The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.
How do you solve for the larger acute angle of ΔABC ?Let's denote the angles of triangle ΔABC as follows:
∠A = x
∠B = y
∠C = 90° (right-angled triangle)
Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.
Since CD is the median, we know that angle ∠ECD = φ.
In right-angled triangle ΔCEB, we have:
∠CEB = 90° - y
Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:
∠CED + ∠CEB + ∠ECD = 180°
Substitute the known values:
∠CED + (90° - β) + φ = 180°
Since ∠CED and ∠A are supplementary angles, we can also write:
∠CED = 180° - x
Now substitute this value into the previous equation:
(180° - x) + (90° - y) + φ = 180°
Simplify the equation:
270° - x - y + φ = 180°
Subtract 90° from both sides:
180° - x - y + φ = 90°
From this equation, we get:
x + y = 90°
Substitute this value back into the equation involving φ:
180° - (90°) + φ = 90°
Simplify:
90° + φ = 90°
Therefore, the measure of the larger acute angle of ΔABC is:
x = 45° + φ/2 (option a)
the above answer is in response to the full question below;
Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:
a. 45⁰ + φ/2
b. 60⁰ + φ/2
c. 90⁰ - φ/2
d. 2φ
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Help me please I got an exam tomorrow
Answer:
Domain(-infinity,infinity) Range(-infinity,infinity) Zeros(0,0), (-4,0), (8,0) and (4,0) y-intercept at 0, even, y-axis, 2, -4
Step-by-step explanation:
qwtq4rg
Y= 1/2x+5
X _ Y
-4. ?
-2. ?
0. ?
2. ?
Answer: 0.
Step-by-step explanation:
y-(1/2*x+5)=0 STEP 1:
simplify 1/2
Equation at the end of step 1: 1
y - ((— • x) + 5) = 0
Rebecca used 4.25pt of milk in her baking recipe. How many cups of milk did she use?
Answer: 8.25
Step-by-step explanation:
A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?
Group of answer choices
(x − 4)2 + (x + 7)2 = 5
(x − 4)2 + (x + 7)2 = 25
(x + 4)2 + (x − 7)2 = 5
(x + 4)2 + (x − 7)2 = 25
The equation of circle whose center is at (4,-7) and radius is "5 units", is (b) (x − 4)² + (x + 7)² = 25.
We know that the equation of a circle which have center at the coordinate (h, k) and has a radius as "r" is represented by the formula ⇒ (x - h)² + (y - k)² = r²,
In this case, the center of the circle is situated at the coordinate (4, -7) and the radius is 5.
So, we substitute these values into the "circle-equation" to get;
⇒ (x - 4)² + (y + 7)² = 5²,
⇒ (x - 4)² + (y + 7)² = 25,
Therefore, the correct option is (b): (x − 4)² + (y + 7)² = 25.
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The given question is incomplete, the complete question is
A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?
(a) (x − 4)² + (x + 7)² = 5,
(b) (x − 4)² + (x + 7)² = 25,
(c) (x + 4)² + (x − 7)² = 5,
(d) (x + 4)² + (x − 7)² = 25.
Cheryl and her sister Diane walk to school along the same route. Cheryl walks at an average of
80 steps per min while Diane walks at an average of 90 steps per min. Cheryl takes steps
of 81 cm each. She takes 12 min to walk to school.
A) If each of Diane's steps in 72 cm, how long does Diane take to walk to school?
Answer: Let's first convert Cheryl's walking speed to meters per minute. Since she takes 80 steps per minute and each step is 81 cm, her walking speed is:
80 steps/min x 81 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
Now, let's find out the distance Cheryl walks to school. Since she walks for 12 minutes at a speed of 64.8 m/min, the distance she covers is:
distance = speed x time = 64.8 m/min x 12 min = 777.6 m
Next, let's find out how many steps Diane takes per minute on average:
90 steps/min
Since each of Diane's steps is 72 cm long, her walking speed is:
90 steps/min x 72 cm/step = 6480 cm/min
To convert this to meters per minute, we can divide by 100:
6480 cm/min ÷ 100 cm/m = 64.8 m/min
So Diane's walking speed is the same as Cheryl's. To find out how long it takes Diane to walk to school, we can use the formula:
distance = speed x time
Since Diane and Cheryl walked the same distance, we can use the distance we found for Cheryl:
777.6 m = 64.8 m/min x time
Simplifying this equation, we get:
time = 12 minutes
Therefore, Diane takes 12 minutes to walk to school.
Answer:
12 min
Step-by-step explanation:
You want to know how long it takes Diane to walk to school if she takes 90 steps of 72 cm per minute, while Cherly takes 80 steps of 81 cm per minute and traverses the distance in 12 minutes.
