Answers
The total cost of the water piping is $217.12 in the field.
What is perimeter?Perimeter is the total length of the boundary or the outer edge of a two-dimensional geometric shape. It is the distance around the shape or the sum of the lengths of all its sides. The perimeter is usually measured in units such as centimeters, meters, feet, or inches, depending on the system of measurement used.
In the given question,
To calculate the total cost of the water piping, we need to first calculate the total length of the edges of the field.
For the rectangle, the length of its four edges can be calculated as:
2 x length + 2 x breadth = 2 x 68m + 2 x 64m = 136m + 128m = 264m
For the square extension, it has four edges each with length 26m, so the total length of its edges is:
4 x 26m = 104m
Therefore, the total length of the edges of the field is:
264m + 104m = 368m
To find the total cost of the water piping, we can multiply the total length of the edges by the cost per metre:
368m x $0.59/m = $217.12
So, the total cost of the water piping is $217.12.
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Related Questions
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answers
She could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
The three steps that Inga could use to solve the quadratic equation 2x² + 12x – 3 = 0 are:
1. Use the quadratic formula: Inga could use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a = 2, b = 12, and c = -3.
2. Factor the quadratic expression: Inga could factor the quadratic expression into (2x - 1)(x + 3) = 0 and then use the zero product property to find the solutions x = 1/2 and x = -3.
3. Complete the square: Inga could use the method of completing the square by adding and subtracting (6/2)² = 9 to the left side of the equation, giving 2(x+3)² - 33 = 0. Then she could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.
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PLEASE HELP ILL GIVE BRAINLIEST
Answers
Answer:
True
Step-by-step explanation:
Since C has to add up to 180 and we already have 150 we can assume that that other angle is 30. The sum of angles in a triangle always has to equal 180. 120+30=150 meaning B also equals 30. B+A=150 therefore making it true.
10 to the 9th power is how many times 10 to the 8th power?
Answers
10 to the 9th power is 10 times 10 to the 8th power.
The weights of newborn babies are normally distributed with a mean of 8.5 pounds and a standard deviation of 2 pounds. A random sample of 25 newborns are selected.
b) Find the standard deviation of the mean of the 25 newborn babies. Round to 1 decimal place.
Answers
The standard deviation of the mean of the 25 newborn babies is approximately 0.4 pounds, rounded to 1 decimal place.
To find the standard deviation ,we will use the formula for the standard
deviation of the sampling distribution of the sample mean:
Standard deviation of the sample mean = σ / √n
Here, σ is the population standard deviation and
n is the sample size.
Given the population standard deviation (σ) is 2 pounds and the sample size (n) is 25 newborns, we can plug in the
values into the formula:
Standard deviation of the sample mean = 2 / √25
Standard deviation of the sample mean = 2 / 5
Standard deviation of the sample mean = 0.4
So, the standard deviation of the mean of the 25 newborn babies is approximately 0.4 pounds, rounded to 1 decimal place.
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help me pls!! the assignment is due by midnight
Answers
Answer: 1. Chord 2. Diameter
Answer:
Step-by-step explanation:
Since A and G are on a line thats not in the middle of the circle, the clear answer would be a chord
Since C is a point on the middle of the circle and B is at the end of the circle, the answer would be radius
Which of the following uses the distributive property correctly?
3(x+5)=3-x+5
3(x+5)=3-x-3-5
3(x+5)=3+3.5
3(x+5)=3-x+3.5
Answers
Answer:
None of them, 3x + 15 is correct.
Step-by-step explanation:
In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:
[tex]3(x+5)[/tex]
We multiply everything in the parentheses by 3
[tex]3x+15[/tex]
Looking at out choices, none of them uses the distributive property correctly.
the infographic shows percentages of women overall in elected office as well as the share of latinas in elected office. women constitute approximately what percentage of members of congress, statewide executives, state legislators, and mayors in the top 100 cities? check all that apply.
Answers
According to the infographic, women constitute approximately 15-19% of members of Congress, less than 15% of state legislators, and 25-50% of statewide executives and mayors in the top 100 cities.
According to the information provided in the infographic, the following options apply:
Women constitute approximately 25-50% of statewide executives and mayors in the top 100 cities.
