An arch is in the shape of a parabola. It has a span of 72 meters and a maximum height of 9 meters.
Answers
Answer:
Equation of the parabola:
[tex]y=-\frac{1}{144}x^2+9[/tex]The height of the arch 18 meters from the center is 6.75m
Explanation:
The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0
Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9
Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.
With all this, we can try to find the general form of a parabola. The general form is:
[tex]y=ax^2+bx+c[/tex]c is the y-intercept. We know that c = 9
We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]SInce the x-coordinate of the vertex is x = 0
[tex]0=-\frac{b}{2a}[/tex]If we solve:
[tex]b=0[/tex]So far we have:
[tex]y=ax^2+9[/tex]Finally, to find a, we can use the point (36, 0) (one of the roots)
[tex]0=a(36)^2+9[/tex]And solve:
[tex]\begin{gathered} 324a=-9 \\ . \\ a=-\frac{9}{1296}=-\frac{1}{144} \end{gathered}[/tex]Thus, the equation of the arch is:
[tex]y=-\frac{1}{144}x^2+9[/tex]Evaluating this equation for x = 18, we can find the height of the arch:
[tex]y=-\frac{1}{144}(18)^2+9=-\frac{9}{4}+9=-6.75[/tex]Related Questions
A factory produce 11,650 gallon of lemonade 4,950,fewer gallons of ice tea than lemonade
Answers
Factories produce a total of 21550 gallons in a calendar year.
The gallon is used as a unit of volume in both imperial and US customary measurements.
Eight pints make up a gallon, which is a unit of measurement for liquids. It is equivalent to roughly 4.546 litres in Britain. It is roughly equivalent to 3.785 litres in America.
Lemonade, it has been stated, equals 11,650 gallons.
Lemonade = 4,950 fewer than ice tea.
Ice tea: 3,500 fewer than Root beer.
Using the formula Ice tea = 11,650 - 4,950
6700 gallons of iced tea
Root beer = 6700 - 3,500
3200 gallons equals root beer.
Total manufacturing output for a year is equal to 11,650 + 6700 + 3200
Thus, 21550 gallons are produced in total by factories each year.
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Graph the following Absolute Value Functions.
Analyze when the function is positive, negative,
increasing, or decreasing. Then describe the end
behavior of the function.
▶1. f(x) = x+3/+2
2. f(x)=x-7/+2
3. f(x) = -x-4-9
4. f(x) = x+8 -1
5. f(x) = 3|x-1| +5
6. f(x) = -x +4+3
7. f(x) = -x-6-10
8. f(x) = -2/x+2-8
Help please
Answers
The absolute value of the given functions are ;
1. increasing
2. increasing
3. decreasing
4. increasing
5. increasing
6. decreasing
7. decreasing
8. decreasing
What are increasing and decreasing functions?Calculus functions called increasing and decreasing functions have f(x) values that change according to how much x rises or decreases. The behavior of growing and decreasing functions is examined using the derivative of the function f(x). If the value of f(x) grows as the value of x increases, the function is said to be increasing; conversely, if the value of f(x) decreases as the value of x increases, the function is said to be declining.
Like wise in this question we just have to find the d/dx and if it comes out positive then the function is increasing and if it is negative then it is decreasing.
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you can swim 915 feet, tread water for 4 minutes, and swim 18 feet underwater without taking a breath. Do you satisfy the requirements of the course? explain.
Answers
The values of the swimmer is 305 yards which is less than 350 yards required, thus the course is not suitable for swimmer.
What is defined as the unit conversion?Unit conversion is a multi-step process that involves multiplying or dividing by a mathematical factor or, more particularly, a conversion factor.For the given question;
The data of the swimming is given as;
915 feet, Tread water for 4 minutes, 18 feet under water.The life guard requirement is -
Swim at least 350 yard.Tread water at least 2 minutes.Underwater swim 5 yards.To compare the requirements, convert the given values in feet to yard.
1 foot = 0.33 yards.
915 feet = 0.33×915 yards
915 feet = 305 yards
305 yards < 350 yards, not suitable.
18 feet under water.
18 feet = 0.33×18 yards
18 feet = 6 yards , suitable
Tread water at least 4 minutes > Tread water at least 2 minutes required, suitable.
As, the values of the swimmer is 305 yards which is less than 350 yards required, thus the course is not suitable for swimmer.
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Suppose that country A and country B initially have the same per capita GDP. After that, country A grows at 3.5 percent per year and country B grows at 7 percent per year. According to the rule of 70, after 40 years what is the ratio of country B's GDP to country A's?
Answers
Using the Rule of 70, it is found that after 40 years, the ratio of country B's GDP to country A's is of 2.
What is the Rule of 70?The rule of 70 is a rule that is used to determine how long it takes for an amount to double, dividing 70 by the variable's growth rate, as a percentage.
Country A grows at 3.5 percent per year, hence the time it takes to double is:
70/3.5 = 20 years.