SpeedThe speed of each girl is the product of the number of steps per minute and the length of the step:
Cheryl: (80 step/min)(81 cm) = 6480 cm/min
Diane: (90 step/min)(72 cm) = 6480 cm/min
Both girls travel at the same speed, so will take the same amount of time to get to school. It takes Diane 12 minutes to walk to school.
HELP ME PLEASE :DDDDDDDD
The expression to find the angle BGC is 11x + 34.
The equation that would help us find the angles of AGB and BGC is 90 = 11x + 46.
The correct equation that would help us find the angles of ABG, AGF, and AGE is 15x + 120 = 180.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
∠AGB + ∠BGC = 90.
12 + 11x + 34 = 90
11x + 46 = 90
90 = 11x + 46.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of angles ABG, AGF, and AGE are supplementary angles:
12 + 90 + 15x + 18 = 180°
120 + 15x = 180°
15x + 120 = 180
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This is for precalc can someone help please
Mr Tan calculated the average amount of money collected by all the students in his class during a fund-raising event. If three of his students each collected $32 less, the average amount of money collected would be $146. If eight of his students each collected $18 more, the average amount of money collected would be $156. How many students were there in Mr Tan's class?
There were 56 students in Mr Tan's class.
To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:
nx = sum of all amounts collected
Now, if three students each collected $32 less, the new sum of amounts collected would be:
(nx - 3*32) = (n-3)(x-32)
And the new average would be:
(n-3)(x-32) / n = 146
Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:
(nx + 8*18) = (n+8)(x+18)
And the new average would be:
(n+8)(x+18) / n = 156
Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:
n = 56 and x = 104
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Question 7 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. x = 5, y = -2
B. More than 1 solution
O C. No solution
OD. x= -2, y = 5
y+ x = 3
y-2x = -12
The solution to the system of equations shown above include the following: A. x = 5, y = -2
How to graphically solve this system of equations?In order to graphically determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;
y + x = 3 ......equation 1.
y - 2x = -12 ......equation 2.
Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is represented by this ordered pair [5, -2].
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Use the following formula to find the correct answers: FV = PV. (1+i)"
You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years. How much money will you have by then?
O$677.23
O $746.93
$467.39
O $725.30
The savings amount balance in the account is $ 467.39
Given data ,
You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years.
Using the formula FV = PV * (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods, we can calculate the future value of the savings account after 15 years.
PV = $300 (the initial deposit)
i = 0.03 (the interest rate per period)
n = 15 years (the number of periods)
FV = $300 (1 + 0.03)^15
FV = $300 ( 1.5579 )
FV = $467.39
Hence , after 15 years, the savings account will have a balance of $ 467.39
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DISCUSSION QUESTIONS 1. Ongoing efforts have been undertaken in Malaysia to improve the financial reporting and accountability in government agencies. Discuss the efforts. 2. Discuss the extent of application for the key accounting concepts in the public sector. 3. Clearly describe the regulatory framework and procedures for financial reporting in the public sector.
Answer:
1.Ongoing efforts have been undertaken in Malaysia to improve the financial reporting and accountability in government agencies. Discuss the efforts.
Malaysia has been making efforts to improve financial reporting and accountability in government agencies for several years. In 2015, the Malaysian government introduced a new financial reporting framework for government agencies called the Malaysian Public Sector Accounting Standards (MPSAS). This framework is designed to improve financial reporting and ensure that government agencies are held accountable for their financial performance.
The MPSAS framework is based on international accounting standards and is meant to increase transparency and consistency in financial reporting. It includes guidelines for budgeting, financial management, and reporting of financial performance. Additionally, the Malaysian government has established the Accountant General's Department, which is responsible for overseeing financial reporting in government agencies.
Other initiatives aimed at improving financial reporting and accountability in Malaysia include the implementation of electronic financial management systems, the introduction of new financial management guidelines, and the establishment of a Financial Management Committee to oversee financial management across all government agencies.
2.Discuss the extent of application for the key accounting concepts in the public sector.
The key accounting concepts that are applicable to the public sector are similar to those used in the private sector, with some important differences. One of the key differences is that in the public sector, accounting practices are focused on ensuring accountability to the public and ensuring that public funds are used responsibly.
Some of the key accounting concepts that are applicable in the public sector include accrual accounting, budgeting, and financial reporting. Accrual accounting is used to record financial transactions as they occur, regardless of when payment is made or received. This helps to ensure that all financial transactions are recorded accurately and transparently.