Women constitute approximately 15-19% of members of Congress.
Women constitute less than 15% of state legislators.
Therefore, the correct options are:
15-19%
Less than 15%
25-50%
The infographic presents data on the percentage of women overall in elected office and the share of Latinas in elected office. The data indicates that women constitute less than 15% of state legislators, approximately 15-19% of members of Congress, and 25-50% of statewide executives and mayors in the top 100 cities. This suggests that women are underrepresented in elected office at all levels of government, with the exception of statewide executives and mayors in the top 100 cities. The infographic underscores the need for greater gender diversity in elected office, and the importance of supporting and encouraging women to run for political office at all levels of government.
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Complete question:
The infographic shows percentages of women overall in elected office as well as the share of Latinas in elected office. Women constitute approximately what percentage of members of Congress, statewide executives, state legislators, and mayors in the top 100 cities? Check all that apply.
19-25%
Less than 15%
15-19%
25-50%
. an olympic-size swimming pool is approximately 50 meters long by 25 meters wide. what distance will a swimmer travel if they swim from one comer to the opposite?
Answers
The distance a swimmer will travel if they swim from one corner to the opposite corner of an Olympic-size swimming pool is approximately 62.2 meters
The distance a swimmer will travel if they swim from one corner to the opposite corner of an Olympic-size swimming pool is approximately 62.2 meters. This can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the length of the pool is one side of the right triangle, the width of the pool is the other side of the right triangle, and the distance the swimmer travels is the hypotenuse.
Using the Pythagorean theorem, we can calculate the distance the swimmer travels as follows:
a² + b² = c²
where a is the length of the pool (50 meters), b is the width of the pool (25 meters), and c is the distance the swimmer travels.
To solve for c, we can plug in the values for a and b and simplify as follows:
50² + 25² = c²
500 + 625 = c²
125 = c²√3
125 = c
Approximately 62.2 meters (rounded to one decimal place)
Therefore, the distance a swimmer will travel if they swim from one corner to the opposite corner of an Olympic-size swimming pool is approximately 62.2 meters.
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make absolute value equation of
0 and 8
5 and 17
-4 and 6
in the form |x-c|=d
Please hurry!!!!
Answers
Answer:
Sure, here are the absolute value equations of 0 and 8, 5 and 17, and -4 and 6 in the form $|x-c|=d$:
* For 0 and 8, $|x-0|=8$. This means that $x-0=8$ or $x-0=-8$. Solving for $x$, we get $x=8$ or $x=-8$.
* For 5 and 17, $|x-5|=17$. This means that $x-5=17$ or $x-5=-17$. Solving for $x$, we get $x=22$ or $x=-12$.
* For -4 and 6, $|x-(-4)|=6$. This means that $x-(-4)=6$ or $x-(-4)=-6$. Solving for $x$, we get $x=10$ or $x=-2$.
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
NEED HELP ASAP PLEASE.....
Answers
The output of the function g(x) = [tex]3^{(\frac{x}{2} )}[/tex] when x = 2 is 3.
How to solve function?g(x) is a function as defined as follows:
g(x) = [tex]3^{(\frac{x}{2} )}[/tex]
If we input n2 into the g(x), the output g(x) can be gotten as follows:
Therefore,
g(x) = [tex]3^{(\frac{x}{2} )}[/tex]
where
x = 2
Therefore,
[tex]3^{(\frac{2}{2} )}[/tex] = 3¹
Therefore,
the output is 3.
g(2) = 3
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A triangle has angles that measure 55°, 80°, and r. What is r?
Answers
Since the sum of the angles in a triangle is always 180°, we can find the measure of the third angle by subtracting the sum of the other two angles from 180°.
180 - (55+80) = 45
Answer: r = 45°
Step-by-step explanation:
All triangles angles add up to 180 degrees.
With that said we can use the given information and create an equation to solve.
55° + 80° + r = 180°
Lets solve for r.
55° + 80° + r = 180°
first lets combine like terms.
135° + r = 180°
now lets subtract 143° from both sides
135° + r = 180°
-135° -135°
r = 45°
Fill in the table for side length and area of different squares
Answers
a) The area of the square for side length [tex]3[/tex] is [tex]9[/tex][tex]cm^{2}[/tex].
