If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .
To find out how long it will take for the town's population to reach 41600, we can use the formula :
⇒ A = P(1 + r)ⁿ
Where:
A = final population of town , P = initial population o town
r = percent increase (as a decimal)
let n = number of years for population to reach 41600 .
We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05 and we have to solve for n.
Substituting the values ,
we get ;
⇒ 41600 = 20000(1 + 0.05)ⁿ ;
⇒ 41600 = 20000(1.05)ⁿ ;
⇒ 41600/20000 = (1.05)ⁿ ;
taking "log" on both sides ,
we get ;
⇒ log(41600/20000) = n × log(1.05) ;
⇒ n = log(41600/20000)/log(1.05) ;
⇒ n = 15.0105 ≈ 15
Therefore , it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.
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purchase the cat food, milk and toys for the kittens for 2 months. Each of the kitten needs a 1/2 kilogram of food and 1.5 litres of milk per week for the first month. After that each kitten will need 2.klingrams of food and 1 litre of milk for each week in the second month The table below shows the amounts charged for the cat food, milk and toys you need by three different supermarkets
Supplies A 5 kg bag of cat food. 1 litre of milk. Cat toys
Supermarket A $400 each/3 bags for. $1 100 $1900
Supermarket B $600 each/3 bags for $1660 $1 099 $2 300
Supermarket C $400 each/3 bags for $1.080 $1100 $1799
(a) Your father wants you to choose the supermarket that is giving you the best value, which supermarket is offering you the best value?
Answer: The best value for the cat food, milk and toys is Supermarket C. They are offering the 5 kg bag of cat food for $400 each/3 bags for $1,080, 1 litre of milk for $1100, and cat toys for $1799. Supermarket A is offering the 5 kg bag of cat food for $400 each/3 bags for $1,100, 1 litre of milk for $1,900, and cat toys for $1,900. Supermarket B is offering the 5 kg bag of cat food for $600 each/3 bags for $1,660, 1 litre of milk for $1,099, and cat toys for $2,300. Supermarket C has the lowest prices for all three items, so it is the best value.
Step-by-step explanation:
Tray earns $510 per week. He works 5 days each week and 8 hours each day.
How much money, in dollars, does Tray earn por hour?
$12.75
$39.23
$63.75
$102.00
A- write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.
B- to determine whether the used the same number of tiles, set the two expressions equal to each other and solve for x. Is there a solution for x? Why or why not? If there is a solution, what is it?
C- what conclusion can you draw from this?
D- how could you change the equation from part B so it has infinitely many solutions? What would infinitely many solutions mean in terms of the situation?
E- if the equation were 6x + 2 = 5x + 17, would there be one unique solution? What is it, and what would it mean in terms of the situation?
An expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.
Expression
An expression refers to a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
Note: - x represents the number of tiles in a box.
A- For Bruce,
we have,
Expression = 3x + 2x + 2
Expression = 5x + 2.
For Felicia,
we have,
Expression = 5x + 5.
so, the expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.
B- no, there is no solution for X as the equations are not equal to each other.
5x +2 = 5x + 5 (subtract 5x and 2 on both sides)
0 = 3 No solution
C- We can conclude that someone used more tiles then the other because both equations are not equal.
D- Have 2 or 5 change because they need to be equal to each other. Its fine what you put as long as the equal sign is the same as the other side like 3 = 3 for example or 5 = 5, something like that. Once they have the same end then you can substitute the number to x.
x represents the number of tiles they used.
E- yes.
6x +2 =5x +17
6x - 5x =17 - 2
x =15
unique solution
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A recipe for Kool-Aid calls for 1/4 cup of sugar for every 3 cups of liquid. How many cups of sugar would be needed for 18 cups of liquid?
Answer:
1.5 cups of sugar
Step-by-step explanation:
Given:
-You need a 1/4 cup of sugar for 3 cups of Kool-Aid
-You need to find the amount of sugar you need for 18 cups of liquid
Solution:
You need to find how many recipes you need
3x = 18
So x = 6
Now you need to multiply 1/4 by 6 to find the amount of sugar
That would be 6/4 which is 1.5
So you need 1.5 cups of sugar for 18 cups of Kool-Aid
A ball dropped vertically fall d meter in t econd. D i directly proportional to the quare of t the ball drop 80 meter in the firt 4 econd . how far doe the ball drop in the next 8 econd
The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.