Budgeting is also an important accounting concept in the public sector. Governments typically create budgets to allocate funds to various programs and projects. These budgets are then used to monitor financial performance and ensure that resources are used efficiently.
Financial reporting is another key accounting concept in the public sector. Governments are required to report on their financial performance to ensure transparency and accountability. This includes reporting on revenue and expenses, assets and liabilities, and cash flow.
3.Clearly describe the regulatory framework and procedures for financial reporting in the public sector.
The regulatory framework for financial reporting in the public sector typically involves a combination of national and international accounting standards. In Malaysia, the regulatory framework is based on the Malaysian Public Sector Accounting Standards (MPSAS), which are based on international accounting standards.
Under this framework, government agencies are required to prepare financial statements in accordance with MPSAS. These statements include the statement of financial position, statement of financial performance, statement of changes in equity, and statement of cash flows.
Additionally, the Accountant General's Department is responsible for overseeing financial reporting in government agencies. They are responsible for ensuring compliance with MPSAS and for providing guidance on financial reporting issues.
Government agencies in Malaysia are required to submit their financial statements to the Accountant General's Department for review and approval. Once approved, these statements are published and made available to the public.
Overall, the regulatory framework and procedures for financial reporting in the public sector are designed to ensure transparency and accountability in the use of public funds.
please helppp
here is the picture is about Row Ops
Multiplying row 1 of the matrix by 1 / 4 would give a resultant matrix of [ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ].
How to multiply the matrix row ?The question wants to multiply the first row of the matrix alone, with the fraction, 1 / 4.
First step is then to multiply the first row by the fraction of 1 / 4 :
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
The results acquired can then be input into the matrix which would then give a resultant matrix of :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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9. Economists in the country of Flatland, a closed economy, have collected the following information about their economy for a particular year: Y=15,000; C=9,000; T=3,000; G=3,600. The economists also estimate that the investment function is I=3,900-100r, where r is the country’s real interest rate, expressed as a percentage.
Calculate private saving, public saving, national saving, investment, and the equilibrium real interest rate. Does the government of Flatland have a budget surplus or budget deficit?
Answer:
Private saving (Sprivate) is equal to disposable income minus consumption:
Sprivate = Y - T - C = 15,000 - 3,000 - 9,000 = 3,000
Public saving (Spublic) is equal to government revenue minus government spending:
Spublic = T - G = 3,000 - 3,600 = -600
National saving (S) is equal to the sum of private and public saving:
S = Sprivate + Spublic = 3,000 - 600 = 2,400
Investment (I) is given by the investment function:
I = 3,900 - 100r
Equating investment to national saving gives:
I = S
3,900 - 100r = 2,400
Solving for r:
r = 15%
Therefore, the equilibrium real interest rate is 15%.
Substituting r = 15% into the investment function gives:
I = 2,400
Therefore, investment is 2,400.
Finally, to determine if the government has a budget surplus or deficit, we need to calculate the government's budget balance, which is equal to government revenue minus government spending:
Budget balance = T - G = 3,000 - 3,600 = -600
Since the budget balance is negative, the government of Flatland has a budget deficit.
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
23098376=890754730.0%
On their farm, Adam’s family maintains a storage that can hold 14.3 cubic yards (yd3) of grain. Use the fact that 1 yard is approximately equal to 0.9144 m to convert this volume to m3. Round your answer to the nearest hundredth. Do not type the units in the space below.
The storage can hold approximately 10.94 cubic meters of grain.
Unit conversion:
Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.
To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.
Here we have
Adam’s family maintains storage that can hold 14.3 yd³ of grain.
Given that 1 yard is approximately equal to 0.9144 meters
To convert cubic yards (yd³) to cubic meters (m³),
Use the conversion factor:
1 yd³ = (0.9144 m)³
So, we can convert 14.3 cubic yards of grain to cubic meters as follows:
14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³
Rounding this answer to the nearest hundredth gives us:
10.94 m³ rounded to the nearest hundredth = 10.94 m³
Therefore,
The storage can hold approximately 10.94 cubic meters of grain.
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Help please!!!!
Whoever answers right gets brainliest!
The simplified form of given expression a³/a⁶b⁻¹ is b/a³.
Hence, the correct option is C.
Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.
In the given expression, a³/a⁶b⁻¹
We can apply the rules of exponents, and we get
= a³⁻⁶/b⁻¹
= a⁻³/b⁻¹
= b/a³
Hence, the correct option is C.
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Solve for x. Round to the nearest tenth, if necessary.
