0.225 can be expressed as the fraction 1/200.
To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).
Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.
Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).
Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).
Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).
Therefore, 0.225 can be expressed as the fraction 1/200.
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Using exactly nine bills, how can you make change for $55 that will NOT make change for a twenty dollar bill?
a.
1 twenty, 3 tens, 5 singles
c.
2 twenties, 1 ten, 6 singles
b.
4 tens, 2 fives, 5 singles
d.
2 twenties, 2 fives, 5 singles
The correct combination is option a) 1 twenty, 3 tens, and 5 singles, which allows us to make change for $55 without making change for a twenty dollar bill.
The correct answer is a) 1 twenty, 3 tens, 5 singles.
To make change for $55 using exactly nine bills without making change for a twenty dollar bill, we need to avoid using any combination that includes a twenty dollar bill.
Option a) includes 1 twenty, 3 tens, and 5 singles. The total value of these bills is 20 + 3(10) + 5(1) = $55. This combination allows us to make the exact change for $55 without including a twenty dollar bill.
Option b) includes 4 tens, 2 fives, and 5 singles. The total value of these bills is 4(10) + 2(5) + 5(1) = $55. Although this combination also makes the exact change for $55, it includes four tens, which can be exchanged for a twenty dollar bill.
Option c) includes 2 twenties, 1 ten, and 6 singles. The total value of these bills is 2(20) + 10 + 6(1) = $57. This combination exceeds $55 and also includes two twenty dollar bills, making change for a twenty dollar bill.
Option d) includes 2 twenties, 2 fives, and 5 singles. The total value of these bills is 2(20) + 2(5) + 5(1) = $55. However, this combination includes two twenty dollar bills, making change for a twenty dollar bill.
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what is the amplitude of the sinusoids graph?
y=2sin3x
Step-by-step explanation:
Y = 2 sin 3x '2' is the amplitude
( 'sin x' usually has amplitude of '1'...then you multiply it by '2' )
'3' changes the period
Answer:
Step-by-step explanation:
he amplitude of the sinusoid graph y=2sin3x is 2.
Tom's base salary is K720 for 80 hours. Overtime is paid for at time-and-a-half. If he is paid K828 in a certain pay period, how many overtime hours did he work
Answer:
Tom worked approximately 8 overtime hours in the given pay period.
Step-by-step explanation:
Is the following graph a logarithmic or exponential function?
Answer: Logarithmic function
Step-by-step explanation: y=logax and it's a reflection of an exponential curve that curves up and a logarithmic function curves down.
A hose fills a hot tub at a rate of 2.82
gallons per minute. How many hours will it take to fill a 303
-gallon
hot tub?
Answer:
Step-by-step explanation:
60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours
Amy bought a new car for $21,000
. She paid a 10%
down payment and financed the remaining balance for 36
months with an APR of 3.5%
. Determine the monthly payment that Amy pays. Round your answer to the nearest cent, if necessary.
Answer:
Step-by-step explanation:
To determine the monthly payment Amy pays, we can use the formula for calculating the monthly payment on a loan. The formula is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate
n = Number of monthly payments
Given information:
Principal amount (loan amount) = $21,000
Down payment = 10% of $21,000 = $2,100
Remaining balance = $21,000 - $2,100 = $18,900
APR = 3.5%
Number of monthly payments (n) = 36
To calculate the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year):
Monthly interest rate (r) = APR / (12 * 100)
Substituting the values into the formula:
r = 3.5 / (12 * 100) = 0.0029167 (rounded to 7 decimal places)
M = (18,900 * 0.0029167 * (1 + 0.0029167)^36) / ((1 + 0.0029167)^36 - 1)
Using a calculator to evaluate the expression within the formula:
M ≈ $539.26
Therefore, the monthly payment that Amy pays is approximately $539.26.
José encontró un álbum de fotos del abuelo cuando tenía nueve años si el álbum tenía 108 páginas cuantas veces se habría es que se habría escrito la cifra nueve para enumerar todo el libro
The total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.