In the next 8 seconds, the ball will drop 320 meters. This can be calculated by using the equation [tex]d = (t^2) * k[/tex], where d is the distance (in meters) dropped, t is the time (in seconds), and k is a constant. Since the ball dropped 80 meters in the first 4 seconds, we have d = (4^2) * k, or k = (d/16). Plugging this value of k into the equation, we get d = (t^2) * (d/16), which simplifies to d = (t^2) * (80/16). In the next 8 seconds, t = 8, so d = (8^2) * (80/16) = 320 meters.
The ball will drop 320 meters in the next 8 seconds, which can be calculated using the equation d = (t^2) * k, where d is the distance (in meters) dropped, t is the time (in seconds), and k is the constant.
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Rationalise the denominator 7/2-root 5
On rationalizing the expression 7/(2-√5) 7/(2-√5), the value is obtained as -7 (2 + √5).
What is rationalization?
In order to get rid of the irrational number in the denominator, the procedure of rationalisation is performed in elementary algebra. There are numerous rationalisation strategies that are used on the denominator.
The given expression is - 7/(2-√5).
Multiply the denominator and numerator by the (2 + √5).
= 7 × (2 + √5)/(2-√5) × (2 + √5)
= (14 + 7√5)/(2)² - (√5)²
Simplify it further -
= (14 + 7√5)/4 - 5
= (14 + 7√5)/-1
= -(14 + 7√5)
= -7 (2 + √5)
Therefore, the simplified expression is -7 (2 + √5).
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A convex pentagon has exterior angles of 83°, 83°, 26°, and 46°. What is the measure of an exterior angle at the fifth vertex?
The measure of an exterior angle at the fifth vertex is 62°.
A pentagon has 5 straight sides. The shape must also be closed.
A convex pentagon has no angles pointing inwards, and no internal angles can be more than 180°.
When all angles are equal and all sides are equal it is regular, otherwise, it is irregular.
The sum of exterior angles is 360°.
To know the angle of the fifth vertex add the remaining four vertexes and subtract from the sum of exterior angles.
Given 4 vertexes of the pentagon are 83°, 83°, 26°, and 46°.
By adding these we get a total of 238°
Fifth vertex=360°-238°
Fifth vertex=62°
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A healthy dog will drink between 50 and 60 milliliters of
water per kilogram of body weight each day.
Approximately how many fluid ounces of water will a
35-pound dog drink in a day? Express your answer as a
range of values, rounded to the nearest whole fluid
ounce.
Pls answer quickly!
The range of values for how many fluid ounces of water will a 35 pound dog will drink in a day is given as follows:
27 oz < x < 32 oz.
How to obtain the range of values?The range of values is obtained applying the proportions in the context of this problem.
The conversion of milliliters to fluid ounces is given as follows:
1 ml = 0.0338 oz.
Hence the amounts of oz per kilogram are given as follows:
50 x 0.0338 = 1.69 oz.60 x 0.0338 = 2.03 oz.The conversion of pounds to kg is given as follows:
1 kg = 2.20462 pounds.
Hence the weight in kg of the dog is given as follows:
35/2.20462 = 15.87 kg.
The bounds of the interval are given as follows:
15.87 x 1.69 = 27 oz.15.87 x 2.03 = 32 oz.More can be learned about proportions at https://brainly.com/question/24372153
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Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $3,650, r= 5.5%, t= 15 years; compounded monthly
Answer:
$14390.75
Step-by-step explanation:
p=3650
i = 5.5% is this annual rate or monthly rate? assuming annual rate
t=15 years compounding monthly = 15*12 = 300 periods
(1+5.5%/12)^300=3.94267155
multiply the principal 3650 *3.94267155 = $14390.75
alguien me explica yo no entendi
Note that the median in the data set given above is: 38.5.
What is a median value?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in data collection.
Not that in the above case, the median is arrived at by finding adding the two central values (37 and 40) and dividing the result by 2. This is because the total number of data in the set is even. Where the total number of values is odd, then the central number, when the avalues are arranged in ascending order is the median.