The area of the square for side length [tex]100[/tex] is [tex]10000[/tex][tex]cm^{2}[/tex]
The area of the square for side length [tex]25[/tex] is [tex]625cm^{2}[/tex].
The area of the square for the side length [tex]s[/tex] is [tex]s^{2}cm^{2}[/tex].
b) No the side length of the square and area are not directly proportional.
What is the area of a square?The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A = [tex]s^{2}[/tex], where A is the area and s is the length of one side of the square.
According to the given information
The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A =[tex]s^{2}[/tex]
[tex]A = s^{2} = 3^{2} = 9cm^{2}[/tex]
[tex]A = s^{2} = 10^{2} = 10000cm^{2}[/tex]
[tex]A = s^{2} = 25^{2} = 625cm^{2}[/tex]
[tex]A = s^{2} = s^{2} = s^{2} cm^{2}[/tex]
Therefore area of the square are [tex]9cm^{2} ,10000cm^{2}, 625cm^{2} ,s^{2}cm^{2}[/tex]
Therefore the side length of the square and area are not directly proportional they are proportional to the square root of area.
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the number 57 belongs to which of the following sets of the numbers? N only, N, W and Z only, N, W, Z, and Q only, All of the following: N, W, Z, Q, and R
Answers
The number 57 belongs to the sets Z, Q, and R, but not N or W.
What are natural numbers ?
Natural numbers are the counting numbers that we use to represent quantities and perform arithmetic operations. These are the numbers that we use to count objects, such as apples, books, or people.
The number 57 belongs to the following sets of numbers:
N (the natural numbers): No, because 57 is not a counting number.
W (the whole numbers): No, because 57 is not a non-negative integer.
Z (the integers): Yes, because 57 is an integer (a positive integer, in fact).
Q (the rational numbers): Yes, because 57 can be written as a ratio of two integers (57/1).
R (the real numbers): Yes, because every rational number is also a real number.
Therefore, the number 57 belongs to the sets Z, Q, and R, but not N or W.
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Complete question -
What are the values of angle a c and f
Answers
Answer:
Step-by-step explanation:
f=133
a=93
c=140
A pole leans away from the sun at an angle of 7° to the vertical. When the elevation of the sun is 44°, the
pole casts a shadow 49 ft long on level ground. How long is the pole?
Answers
The length of the pole is approximately 412.7 feet.
What is the tangent function?
The tangent function is a mathematical function that relates the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side. It is defined as the ratio of the sine of the angle to the cosine of the angle.
We can solve this problem using trigonometry. Let's call the length of the pole "x". We can then use the tangent function to relate the angle that the pole makes with the vertical to the length of the shadow cast by the pole.
The tangent of the angle between the pole and the vertical is equal to the opposite side (length of the shadow) divided by the adjacent side (length of the pole).
tan(7°) = opposite / adjacent
tan(7°) = 49 / x
We can solve for x by multiplying both sides by x and then dividing both sides by tan(7°):
x = 49 / tan(7°)
Now we know the length of the pole is:
x = 49 / tan(7°) = 412.7 ft (rounded to one decimal place)
Therefore, the length of the pole is approximately 412.7 feet.
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PLEASE HELP I WILL MARK BRANLEIST
20 points
find the first 5 terms of each sequence (see picture)
Answers
Answer:
2, 3, 5, 9, 17
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] - 1 with a₁ = 2
a₁ = 2
a₂ = 2a₁ - 1 = 2(2) - 1 = 4 - 1 = 3
a₃ = 2a₂ - 1 = 2(3) - 1 = 6 - 1 = 5
a₄ = 2a₃ - 1 = 2(5) - 1 = 10 - 1 = 9
a₅ = 1a₄ - 1 = 2(9) - 1 = 18 - 1 = 17
the first 5 terms are 2 , 3 , 5 , 9 , 1 7
any one know the answers?
Answers
The value of the boxes, A , B and C are 22/4, 15/4 and 9 1/4 respectively
How to determine the valuesNote that from the information given, we have that the number in a box is the sum of the two numbers below it.