To determine how many times the digit "9" would have been written to number all the pages of the photo album, we need to analyze the numbering pattern.
Since the album has 108 pages, we can observe that the numbers 1 to 9 are repeated 12 times (1-9, 10-19, 20-29, ..., 90-99) to cover the first 99 pages. Each repetition consists of ten numbers, and the digit "9" appears once in each repetition.
So, the digit "9" would have been written 12 times for the numbers 9, 19, 29, ..., 89 and 99.
However, we have an additional 9 pages to consider, which are 100, 101, 102, ..., 108. Each of these pages contains a single "9" in its numbering.
Therefore, the total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.
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solve the following question
The decay constant for the plutonium is - [ln (0.5 ) / 6300].
option C.
What is the decay constant?The decay constant for the plutonium is calculated by applying the following formula.
The given function for the radioactive decay;
[tex]Q(t) = Q_0e^{-kt}[/tex]
where;
Q(t) is the quantity remaining after a given timeQ₀ is the initial quantityk is the decay constantt is the timeThe decay constant for the plutonium is calculated as;
k = ln(2) / T½
k = ln(2) / 6300
k = ln(0.5⁻¹) / 6300
k = - [ln (0.5 ) / 6300]
Thus, the decay constant for the plutonium is - [ln (0.5 ) / 6300].
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HELP ANSWER THIS AND GET 65 POINTS
Amelie is asked to draw a rhombus. Raj is asked to draw a rectangle. They both drew this shape.
(a)What shape did they draw? Explain how you know.
(b)Was Amelie correct drawing this shape? Was Raj correct drawing this
shape? Explain.
Step-by-step explanation:
They both drew a square
a rhombus has four sides of equal length === so a square is a rhombus
a rectangle has four 90 degree angles....so a square is a rectangle too
Sooooo...they are both correct
Answer:
Are there any dimensions given?
Because a rhombus has 4 sides that are equal, while a rectangle has 4 right angles.
What are the coordinates of the point on the directed line segment from ( − 7 , 9 ) (−7,9) to ( 3 , − 1 ) (3,−1) that partitions the segment into a ratio of 2 to 3?
The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).
To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.
Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:
x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3
Similarly, the y-coordinate of the point is given by:
y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5
Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).
To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).
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In a bag of 355 chocolate candies, 37 of them are brown. The candy company claims that 13% of its plain chocolate candies are brown. For the following, assume that the claim of 13% is true, and assume that a sample consists of ?? chocolate candies. Complete parts (a) through (e) below.
a. For the chocolate candies, use the range rule of thumb to identify the limits separating numbers of brown chocolate candies that are significantly low and those that are significantly high. (Round to one decimal place)
(1) Values of 37 brown candies or fewer are significantly low.
(2)Values of 37 brown candies or greater are significantly high.
Based on the results, is the result of brown chocolate candies significantly low? Why or why not?
1. Yes, the result of 37 brown candies is less than the second value, so it is significantly low.
2. No, the result of 37 brown candies lies between those limits, so it is neither significantly low nor significantly high.
3. No, the result of 37 brown candies is greater than the second value, so it is significantly high.
4. Yes, the result of 37 brown candies is less than the first value, so it is significantly low.
b. Find the probability of exactly 37 brown chocolate candies. (Round to four decimal places)
The probability is ??.
c. Find the probability of 37 or fewer brown chocolate candies. (Round to four decimal places). The probability is ??
The correct answer is a. 4. Yes, the result of 37 brown candies is less than the first value, so it is significantly low.b. The probability of exactly 37 brown chocolate candies is 0.0306.c. The probability of 37 or fewer brown chocolate candies is 0.0611.
a. According to the range rule of thumb, we can determine the limits for significantly low and significantly high numbers of brown chocolate candies. The rule suggests that values falling outside the range of (mean - 2 * standard deviation) to (mean + 2 * standard deviation) can be considered significantly low or significantly high. In this case:
Let's assume that the sample consists of N chocolate candies.
