66
What is meant by interest rate?A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe.
This year, the Bank of Canada quickly increased its policy rate, taking it from 0.25% in March 2022 to 4.25% in December 2022, and in the process, driving up mortgage and prime rates. An interest rate is the portion of a loan, deposit, or borrowing that must be paid in interest each period. The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.
Given,
r=4%
T=5 years
Total amount=SI+P
=20000
SI+P=20000
SI=20000-P
SI=PTR/100
20000-P=(P×5×4)/100
2000000-100P=20P
120P=2000000
P=16666.66
Therefore, The amount of money he must put in the account is $16666.66.
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You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 7.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 95.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
ta/2 = ±
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
The distribution of the sample mean will be roughly normally distributed, according to the Central Limit Theorem, if we have an unknown population with a mean and standard deviation and adequately small random samples (n < 30) are chosen from the population with replacement.
Then, the mean of the sample means is given by,
μ(x) = μ
And the standard deviation of the sample means is given by,
σ = σ / [tex]\sqrt{n}[/tex]
In this case the sample selected is of size, n = 7.
As the sample size n = 7 < 30, the sampling distribution of sample mean will be approximately normal.
So, a z-interval will be used to estimate the population mean.
The confidence level is, 95.9%.
The value of α is:
∝ = 1 - confidence level
∝ = 1 - 0.959
∝ = 0.041
The critical value is:
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{\frac{0.041}{2} }[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{0.0205}[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = -1.99
[tex]z_{1-∝/2}[/tex] = 1.99
Use a z-table.
Therefore,
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
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Cone W has a radius of 6 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.
Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
Define cone and square pyramid
A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.
on the other hand ,
A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.
CalculationCone W has a radius of 6 cm and a height of 5 cm.
The base area of the cone will be
A = πr²
A = π (6)²
A = 113.04 square cm
Then the volume of the cone will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm
Square pyramid X has the same base area and height as cone W.
Then the volume of the square pyramid will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm.
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
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please help meeeeeeee
Answer: B & A
Step-by-step explanation: I think?
a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
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If h= 12 and g = 4, which of the following has a value of 3?
g+1
h-g
H/g
h÷3
Answer:
h/g is 3
Step-by-step explanation:
h=12 and g=4 12/4 is 3 so its h/g
Answer:
H/g
Step-by-step explanation:
12/4 = 3
convert the following equation into standard form.
Y = -2x
2x − y = 0
The standard form of a linear equation is:
Ax + By= C
where, if at all possible, A, B, and C are integers, A is non-negative, and, A, B, and C have no common factors other than 1.
The equation in the problem can be converted into standard form by the following method:
−2x + y= −2x + 2x
−2x + y = 0
−1(−2x+y) = −1 × 0
2x − y = 0
2x − 1y = 0
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An aircraft is flying at altitude H when it begins its descent to an airport runway that is at a horizontal ground distance L from the airplane. Assume that the landing path is described by the cubic polynomial function y=ax3+bx2+cx+d where y(-L)= H and y(0)= 0.a. What is dy\dx at x= 0?b. What is dy\dx at x= -L?
a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]
b. [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]
a. The derivative of a cubic function
[tex]y=ax^3+bx^2+cx+d[/tex] is [tex]y'=3ax^2+2bx+c[/tex].
Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.
b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].
Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]
A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.
A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3
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In APQR, m/P = (x + 13)°, m/Q = (10x + 13)°, and
m/R = (2x − 2)°. Find m/Q.
Answer:
[tex]133^{\circ}[/tex]
Step-by-step explanation:
Angles in a triangle add to [tex]180^{\circ}[/tex].
[tex]x+13+10x+13+2x-2=180 \\ \\ 13x+24=180 \\ \\ 13x=156 \\ \\ x=12 \\ \\ m\angle Q=10(12)+13=133^{\circ}[/tex]
The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours
Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.
How to write a linear function for the total amount of money Radda earns?In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;
T = mx + b
Where:
T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;
f(x) = T = 9.25x + 3
When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;
f(1) = T = 9.25(1) + 3
f(1) = T = 9.25 + 3
f(1) = T = $12.25.
In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.
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Complete Question:
The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?
Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 6 + 2 cos(t), π/2 ≤ t ≤ 2π The motion of the particle takes place on an ellipse centered at (x, y) = 1,6 . As t goes from π/2 to 2π, the particle starts at the point (x, y) = 1,6 and moves clockwise three-fourths of the way around the ellipse to (x, y) = .
Two foci of the ellipse are ( 2 - √3) and moves clockwise three fourth is ( 2 + √3).
As given in the question,
Given equations are :
x = 1 + sin(t)
⇒ sin(t) = (x - 1)
y = 6 + 2cos(t)
⇒cos(t) = (y - 6)/2
We know that,
sin²t + cos²t = 1
Substitute the value of sin(t) and cos(t) we get,
(x - 1)²/ 1² + (y - 6)²/ 2² = 1
Standard Equation of the ellipse is:
( x -h)²/b² + (y - k)²/a² = 1
Center of the ellipse = (h , k)
(h , k) = (1, 6)
here b = 1 and a = 2
'c' is the distance from focus to the center
c = √a² - b²
= √4 -1
= √3
Therefore , two foci for the given ellipse are ( 2 - √3) and moves clockwise three fourth is ( 2 + √3).
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