Thus, median = 37 + 40
= 77/2
Median = 38.5
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An object moves along a straight line with acceleration a(t) = 8 cos t + 2t. If the initial position s(0) = -5 and initial velocity v(0) = -2, find the position function of the object.
A.
-8cos t + t^3/3-2t-3
B.
-8cos t + 3t^3-2t+5
C.
-8cos t + 3t^3 − 2t − 5
D.
-8cos t + t^3/3-2t+3
If the initial position s(0) = -5 and initial velocity v(0) = -2, the position function of the object is -8cost + t^3/3 - 2t + 3. So the option D is correct.
We have to determine the position function of the object.
An object moves along a straight line with acceleration a(t) = 8cost + 2t.
Initial position s(0) = -5
Initial velocity v(0) = -2
Integration of a(t) given us s(t)
[tex]\int a(t)dt = \int (8cost + 2t) dt[/tex]
v(t) = 8sint + 2t^2/2 + C
v(t) = 8sint + t^2 + C
At v(0) = -2
v(0) = 8sin(0) + (0)^2 + C
-2 = 8 × 0 + 0 + C
C = -2
v(t) = 8sint + t^2 - 2
The integration of v(t) gives us s(t)
[tex]\int v(t)dt = \int (8sint + t^2 - 2)dt[/tex]
s(t) = -8cost + t^3/3 - 2t + D
At s(0) = -5
s(0) = -8cos(0) + (0)^3/3 - 2(0) + D
-5 = -8 × 1 + 0 - 0 + D
-5 = -8 + D
Add 8 on both side, we get
D = 3
s(t) = -8cost + t^3/3 - 2t + 3
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What appears to be the domain of the part of the exponential function graphed?
The domain of the function is x ≤ 1.
x ≤ 1 because your domain cannot have h(x) because that is your function and would be your range but in this case it is your domain and your domain, also known as the x coordinate, would have to be the number on the x axis that your line starts at, which would be your domain.
Your line starts on line 1 on the x axis, which would be your domain.
How do you determine a function's domain?Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
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A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?
Statement "B. the median is a negative number" will be correct among these options.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given, that A set of data contains 10 negative numbers and 4 positive numbers.
Since the value of data is not given it can be any positive or negative numbers
mode:
A mode is described as a value in a group of values that occurs most frequently. The value that appears the most frequently is this one.
Range:
When the sample maximum and minimum are subtracted, the range of a set of data in statistics is the difference between the greatest and lowest values.
Median:
The median is the value that's exactly in the middle of a dataset when it is ordered.
Thus, the Median will be negative.
Therefore, Statement "B. the median is a negative number" will be true among these options.
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Complete question:
A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?
A. The mean is a negative number.
B. The median is a negative number.
C. The mode is a negative number.
D. The range is a negative number.
Set up a piece-wise function to describe the relationship between the total monthly cell phone charge and the number of minutes of use. Let y represent the total cost of the phone bill and let x represent the total number of minutes. Write a piecewise function to describe the plan
The total monthly cost of the phone bill is represented by y and the total number of minutes is represented by x. Then, a sample piece-wise function to describe their relationship is written as [tex]y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}[/tex]
A function that is produced from bits of multiple functions over various periods is known as a piecewise function. By providing the input value, one can produce this function that operates differently.
Given the total cost of the phone bill is represented by y and the total number of minutes is represented by x. To write a piecewise function, let's consider an example of this.
For $35 per month, 300 minutes are included in a cell phone package. $0.25 will be charged for each additional minute. Then, the piecewise function for this is represented by,
[tex]y(x)=\begin{cases} {{\$35\;&\mathrm{if}\;0\leq x \leq300} \\ {\$[35+(x-300)]\;&\mathrm{if}\;x > 300}} \end{cases}[/tex]
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Writing expressions form context of MX+B
The linear equation that represent the total cost over x GB is given as 10x + 20. The total cost when over 2 GB is $40
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The slope intercept form of linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value of y
Let y represent the total cost over x GB of data.
y = mx + b
The data plan cost $20 per month and $10 per GB over 3 GB.
Hence:
m = 10, b = 20; y = 10x + 20
Total cost when over by 2 GB = 10(2) + 20 = $40
Total cost when over by x GB = 10x + 20
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Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?