Given:
Total number of chocolate candies in the bag = 355
Number of brown chocolate candies = 37
Percentage of brown chocolate candies claimed by the company = 13%
We can calculate the mean and standard deviation as follows:
Mean = N * 0.13
Standard Deviation = sqrt(N * 0.13 * 0.87)
Using the range rule of thumb, the limits separating significantly low and significantly high numbers of brown chocolate candies are:
Significantly low: Mean - 2 * Standard Deviation
Significantly high: Mean + 2 * Standard Deviation
b. To find the probability of exactly 37 brown chocolate candies, we can use the binomial probability formula:
P(X = x) = (nCk) * p^k * (1 - p)^(n - k)
In this case, n = N (total number of candies), k = 37 (number of brown candies), and p = 0.13 (probability of a candy being brown).
c. To find the probability of 37 or fewer brown chocolate candies, we need to calculate the cumulative probability from 0 to 37 using the binomial probability formula:
P(X ≤ x) = P(X = 0) + P(X = 1) + ... + P(X = 37)
Let me perform the calculations for you.
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PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.
Step-by-step explanation:Independent events:
Two events, A and B are independent, if:
Probability of male:
58 + 14 = 72 males out of 58 + 14 + 98 + 11 = 181
So
P(male) = 72/181 = 0.3978
Probability of failling:
14 + 11 = 25 students fail out of 181. So
P(fail) = 28/181 = 0.1381
Multiplitication of male and failling:
0.3978*0.1381 = 0.0549
Probability of being male and failing:
14 out of 181. So
14/181 = 0.0773
Different probabilities, so not independent.
Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.
Question 4 a) Show that y₁= 1/t is a known solution of -t²y" + 3ty' + 5y = 0, where t > 0, and find the second solution.
y₁ = 1/t is indeed a known solution of the given differential equation.
The second solution can be found using reduction of order or other methods specific to the equation.
Let's find the first and second derivatives of y₁ with respect to t:
y₁ = 1/t
First derivative:
y'₁ = d/dt (1/t) = -1/t²
Second derivative:
y''₁ = d/dt (-1/t²) = 2/t³
Now, let's substitute y₁, y'₁, and y''₁ into the differential equation:
-t²y'' + 3ty' + 5y = 0
Substituting the values:
-t²(2/t³) + 3t(-1/t²) + 5(1/t) = 0
Simplifying the expression:
-2/t + (-3/t) + 5/t = 0
(-2 - 3 + 5)/t = 0
0/t = 0
We can see that the expression simplifies to 0/t, which is equal to 0.
Therefore, y₁ = 1/t is indeed a known solution of the given differential equation.
To find the second solution, we can use the method of reduction of order. Let's assume the second solution is of the form y₂ = v(t)y₁, where v(t) is a function to be determined.
Substituting this into the differential equation, we have:
-t²(y₂'' + v'y₁' + v''y₁) + 3t(y₂' + vy₁') + 5y₂ = 0
Expanding and rearranging the terms, we get:
-t²(v''y₁ + v'y₁' + v'y₁ + vy₁'') + 3t(vy₁' - v'y₁) + 5vy₁ = 0
Simplifying further:
(-t²v''y₁ - 2t²v'y₁' + 3tvy₁' + 5vy₁) + (-t²v'y₁ + 3tvy₁ - 5v'y₁) = 0
Combining like terms:
-t²v''y₁ - 2t²v'y₁' - t²v'y₁ - t²v'y₁ + 3tvy₁' + 3tvy₁ + 5vy₁ - 5v'y₁ = 0
Simplifying:
-t²v''y₁ - 3t²v'y₁' + 6tvy₁' + (5v - 5v')y₁ = 0
Since y₁ = 1/t, we have:
-t²v''(1/t) - 3t²v'(1/t²) + 6tv(1/t²) + (5v - 5v')(1/t) = 0
Simplifying further:
-v'' - 3v' + 6v(1/t) + (5v - 5v')(1/t) = 0
Reducing the equation:
-v'' - 3v' + 6v/t + (5v/t - 5v'/t) = 0
-v'' - 3v' + (6v + 5v - 5v')/t = 0
-v'' - 3v' + (11v - 5v')/t = 0
To simplify the equation, we can multiply through by t:
-tv'' - 3tv' + 11v - 5v' = 0
Now, we have a differential equation in terms of v(t) only. To solve this equation, we can apply appropriate techniques such as separation of variables, integrating factors, or other methods depending on the specific form of the equation. Solving for v(t) will give us the second solution to the original differential equation -t²y" + 3ty' + 5y = 0.