Using the sine ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Sine Ratio?The sine ratio is part of the trigonometry ratios that can be applied to solve a right triangle, and it is written as:
sin ∅ = length of the opposite side / length of the hypotenuse of the right triangle
We are given the following information from the image above:
Reference angle (∅) = 75 degrees
length of the opposite side = x
length of the hypotenuse = 9
Plug in the values:
sin 75 = x/9
9 * sin 75 = x
x = 8.7 [to the nearest tenth]
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7: An entrance examination for a job consists of 25% English, 30% Mathematics, 25% computer and 20% accounting, and the passing mark is 45. If an applicant sat for the examination and scored 60% in English, 35% in Mathematics, 80% in computer and 50% in Accounting, do you think she will be accepted?
Answer: The overall score obtained is 55.5, which is higher than the passing mark of 45. Therefore, the applicant will be accepted.
Step-by-step explanation:To determine if the applicant will be accepted, we need to calculate their overall score based on the percentage weights and passing mark given for each subject.
The overall score can be calculated as follows:
Overall score = (0.25 x English score) + (0.3 x Math score) + (0.25 x Computer score) + (0.2 x Accounting score)
Substituting the given scores, we get:
Overall score = (0.25 x 60) + (0.3 x 35) + (0.25 x 80) + (0.2 x 50)
= 15 + 10.5 + 20 + 10
= 55.5
A farmer separated 7 hens from a group of chickens and placed them in a new coop If these 7 hens represent 20% of the total number of chickens the farmer owns, how many chickens does the farmer own?
The total number of chickens the farmer owns is 35.
What is percentage?A quantity or proportion can be expressed as a percentage of 100 by using the word "percentage." It is represented by the sign %.
For instance, when we state that 50 percent of a group of people are women, we mean that 50 out of every 100 people in the group are women.
We can deduce here the total chickens the farmer owns in % = 100%
Hens placed in a new coop = 20% = 7
Let the total number of chickens = x
Thus,
7 / x = 20 / 100
To solve for x, we can cross-multiply and simplify:
7 × 100 = 20 × x
700 = 20x
x = 35
Thus, the total number of chickens = 35.
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Find the length of the third side. If necessary, round to the nearest tenth.
6 and 10
The length of the third side is 8units
What is Pythagoras theorem?Pythagoras theorem states that : the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If a and b are the legs of the triangle and c is the hypotenuse,then
c² = a²+b²
For example , if a = 3 and b = 4 , then
c = √3²+4²
c = √ 9+16
c = √25
c = 5units.
Similarly, c = 10, a= 6, and b is unknown
therefore
10²= 6²+b²
b² = 10²-6²
b² = 100-36
b² = 64
b = √64
b = 8units
therefore the length of the third leg is 8units.
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What is 6+4 3/4+(-2.5)= explain your answer
The value of 6+4 3/4 +(-2.5) is 3 3/10
What is PEDMAS?PEDMAS is an acronym that shows the correct order of operations in mathematical problems. The full meaning of PEDMAS is ;
Parentheses
Exponents
Division
Multiplication
Addition
Subtraction
This order is followed when solving mathematical problems.
Solving 6+4 3/4 +(-2.5)
= 6+ 19/4 - 5/2
= ( 24+19-10)/4
= 33/10
= 3 3/10
Therefore the value of 6+4 3/4 +(-2.5) is 3 3/10
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Determine whether y=9(-5)^x represents an exponential function
Answer: Yes, y = 9(-5)^x represents an exponential function.
An exponential function is a function in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The base, b, is raised to the power of x, and the resulting value is multiplied by the constant a.
In the given function, we have a = 9 and b = -5. Although b is negative, it is still a real number not equal to 1, so the function is still considered exponential. Furthermore, the exponent x is a variable, which is raised to a constant base -5, meeting the definition of an exponential function.
Therefore, y = 9(-5)^x is an exponential function.
Step-by-step explanation:
Seven undergraduate students tagged A, B, C, D, E, F & G are to be allocated seven bed spaces in a hall in the University’s hostel. Student A doesnot want a bed next to student B because he is aware that student B snores. In how many ways can the bed spaces be allocated to them if the concern of student A is to be honoured?
By permutation and combination we can say there are 25200 ways to allocate the bed
What exactly are permanence and combination?Mathematical concepts like permutation and combination count the number of possible arrangements or choices for an object.
The quantity of possible arrangements of objects in a given order is referred to as a permutation.
Combination refers to the variety of possible selections of objects that are made without respect to their sequence.
The number of ways to distribute the seven students' beds in a way that ensures student A doesn't share a bed with student B is equal to the number of ways to distribute the six students' beds in a way that ensures student A doesn't share a bed with student B multiplied by two. (since there are two possible positions for student B).