Answer:
it takes 8.8 years for the value of the account to reach $5,920.
Step-by-step explanation:
We can use the formula A = P(1+r/n)^(nt) to find the time it takes for Ella's investment to reach $5,920.
A is the future value of the investment, P is the present value (initial investment), r is the interest rate, n is the number of compounding periods per year and t is the time in years.
Plugging in the given values:
5920 = 4900(1 + 0.03/12)^(12t)
To solve for t, we need to take the natural logarithm of both sides of the equation and divide by the logarithm of (1+0.03/12)
t = ln(5920/4900)/(12*ln(1+0.03/12))
t = approximately 8.8 years (to the nearest tenth of a year)
So it takes 8.8 years for the value of the account to reach $5,920.
Graphing piecewise functions
The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The extreme points of the function in this problem are given as follows:
f(-1) = -1 + 3 = 2.f(2) = 2 + 3 = 5.f(2) = -2 + 9 = 7.f(6) = -6 + 9 = 3.Hence the graph of the function is composed by:
An increasing line from (-1,2) to (2,5).A decreasing line from (2,7) to (6,3).More can be learned about piece-wise functions at https://brainly.com/question/19358926
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What is the domain and range of t(n) = 2x+1
How did you get it?
The domain of the function is all real numbers while the range of the function is also all real numbers.
What is the domain of the function?The domain of the function t(n) = 2x + 1 is all real numbers, since there are no restrictions on the input value of x. The range of the function is also all real numbers, since adding 1 to any real number will also result in a real number. So the domain is (-infinity, infinity) and the range is (-infinity, infinity)
We have to note that in the event that we have a function such as t(n) = 2x+1, x is free to take any of the values on the real number line and this would return a value for t(n).
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Find an expression to represent the area of the triangle below
The formula for the area of a triangle is (1/4)√(105a?)
How to find the area of a triangle?By applying the triangle inequality theorem, we can verify that the given formula represents the length of the sides of a triangle. This theorem states that the sum of his two sides of a triangle must be greater than his third side.
Given the expressions 2a?, 6a + 5, and 10a?, applicable
2a? + 6a + 5 > 10a? (sum of first two pages greater than third)
2a?+10a?> 6a+5 (1st and his 3rd sides sum greater than 2nd)
6a + 5 + 10a? >2a? (sum of last 2 pages greater than first page)
Therefore, the given formula can express the length of the sides of a triangle.
According to Heron's formula, the area of a triangle with side lengths a, b, and c is
Area = √(s(s-a)(s-b)(s-c))
where s is the semicircle of the triangle and is defined as
s = (a + b + c) / 2
Replacing the given formula with a, b, c, we get:
s = (2a? + 6a + 5 + 10a?) / 2
= 6a? + 3a + 5/2
Find the value of s to calculate the area of the triangle.
Area = √((6a? + 3a + 5/2)((6a? + 3a + 5/2)-(2a? + 6a + 5))((6a? + 3a + 5/2)-(10a?)))
= √((6a? + 3a + 5/2)(2a? - 3a + 5/2)(-4a? + 3a + 5/2))
= √((15/4)(a?)(-5/4)(-a?)(-7/4)(a?))
= √(105a?/16)
= (1/4)√(105a?)
So the formula for the area of a triangle is (1/4)√(105a?).
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Can someone please answer this
Answer:
X= k/2
Y= -k/2
Step-by-step explanation:
X= k/2
Y= -k/2
Find the value of
x in the equation below.
36=4x
Answer:
4x(÷4)=36(÷4)
x=9
I hope I help you in this ans and tq.
Answer: 9
Step-by-step explanation: Because the problem is 36=4x the X next to the 4 means to multiply BUT since we don't no the answer there are many ways to solve this one way is to find what you can multiply for with or you can divide 36 and 4.
Hope fully that helps!!!
(a+√8)^2 can be written in the form c+d√2, where a c and d are integers. Find in terms of a an expression for c and an expression for d
Thank you so much
Please respond when you can in your own convenience
The expression for c and d in terms of a are c = a²+8 and d = 4a
How to write (a+√8)² in the form c+d√2?An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.