Hence in 40 years, it's GDP will be of:
4n, in which n is the current GDP, and 4 because it will have doubled twice.
Country B grows at 7 percent per year, hence the time it takes to double is:
70/7 = 10 years.
Hence in 40 years, it's GDP will be of:
8n, in which n is the current GDP, and 8 because it will have doubled three times.
Then the ratio of country B's GDP to country A's will be of:
8n/4n = 2.
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The tables show relationships between two quantities. Which table shows a proportional relationship? A INSERT_TEXT B INSERT_TEXT C INSERT_TEXT D INSERT_TEXT
Answers
The table that shows a proportional relationship between the variables a and b is Table B, which is the second table graphed.
What is a direct proportional relationship?In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
Hence, a data-set such as a table will represent a proportional relationship if the ratio between the output and the input is the same for all the terms of the relationship.
In this problem, we have that:
Table 1 does not show a proportional relationship between a and b, as the ratios are of 3, 3 and 4, respectively.Table 2 shows a proportional relationship between a and b, as the ratios are of 5/4, 5/4 and 5/4, respectively, that is, all the ratios are the same.Table 3 does not show a proportional relationship between a and b, as the ratios are of 3, 3 and 4, respectively.Table 4 does not show a proportional relationship between a and b, as the ratios are of 4/3, 3/2 and 4/3, respectively.What is the missing information?In the context of this problem, the tables are missing, and are given by the image at the end of the answer.
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Answer:
its D.
Step-by-step explanation:
i did the test.
Trisha is making flags with 40 5/16 yards of fabric. If each flag requires 3 1/8 yards, how many flags can she make?
Answers
Answer:
I just wanted points please forgive me
Step-by-step explanation:
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Find the final price of each item television: $375.00 discount: 25% tax: 6%
PLEASE HELP MEEEEEEEE!!!
I really need to understand how to work out this problem and solve it!
Thank You!
Answers
The final price of the television is $299.53.
Discount is somewhat a reduction in the actual or usual price of the object or service. Whereas, tax is the money that we have to pay to the government.
Price of television before discount = $375.00 (given)
Discount given = 25% (given)
25% of $375 is,
$375* (25/100)= $93.75.
The cost of the television after sale off and before the sales tax is:
$375- $93.75= $281.25
The sales tax = 6% (given)
$281.25* (6.5/100)= $18.28
The price of the television including everything is,
$281.25+ $18.28= $299.53
Therefore, we can conclude the the final price of television is $299.53.
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Solve each system of equations algebraically.
x + y = 3
- 2x + y = -6
How do you solve this, I can't seem to comprehend this, its hard for me. ;
Answers
The solution to the system of equation is the point where both lines intersect and it is at (3, 0)
System of equations
Given the following system of equations
x + y = 3
- 2x + y = -6
Graphically, the point where both lines intersect on the place is the solution to the given system of equation.
From equation 1, x = 3 - y
Substitute into equation 2:
- 2(3-y) + y = -6
-6 + 2y + y = -6
3y = -6 + 6
y = 0
Substitute y = 0 into any of the equation
x + y = 3
x + 0 = 3
x = 3
Hence the solution to the given system of equation is (3, 0)
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pls help i dont get it
Answers
a.) A triangle is equal to 2 squares.
b.) For this triangle it is equal to 3 circles
c.) Each star is 1 circle
"Your name" solved this by for example question a, splitting the squares on right's into two sections of 2 and 2 which helped me understand that one triangle is equal to 2 squares
b) 3
c) 2
d) subtract the amount of what you need to find. So like for a) you would subtract 4 minus 2 because there are 4 squares on the right side and 2 on the left, so you would get 2 which means that 2 squares equal 1 triangle.
From the 2014-2015 to 2024-2025, the number of student enrolled in an associate degree program is projected to increase by 23.5%. If the enrollment in associate degree in 2014-2014 is 6,600,000, find the increase and the projected number of students in an associate degree program in 2024-2025
Answers
Given,
From the 2014-2015 to 2024-2025, the number of student enrolled in an associate degree program is projected to increase by 23.5%.
The enrollment in associate degree in 2014 is 6,600,000.
The increase and the projected number of students in an associate degree program in 2024-2025 is,
[tex]\begin{gathered} \text{Increase in number of students= total students in 2014}\times\frac{percentage}{100} \\ =6600000\times\frac{23.5}{100} \\ =66000\times23.5 \\ =1551000 \end{gathered}[/tex]Hence, the increase and the projected number of students in an associate degree program in 2024-2025 is 1551000.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
susan says that (-3)(-3)(-3) will be a positive answer. ryan says that the product will be a negative answer. who is correct use words and numbers in your response
Answers
Answer: Ryan is correct
Step-by-step explanation:
-3 multiplied by -3 makes a positive 9. Then you need to multiply that 9 by the other -3 which makes it a negative 27.
(-3) x (-3) x (-3)
9 x -3
-27
Scientific Notation
CO
8
Directions: Select the correct answer from each drop-down menu.