The following formula can be used to determine how many options there are to distribute the six available beds among the students so that Student A does not have a bed next to Student B:
In this instance, seven students with the identifiers A, B, C, D, E, F, and G will each receive seven bed places in a dormitory at the university. Because he is aware that student B snores, student A does not want to share a bed with him. As a result, we can group students A and B together and arrange them in six different ways.
Then we can arrange the remaining students C, D, E, F and G in 5! ways. Therefore, the total number of ways to allocate bed spaces to them if the concern of student A is to be honored is 6! * 5! = 17,280 .
the bed spaces to seven students such that student A does not get a bed next to student B
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Confusing
Kerrin is making an input-output table for the rule "add 5." What is the output value for an input value of 5?
Options:
A: 0
B :5
C: 10
D: 25
The calculated output value for an input value of 5 is (c) 10
What is the output value for an input value of 5?From the question, we have the following parameters that can be used in our computation:
Kerrin is making an input-output table for the rule "add 5."
This means that
Output = input + 5
In this case, we have
input = 5
substitute the known values in the above equation, so, we have the following representation
Output = 5 + 5
Evaluate
Output =10
Hence, the output is 10
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Ashley made 4 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces was $29.20 . If the beads cost a total of $13.60 , how much did each pendant cost?
$3.90
29.20-13.60=15.6
15.6/4= 3.90
find the least common multiple of x^2-25 and x-5
Answer: The least common multiple is (x−5) (x−5)
Step-by-step explanation:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Pleasee help me I donk know what is the answer for the white space
The row operation performed to obtain [0 0 -3 9] is R₃ - R₂.
What is row operation in matrix?A row operation in a matrix involves making a change to one or more rows of the matrix. The three elementary row operations are, interchanging rows, rows addition, and rows multiplication.
The given matrix;
[9 -2 -9 9] [9 -2 -9 9]
[1 2 -6 -1] into [1 2 -6 -1]
[1 2 -9 8] [0 0 -3 9]
If we perform R₃ - R₂, that is row 3 minus row 2, we will have the following;
[1 2 -9 8] - [1 2 -6 -1]
= [(1-1) (2-2) (-9 + 6) (8 + 1)]
= [0 0 -3 9]
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if there are 15 people from the bronx, brooklyn, manhattan queens and staten island and each borough has 3 people, if the people from each borough insist on standing together, how many possible ways are there to stand
There are 10,080 possible ways for the 15 people to stand if the people from each borough insist on standing together.
If there are 15 people from the Bronx, Brooklyn, Manhattan, Queens, and Staten Island, and each borough has 3 people, then there are 5 groups of 3 people. If the people from each borough insist on standing together, we can treat each group of 3 people as a single entity. So, we have 5 entities that need to be arranged.
The number of ways to arrange these 5 entities is 5!, which is equal to 120. However, within each group of 3 people, there are 3! ways to arrange the people. So, we need to multiply the number of ways to arrange the groups by the number of ways to arrange the people within each group. We will get the answer
5! × (3!)⁵ = 120 × 3⁵ = 10,080
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It’s similar figure with proportions
Answer:
x = 72 cm
Step-by-step explanation:
Because the two figures are similar, we can create a proportion between one set of similar sides (i.e., the side measuring 48 cm and the side measuring 6 cm) and another set (the side measuring x cm and the side measuring 9 cm. This, will allow us to solve for x:
[tex]\frac{6}{48}=\frac{9}{x}\\ 432=6x\\ 72=x[/tex]
Another way to solve would have been to notice that the scale factor used to create the bigger puzzle piece is 8 since 6 * 48. In order for the smaller figure to be considered similar to the larger, every side had to be multiplied by the same scale factor. Since the scale factor is 6, x must be 72 cm as 9 * 8 = 72
10. The time it takes to drain a swimming pool varies inversely with the amount of water being
pumped per hour. If a large pool takes 12 hours to empty at 400 gallons an hour, how many
hours faster can the pool be drained if the pumping rate is increased to 500 gallons per hour?
(teal)
To solve this problem, we can use the formula for inverse variation, which is:
time = k/ rate
where k is a constant of proportionality.
We can start by finding the value of k using the given information. We know that when the pumping rate is 400 gallons per hour, it takes 12 hours to drain the pool. Therefore:
12 = k/400
Multiplying both sides by 400 gives us:
k = 4800
Now we can use this value of k to answer the second part of the question. We want to know how many hours faster the pool can be drained if the pumping rate is increased to 500 gallons per hour. Let's call this new time t:
t = 4800/500
t = 9.6 hours
So the pool can be drained 12 - 9.6 = 2.4 hours faster if the pumping rate is increased to 500 gallons per hour.