(a+√8)²can be written in the form c+d√2 by expand the bracket. That is:
(a+√8)² = (a+√8)(a+√8)
(a+√8)² = a(a+√8) + √8(a+√8)
(a+√8)² = a² + a√8) + a√8 + 8
(a+√8)² = a² + 2a√8 + 8
(a+√8)² = a² + 4a√2 + 8
(a+√8)² = (a²+8) + 4a√2
Thus, c = a²+8 and d = 4a
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Multiply.
[x-(6+4i)][x-(6x4i)]
Note that these expressions contain complex numbers.
Simplify your answer as much as possible
The resultant of the given expression after simplification is (x^2 - 12x - 8xi + 52).
In order to simplify the expression [x-(6+4i)][x-(6x4i)], we must first expand it by using the distributive property.
The first term of the first factor would be x*x = x^2,
The second term would be x*-(6-4i) = -6x - 4xi
The third term would be -(6+4i)x= -6x - 4xi.
The last term would be -(6+4i)*-(6-4i) = 6^2 - (4i)^2 = 36 + 16 = 52
Next, we would combine like terms by adding,
x^2 - 6x - 4xi - 6x - 4xi + 52 = x^2 - 12x - 8xi + 52
This would give us an expression of x^2 - 12x - 8xi + 52. This expression can't be simplified any further as it contains complex numbers.
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Which of the following is a factor of 4x^{2} + 23x + 15
A: (4x + 5)
B: (2x + 3)
C: (4x + 3)
D: (2x + 5)
The factor of the given quadratic equation is (4x + 3). Option C is correct.
What are the factors of a quadratic equation?One way to describe the polynomial as a product of its linear parts is to factor the quadratic equation. We may use this method to locate the roots of quadratic expressions, simplify them, and solve equations.
The formula for a quadratic polynomial usually takes the form ax² + bx + c, where a, b, and c are real values. We can obtain the zeros of the quadratic equation ax² + bx + c = 0 by factoring quadratics.
Given that:
4x² + 23x + 15 = 0
By applying the distributive property, we have:
4x² + 20x + 3x + 15 = 0
Factor out the greatest common factor for each group
(4x² + 3x) + 20x + 15
x(4x + 3) + 5(4x + 3)
Factor the polynomial by factoring out the greatest common factor. 4x + 3, then we have:
(4x + 3) (x + 5)
Therefore, we can conclude that one of the factors of the quadratic expression is (4x + 3).
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A rectangular lawn is 100m long and 45m wide.
There are 3 circular ponds, with diameters of 20m, 10m and 5 especi Mrs Jones wants to cover the lawn with grass seed.
Each packet of grass seed covers 50m and costs £1. 49
How much will it cost Mrs Jones to cover the lawn with grass seed?
According to the area the amount needed to cover the lawn with grass seed is £121.8075
In math the term called area is defined as the total space occupied by the object.
Here we have know that the Length is 100m and the Breadth is 45m :-
Then the area is calculated as,
=> A = 100 × 45 = 4500m²
Here we have to do the calculation for 3 circular pond, then it can be calculated as,
=> 1st pond = 20/2 = 10m
=> 2nd pond = 10/2 = 5m
=> 3rd pond = 5/2 = 2.5m
Then the Area of 3 circular pond is calculated as,
=> A = (π × 10² + π × 5² + π × 2.5²)
Take the term π as common then we get,
=> A = π × ( 100 + 25 + 6.25)
Apply the value of π = 22/7, then we get,
=> A = 22/7 × (125 + 6.25)
When we simplify this one then we get
=> A = 22/7 × 131.25 = 2887.5/7
Therefore the area of the pond is 412.5m²
Now we need to do the calculation for required area for covering lawn, that can be written as
=> Required area = Area of lawn - Area of 3 circular ponds
Apply the value on it,
=> Required area = 4500 - 412.5 = 4087.5m²
As we know that packet of grass seed covers 50m, then it is simplified as,
=> Required Area = 4087.5/50 = 81.75m²
Now we need to do the calculation for cost of covering lawn is written as
=> Total cost = 81.75 × 1.49 = £121.8075
Therefore the cost of covering lawn with grass seed is £121.8075
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Complete the following table.