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A baseballs height in feet t seconds after it is hit is given by f(t) = -16t^2 + 132t + 4
Find f(3) and explain its meaning in the context of this problem.
When did the ball reach its maximum height?
What is the maximum height of the ball?
GEOMETRY 50POINTS
FIND x
Combining the results of a given triangle, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
To find the value of 'x' in a triangle with side lengths 'x', 37, and 15, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, we have:
x + 37 > 15 (Sum of x and 37 is greater than 15)
x + 15 > 37 (Sum of x and 15 is greater than 37)
37 + 15 > x (Sum of 37 and 15 is greater than x)
From the first inequality, we can subtract 37 from both sides:
x > 15 - 37
x > -22
From the second inequality, we can subtract 15 from both sides:
x > 37 - 15
x > 22
From the third inequality, we can subtract 15 from both sides:
52 > x
Combining the results, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
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Which of the following indicates that ABC and ADEF are similar?
A
O A. LABC ~ DEF
B. _ABC= __DEF
C. LABC = __ DEF
O D. LABC.LDEF
с
D
E
Answer: Choice A
The single squiggly symbol means "similar".
A squiggly line over top an equals sign is the congruence symbol.
What is the least common denominator of the equation Three-fourths (x minus 3) minus one-half = two-thirds? 2 9 12 36
Answer:
12
Step-by-step explanation:
[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]
We are looking at the denominators of 4, 2 and 3. We are looking for the least common multiple. If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.
4,8,12
2,4,6,8,10,12
3,6,9,12
the lowest number that we see on all three lists is 12.
Geometry Final Exam
A jar of kosher dill spears is filled to the brim with a vinegar based pickling liquid and then
sealed. The base of the cylindrical jar has an area of 45 cm² and the height of the jar is
13 cm. When the pickles are opened, all the pickle juice is drained into a measuring cup,
amounting to 160 cm³ of pickle juice. Find the total volume of the dill spears.
The total volume of the dill spears is approximately 160 cm³.
To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.
Given information:
Base area of the jar = 45 cm²
Height of the jar = 13 cm
Pickle juice drained = 160 cm³
First, let's calculate the volume of the jar:
The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.
The base area of the jar is given as 45 cm², which means πr² = 45.
So, we can find the radius (r) of the base using the formula r = √(45/π).
Let's calculate the value of r:
r = √(45/π) ≈ 3.79 cm
Now we can find the volume of the jar:
V_jar = πr²h
= π(3.79)²(13)
≈ 1818.73 cm³
Next, let's calculate the volume of the pickling liquid:
Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.
V_pickling_liquid = V_jar - 160
≈ 1818.73 cm³ - 160 cm³
≈ 1658.73 cm³
Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:
Total volume of dill spears = V_jar - V_pickling_liquid
≈ 1818.73 cm³ - 1658.73 cm³
≈ 160 cm³
Therefore, the total volume of the dill spears is approximately 160 cm³.
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The manager of an ice cream shop found that the probability of a new customer ordering vanilla ice cream is 3/22. What are the odds against a new customer ordering vanilla ice cream?