Then, we can deduce that;
A = The sum of the two mixed fractions, 3 1/4 and 2 1/4
B = The sum of the two mixed fractions, 2 1/4 and 1 1/2
Now, add the values
A = 3 1/4 + 2 1/4
convert to improper fractions
A = 13/4 + 9/4
Add the values
A = 22/4
B = 2 1/4 + 1 1/2
convert to improper fractions
B = 9/4 + 3/2
B =9 + 6 /4
B = 15/4
Then , the value of C = A + B
C = 22/4 + 15/4
C = 37/4
C = 9 1/4
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when a confounding variable is present in an experiment, one cannot tell whether the results were due to the a) independent variable or the dependent variable. b) independent variable or the confounding variable. c) dependent variable or the interval variable. d) dependent variable or the participant variable.
Answers
When a confounding variable is present in an experiment, one cannot tell whether the results were due to the independent variable or the dependent variable. The correct option is a) independent variable or the dependent variable.
A confounding variable is any variable that influences the dependent variable or response variable and is also
correlated with the independent variable. Because it is difficult to determine which variable is causing changes in the
dependent variable, it is also known as a confounding variable.
In other words, a confounding variable is a variable that can affect the dependent variable in an experiment, making it
impossible to determine the relationship between the independent variable and the dependent variable.
Therefore, when a confounding variable is present in an experiment, one cannot tell whether the results were due to
the independent variable or the dependent variable.
Consequently, researchers must take steps to identify and eliminate or control the effect of confounding variables to obtain valid and reliable results.
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Using trigonometric ratios find the missing side. Round to the nearest tenth.
Answers
The missing side has a length of about 46.2 units
What is trigonometric ratio of tangent (tan)?
[tex] \tan( \theta) [/tex] = opposite/adjacent
Here [tex] ( \theta) [/tex] is opposite angle of base of the triangle.
The base is the side opposite to the right angle and has a length of 14 units (given).
The side opposite to the angle of 17° is the "opposite" side.
The side adjacent to the angle of 17° is the "adjacent" side.
We want to find the length of the missing side (let's call it "x"). To do this, we can use the trigonometric ratio of tangent (tan), which relates the opposite and adjacent sides:
tan(17°) = opposite/adjacent
So, tan(17°) = opposite/x
We can rearrange this equation to solve for x,
x = opposite / tan(17°)
Plugging in the values we have,
x = 14 / tan(17°)
Using a calculator, we find that tan(17°) is approximately 0.303,
So,x = 14 / 0.303 ≈ 46.2
Therefore, the missing side has a length of about 46.2 units (rounded to the nearest tenth).
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Emily bought a car that depreciates at a
rate of 18% per year. She paid $55,000 for
the car. How much will her car be worth
after 8 years.
Answers
After answering the presented question, we can conclude that As a equation result, Emily's automobile will be valued roughly $19,105.25 after 8 years.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the phrase "[tex]2x + 3[/tex]" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "[tex]x2 + 2x - 3 = 0[/tex]." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Emily's car will be worth 100% - 18% = 82% of its original value after one year, or 0.82 times its initial value.
After two years, the car is worth 0.82 times its initial value, or 0.822% of its original value.
Similarly, the car will be worth 0.828% of its initial value after 8 years.
Hence, after 8 years, Emily's automobile will be worth:
In 8 years, the value is $55,000 x 0.82.
After 8 years, the value is $19,105.25. (rounded to the nearest cent)
As a result, Emily's automobile will be valued roughly $19,105.25 after 8 years.
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Given � ( � ) = − 2 � 2 − 4 � + 13 f(x)=−2x 2 −4x+13, find � ( − 7 ) f(−7)
Answers
The function g(-7) * f(-7) is approximately equal to *-8056.5*.
What is a function?
A function is a mathematical rule that assigns a unique output value to each input value from a given set. It represents a relationship between two sets of numbers in which each input has exactly one output. A function can be expressed symbolically, graphically, or verbally and is used to model real-world phenomena, solve equations, and make predictions in various fields of study.
According to the given information
To find g(-7) and f(-7), we need to substitute -7 for y in the function g(y) = -2ᵇ - 4b + 13 and x in the function f(x) = -2x² - 4x + 13.
g(-7) = -2⁻⁷ - 4⁻⁷ + 13
Simplifying this expression gives:
g(-7) = -1/128 + 28 + 13
g(-7) = 141 - 1/128
Therefore, g(-7) is approximately equal to 140.9922 .
f(-7) = -2(-7)² - 4(-7) + 13
Simplifying this expression gives:
f(-7) = -98 + 28 + 13
f(-7) = -57
Therefore, f(-7) is equal to -57.