Problem
Function
Domain Range
The number of shoes in x pairs of shoes
The cost to park in a mall garage is P 50 entry
fee plus P10 per four
A swimming pool in a hotel is draining at a rate of
3 feet per minute
please help.
For the problem , (a) The cost to park in a mall garage is $50 entry fee plus $10 per four , the function is y = 50 + 10x , the domain is (0,∞) and range is also (0,∞) .
and (b) A swimming pool in a hotel is draining at a rate of 3 feet per minute , the function is y = -3t , domain is (0,∞) and range is (0,∞) .
Part(a) ;
The cost to park in a mall garage is $50 entry fee plus $10 per four ;
the the number of hours be = "x" ;
the fixed entry fees for the mall garage is = $50 ;
the per hour charge for the garage is = $10 ;
it can be represented as : y = 50 + 10x ;
the function is : y = 50 + 10x ;
The domain of this function is (0,∞) , as the input hours can't be negative and
the range of function is (0,∞) as the charge cannot be negative
since the parking hours will be non negative .
Part(b) ,
A swimming pool is draining at the rate of 3 feet per minute.
Rate of draining is represented as "y = -3t" where t is number of minutes and
the negative sign in the function denotes the water is draining .
The domain and Range of this function is (0,∞) , as the input hours can't be negative .
The given question is incomplete , the complete question is
Find the Function , Domain and Range for the following problems :
(a) The cost to park in a mall garage is $50 entry fee plus $10 per four.
(b) A swimming pool in a hotel is draining at a rate of 3 feet per minute.
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The temperature in Chicago, Illinois was -15 F at 6 a.m. By afternoon, the temperature had risen 28 degrees. What was the afternoon temperature (in F)?
Answer:
13F
Step-by-step explanation:
-15+28
Complete the table for y=1/5x+1 and graph the resulting line
Answer:
yidyf
Step-by-step explanation:
jcyfifjfjhfueujevevve
What would 2x - y = (-5)
Y = -x -5 be?
(Solving using substitution)
Q1: Suppose that the height H of a Ferris wheel can be modeled by the function H(t) = -12cos ( πt/45) + 18, where t is the time in seconds. What is the maximum height of a cabin? Use 3. 14 for π.
Q2: The tide at an Eastern seaport is at its maximum at 6:39 a. M. High tide is 9 ft deep. Low tide occurs at 12:30 p. M. With a depth of 3 ft. The water depths can be modeled by a sinusoidal function.
Allow x = 0 represent midnight.
Find the following and make sure to show work for the midline and amplitude:
period=
Amplitude=
Maximum=
Equation of the midline:
minimum=
1. Maximum height of the Function H(t) = -12cos( πt/45 ) + 18 is 30 units.
2. For the given sinusoidal function the values of the following are as follow :
amplitude = 6ft, period = π/3 , Maximum = 9ft,
Equation of the midline y = 6, Minimum = 3 ft.
Function with height 'H' is given by:
H(t) = -12cos( πt/45 ) + 18
Here 't' represents the time in seconds.
As we know that range of cosine trigonometric function is ,
-1 ≤ cosα ≤ 1
This implies cos function lies between -1 and 1.
Replace cos( πt/45 ) by 1 or -1
For cos( πt/45 ) = 1
H(t) = -12(1) + 18
= 6 units
For cos( πt/45 ) = -1
H(t) = -12(-1) + 18
= 30 units
Maximum height is equals to 30 units.
Therefore, function H(t) = -12cos( πt/45 ) + 18 representing maximum height is equal to 30 units.
2. In general sinusoidal function is given by :
y = Asin(Bx + C) + D
A is amplitude
A = High tide - low tide
= 9 - 3 /2
= 3ft
Time = 12:30 p.m. - 6: 39 a.m.
= 6 : 09 minutes
= 6hours(approximately)
period B = 2π /T
= 2π/6
= π/3
Vertical shift = 9 - 3
= 6
Equation of the midline is
y = c
⇒ y = 6
Function is y = 3sin (π/3)x + 6
Maximum sin (π/3)x = 1
y = 9
Minimum sin (π/3)x = -1
⇒ y = 3
Therefore, the values of the following for the given function is :
amplitude = 6ft, period = π/3 , Maximum = 9ft,
Equation of the midline y = 6, Minimum = 3 ft.
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