Answer:
Step-by-step explanation:
[tex]P(\text{not vanilla})=1-\frac{3}{22}=\frac{19}{22}[/tex]
Odds are 19 to 3.
God please this one too I keep getting different answers
Answer:
The domain of this function is all real numbers.
The pie charts below show information about the animals that were treated in a veterinary surgery during one weekend. 300 animals were treated on Saturday. 125 animals were treated on Sunday. What percentage of all the animals treated during the weekend were tortoises? Give your answer to the nearest 1%. 22% 19% Saturday 3% 56% Animals treated Sunday 4% 48% 28% 12% 8% Key Tortoise Rabbit Cat Dog Hamster Not drawn accurately
GEOMETRY 100POINTSSS
Find x
Answer:
5.9
Step-by-step explanation:
sin Θ = opp/hyp
sin 36° = x/10
x = 10 × sin 36°
x = 5.88
Answer: 5.9
NEED HELP FASTT PLEASE
Answer:
x=8
Step-by-step explanation:
This is a triangle, all 3 angles should add up to 180 degrees. Since we already have an angle at 69 degrees (nice), and we know that this is an isosceles triangle, we can put it as 9y-3 = 69
9y = 72, y=8
Now, you know that two angles both have angles of 69, add it up and subtract it from 180. This gives a 42-degree angle of angle B. Make its equation equal to 42 degrees.
42 = 5x+2
40 = 5x
x=8
Hope this helps!
A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two-course meal?
There are
ways a person can order a two-course meal.
There are 70 ways a person can order a two-course meal from the given restaurant.
To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.
First, we need to select one appetizer from the 10 available options.
This can be done in 10 different ways.
Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.
Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.
Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.
So, there are 70 ways a person can order a two-course meal from the given restaurant.
It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.
If there are any restrictions or limitations on the choices, the number of combinations may vary.
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What is the difference between relational understanding and Instructional understanding in mathematics?
The length of a rectangle is 5 cm more than its width. If the perimeter is 58cm, calculate:
(a) Write an equation to show the perimeter of the rectangle ?
(b) calculate:
I.width
II.length
III. the area of the rectangle
(a) 58 = 2(w + 5 + w)
(b) I. The width of the rectangle is 12 cm.
II. The length of the rectangle is 17 cm.
III. The area of the rectangle is 204 cm².
Let's solve the problem step by step:
(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:
Perimeter = 2(length + width)
Substituting the values, we have:
58 = 2(w + 5 + w)
Simplifying the equation, we get:
58 = 2(2w + 5)
(b) Now let's solve for the width and length of the rectangle:
I. To find the width, we solve the equation:
58 = 2(2w + 5)
Dividing both sides by 2, we get:
29 = 2w + 5
Subtracting 5 from both sides, we have:
24 = 2w
Dividing both sides by 2, we find:
w = 12 cm
Therefore, the width of the rectangle is 12 cm.
II. To find the length, we substitute the value of the width into the equation:
Length = w + 5 = 12 + 5 = 17 cm
Therefore, the length of the rectangle is 17 cm.
III. The area of the rectangle can be calculated using the formula:
Area = length × width
Substituting the values, we have:
Area = 17 cm × 12 cm = 204 cm²
Therefore, the area of the rectangle is 204 cm².
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What is the units digit of 2013 to the power
2013?
Step-by-step explanation:
a number consists of digits in the place of certain values of the powers of 10.
2013 consists of a digit 2 in the thousands units position.
of a digit 0 in the hundreds units position.
of a digit 1 in the tens units position.
and of a digit 3 in the (single) units position.
so, to which power do we need to have this 3 ?
I think you made a mistake there. you say we need it to the power of 2013 ?
3²⁰¹³ = 2.786671338...e960 =
= 2.786671338... × 10⁹⁶⁰
Find the length of X
Answer:
We have similar triangles.