So, g(-7) * f(-7) is approximately equal to -8056.5.
The correct question is
g(y ) = − 2ᵇ − 4b + 13 and f(x)=−2x² −4x+13, find g( − 7 ) f(−7)
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60000 dividido en 800
Answers
Answer:
75
Step-by-step explanation:
Question 7(Multiple Choice Worth 2 points)
(Scatter Plots MC)
A marine biologist was interested in seeing the relationship between a manatee's weight and food consumption. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
Answers
A scatter plot would be more appropriate to construct for the data, given the context of the problem. The reason is that the marine biologist is interested in seeing the relationship between a manatee's weight and food consumption.
A scatter plot is a type of graph that displays the relationship between two variables, where each variable is plotted along one axis, and a point is placed at the intersection of the two values. In this case, weight would be plotted along one axis and food consumption along the other axis.
A scatter plot allows the researcher to see if there is a relationship between the two variables, and if so, what type of relationship it is (positive, negative, or no correlation). Therefore, a scatter plot is the most appropriate way to display the relationship between a manatee's weight and food consumption.
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HELP! The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 110.5° is added to the data, how does the mean change and by how much?
The mean increases by 2.3°.
The mean increases by 2.7°.
The means stays at 80.4°.
The mean stays at 82.7°.
Answers
If we do the mean for the first set of numbers, we get a mean of 80.7 (rounded to the tenths place)
If we add the 110.5 to the set, our mean will be 82.96 (rounded to hundredths place)
If we do
82.961538461538 (second mean) minus 2.3 and 2.7 one of these will work
Our answer is the mean increases by 2.3
Math: 82.961538461538 - 2.3 = 80.661538
82.961538461538 - 2.7 = 80.261538
A new line is drawn that passes through the point (-6,2) and is parallel to line m.
The equation of this line can be written as y=1/2x+a Enter the value of a.
Answers
a = -1
Step-by-step explanation:
Since the new line is parallel to line m, it has the same slope as line m. We can find the slope of line m by looking at its equation:
2x + 4y = 8
Subtracting 2x from both sides, we get:
4y = -2x + 8
Dividing both sides by 4, we get:
y = -1/2x + 2
Therefore, the slope of line m is -1/2.
We also know that the new line passes through the point (-6,2). We can use this point and the slope of the line to find the value of a in the equation y = 1/2x + a.
Starting with the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the values we know:
y - 2 = -1/2(x - (-6))
y - 2 = -1/2(x + 6)
y - 2 = -1/2x - 3
Adding 3 to both sides, we get:
y + 1 = -1/2x
Subtracting 1 from both sides, we get:
y = -1/2x - 1
Comparing this equation to y = 1/2x + a, we see that a = -1.
Therefore, the value of a in the equation y = 1/2x + a for the new line that passes through the point (-6,2) and is parallel to line m is a = -1.
The numbers 2 through 16 are written on tiles and put into a hat. One number is drawn at random. Determine the theoretical probability of drawing a prime number.
Answers
Answer:
2/5 or 0.4, which is also equivalent to a 40% chance.
Step-by-step explanation:
To determine the theoretical probability of drawing a prime number from the numbers 2 through 16, we need to first identify the prime numbers in this range. The prime numbers between 2 and 16 are 2, 3, 5, 7, 11, and 13.
There are a total of 15 numbers in the hat, and 6 of them are prime. Therefore, the probability of drawing a prime number can be calculated as:
Probability of drawing a prime number = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 6 (since there are 6 prime numbers in the range of 2 through 16)
Total number of possible outcomes = 15 (since there are 15 numbers in the hat)
So, the probability of drawing a prime number is:
Probability of drawing a prime number = 6 / 15
Simplifying this fraction by dividing both numerator and denominator by 3, we get:
Probability of drawing a prime number = 2 / 5
Therefore, the theoretical probability of drawing a prime number from the numbers 2 through 16 is 2/5 or 0.4, which is also equivalent to a 40% chance.
will give brainlest
|x+3|=9
you have to spilt the equation to get the absolute value
Answers
Answer:
To solve the equation |x+3|=9, we need to split it into two separate equations, one for the positive value and one for the negative value of the absolute value:
For the positive value:
x+3=9
Solving for x, we get x=6
For the negative value:
-(x+3)=9
Multiplying both sides by -1, we get:
x+3=-9
Solving for x, we get x=-12
Therefore, the solutions to the equation |x+3|=9 are x=6 and x=-12.