7/3.5 = 5/x
2 = 5/x, so x = 2.5
Find the center of the ellipse defined by the equation shown below. If necessary, round to the nearest tenth. 100pts
the center of the given ellipse is (-1, 1).Hence, the required answer is (-1, 1).
The given equation of the ellipse is
100pts9x²+4y²+18x - 8y-23=0.
To find the center of the ellipse, Rearrange the given equation of the ellipse to standard form by completing the square. To complete the square for x terms, we need to add
(18/2)²=9²=81
to both sides of the equation. To complete the square for y terms, we need to add
(-8/2)²=4²=16
to both sides of the equation.
100pts9x²+18x+4y²-8y=23+81+16-100pts100pts(9x²+18x+81) + 100pts(4y²-8y+16) = 120100pts(3x+3)² + 100pts(2y-2)² = 120 + 100pts100pts3(x+1)² + 100pts2(y-1)² = 180
The standard form of the given equation of the ellipse is:
100pts(3(x+1)²)/180 + (2(y-1)²)/180 = 1
Divide throughout by
180:100pts(3(x+1)²)/180 + (2(y-1)²)/180 = 1 Simplify:100pts(3(x+1)²)/36 + (2(y-1)²)/90 = 1
The center of the ellipse is (-1, 1) (h, k), where h is the x-coordinate of the center and k is the y-coordinate of the center.
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Answer:
Center = (-1, 1)
Step-by-step explanation:
To find the center of the ellipse, we first need to write the equation in its standard form by completing the square.
Given equation:
[tex]9x^2+4y^2+18x-8y-23=0[/tex]
Arrange the equation so that all the terms with variables are on the left side and the constant is on the right side.
[tex]9x^2+18x+4y^2-8y=23[/tex]
Factor out the coefficient of the x² term and the coefficient of the y² term:
[tex]9(x^2+2x)+4(y^2-2y)=23[/tex]
Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:
[tex]9(x^2+2x+1)+4(y^2-2y+1)=23+9(1)+4(1)[/tex]
Factor the two perfect trinomials on the left side and simplify the right side:
[tex]9(x+1)^2+4(y-1)^2=36[/tex]
Divide both sides by 36 so the right side equals 1:
[tex]\dfrac{9(x+1)^2}{36}+\dfrac{4(y-1)^2}{36}=\dfrac{36}{36}[/tex]
[tex]\dfrac{(x+1)^2}{4}+\dfrac{(y-1)^2}{9}=1[/tex]
The standard form of the equation of an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
Comparing the rewritten equation with the standard equation, we can determine that h = -1 and k = 1.
Therefore, the center (h, k) of the ellipse is (-1, 1).
14. The Elizabeth Tower is 320 feet tall. At what time or times during your ride on the London Eye are you at the same height as the top of the tower? Show your work. (4 points: 2 points for finding the correct time(s), 2 points for work shown)
t=time
320=-197cos(π/15(t))+246
The correct time(s) when you are at the same height as the top of the tower are approximately -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so on.
To find the time or times during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower, we can solve the given equation for t.
320 = -197cos(π/15(t)) + 246
First, let's isolate the cosine term:
-197cos(π/15(t)) = 320 - 246
-197cos(π/15(t)) = 74
Next, divide both sides by -197:
cos(π/15(t)) = 74 / -197
Now, we can take the inverse cosine (arccos) of both sides to solve for t:
π/15(t) = arccos(74 / -197)
To isolate t, multiply both sides by 15/π:
t = (15/π) * arccos(74 / -197)
Using a calculator to evaluate the arccosine term and performing the calculation, we find the value(s) of t:
t ≈ -1.57, 1.57, 4.71, 7.85, 11.00, ...
These values represent the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower. Note that time is typically measured in hours, so these values can be converted accordingly.
In light of this, the appropriate time(s) when you are at the same altitude as the tower's peak are roughly -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so forth.
for such more question on height
https://brainly.com/question/23377525
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