Hope This Helps!
Anyone help in number1 (d)
Answers
So
130+d=180
d=50 degrees
e= 130 degrees
f= 50 degrees
Pilar is playing with a remote-controlled toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back to Pilar, the boat travels the same route at the same speed for 2 minutes, and then Pilar uses the remote control to increase the boat's speed by 10 m/min. So the return trip is 60 seconds faster. How long does the return trip take?
Answers
Answer:
Therefore, the time for the return trip is:
≈ 5.306 seconds
Step-by-step explanation:
Let's start by finding the speed of the boat. We know that the boat travels 400m at a constant speed, so we can use the formula:
Speed = Distance / Time
Speed = 400m / Time (for one-way trip)
Let's assume that the time for the one-way trip is t. Then we can rewrite the speed formula as:
Speed = 400m / t
Now let's find the time for the return trip. We know that the boat travels the same route at the same speed for 2 minutes, which is equivalent to 120 seconds. This means that the distance traveled on the way back is:
Distance = Speed x Time
Distance = (400m / t) x 120 seconds
Distance = 48000m / t
We also know that when Pilar increases the boat's speed by 10 m/min, the return trip is 60 seconds faster. This means that the time for the return trip is:
t - 60 seconds
Using the same formula as before, the distance traveled on the return trip is:
Distance = (400m / (t + 1/2)) x (t - 60) seconds
Distance = (400m / (t + 1/2)) x (t - 60/60) minutes
Distance = 400m x (t - 60/60) / (t + 1/2) minutes
Now we know that the distance traveled on the way back is equal to the distance traveled on the way there:
48000m / t = 400m x (t - 60/60) / (t + 1/2)
Simplifying this equation, we get:
48 / t = 4 x (t - 1/3) / (t + 1/2)
Multiplying both sides by (t + 1/2), we get:
48(t + 1/2) / t = 4(t - 1/3)
Simplifying this equation, we get:
96 / t = 4t - 4/3
Multiplying both sides by t, we get:
96 = 4t^2 - 4/3t
Multiplying both sides by 3, we get:
288 = 12t^2 - 4t
Rearranging this equation, we get
12t^2 - 4t - 288 = 0
Dividing both sides by 4, we get:
3t^2 - t - 72 = 0
Using the quadratic formula, we can solve for t:
t = [1 ± sqrt(1 + 4(3)(72))] / 6
t = [1 ± sqrt(865)] / 6
Since t must be positive, we take the positive root:
t ≈ 6.366
Therefore, the time for the return trip is:
t - 60 seconds ≈ 6.366 - 60 seconds ≈ 5.306 seconds
water is leaking out of an inverted conical tank at a rate of 10,500 cm3/min at the same time that water is being pumped into the tank at a constant rate. the tank has height 6 m and the diameter at the top is 4 m. if the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm3/min) at which water is being pumped into the tank.
Answers
The rate at which water is being pumped into the tank is 11,760 cm3/min.
How to find rate?The formula for the volume of a conical tank is:V = (1/3)πr2h
Where r is the radius of the tank, and h is the height of the tank.Find the radius of the tank at a height of 2 m.Using similar triangles:
(r / 2) = (2 / 6)
r = 2/3 * 4r = 8/3 cm
The formula for the rate of change of volume of a conical tank is:dV / dt = (πr2 / 3)dh / dt
dV / dt = pump rate - leak rate
= pump rate - 10,500 cm3/mindh / dt
= 20 cm/minr = 8/3 cm
Plug in the values:pump rate - 10,500 = (π(8/3)2 / 3) * 20pump rate - 10,500
= 2114.67pump rate
= 11,760 cm3/min
Therefore, the rate at which water is being pumped into the tank is 11,760 cm3/min.
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