In a particular year, the population of Dallas, TX, was approximately 1 x 106 people. If the population of Los Angeles, CA, was
approximately three times that of Dallas, there were about
people living in Los Angeles that year.
The population of Pittsburgh, PA, was approximately 3 x 105 people during the same year, which was about
that of Dallas.
Reset
Submit
times
Answers
Dallas, Texas, had a population of about 1 x 106 peoples in that specific year. There were above 3×10⁶ people in Los Angeles; The population of Pittsburgh was about 0.3 times of Dallas.
Given that,
Dallas, Texas, had a population of about 1 x 106 peoples in that specific year. If Los Angeles, California, had a population of
There were almost three times as many people there as in Dallas.
peoples who called Los Angeles home in that year.
In the same year, there were about 3 x 105 peoples living in Pittsburgh, Pennsylvania. one from Dallas.
In Dallas the population is P₁=1×10⁶
Then in Las Angeles the population is P₂=3P₁=3(1×10⁶)= 3×10⁶
In Pittsburgh the population is P₃=3×10⁵
P₃÷P₁=(3×10⁵)÷(1×10⁶)=0.3
Therefore, There were above 3×10⁶ people in Los Angeles; The population of Pittsburgh was about 0.3 times of Dallas.
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I'm safe 35% of 400 he needs to save to buy a bike how much money has Adam saved so far
Answers
∵ The percentage of the saving is 35%
∵ The total money is 400
→ Multiply 35% by 400 to fin
5x 4091+921
What will it be be
Cause hard
Answers
An easy way to find it is by multiply each number by 5 or by using a calculator.
4091
X. 5
20455
2) Next add the 921
20455 + 921 = 21376
3) Answer is 21376
Identify the missing statement or reason
A. Definition of midpoint
B. Definition of angle bisector
C. Reflexive property
D. Alternate interior angles Theo
Answers
Answer:Definition of Midpoint-A
Step-by-step explanation:
Here are three different recipes for Orangey-Pineapple Juice. Two of these mixtures taste the same and one tastes different.
Recipe 1: Mix 4 cups of orange juice with 6 cups of pineapple juice.
Recipe 2: Mix 6 cups of orange juice with 9 cups of pineapple juice.
Recipe 3: Mix 9 cups of orange juice with 12 cups of pineapple juice.
Which two recipes will taste the same, and which one will taste different? Explain or show your reasoning.
Answers
Using ratio we can conclude that Recipe 1 and recipe 2 tastes the same.
The multiplicity of two integers is shown by a ratio. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
An ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or the value represented by this fraction are all ways to conceptualize ratios. Rational numbers, and occasionally natural numbers as well, are ratios of counts stated in terms of (non-zero) natural numbers. When two numbers are compared using the same unit of measurement, which frequently occurs, their ratio is a dimensionless number. A rate is created by multiplying two amounts with different unit measurements.Let us consider the ratio of the orange juice top the pineapple juice for the 3 recipes.
Recipe 1 = 4 : 6 = 2 : 3
Recipe 2 = 6 : 9 = 2 : 3
Recipe 3 = 9 : 12 = 3 : 4
Hence from the above ratios we can conclude that Recipe 1 and recipe 2 tastes the same.
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Please help me I would sincerely appreciate it
Find the domain and range of the function graph
Domain:
Range:
Answers
Based on the graph of the function shown, we can logically deduce the following:
The domain of this graph is equal to (-∞, ∞).The range of this graph is equal to [-∞, -5] ∪ [-3, ∞].How to identify the range and domain of this function graph?In Mathematics, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Also, the horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph of the given function shown above, we can reasonably infer and logically deduce the following:
The domain = (-∞, ∞).The range = [-∞, -5] ∪ [-3, ∞].In conclusion, we can reasonably infer and logically deduce that the function which this graph represents is a piecewise function.
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Calculate both outliers
Answers
The outlier for Hits in league A is 40
The outlier for Hits in league B is 260
What is an outlier?An outlier can simply be defined as a data point that varies enormously or significantly from other recorded observations in a data set.
It occurs due to certain variability in the measurement of a data set or research.
It is known as an indicator of experimental errors.
It is also known to be the cause serious of errors in statistical analyses.
From the images shown, we have;
For Hits in league A;
The data set is; 20 - 40, 100 - 120, 120 - 140, 140 - 160, 160 - 180, 180 - 200, 200 - 220
We can see that the outlier is 40
For Hits in league B;
The data set is; 120 - 140, 140 - 160, 160 - 180, 180 - 200, 200 - 220, 240 - 260
The outlier is 260
Hence, the outliers are 40 and 260
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June has 72 gallons of punch for a party. June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Answers
If June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
The bigger cooler is five times as large as the smaller cooler
Consider the capacity of smaller cooler as x
The capacity of bigger cooler=5x
June has 72 gallons of punch for a party
Then the linear equation will be
x+5x=72
6x=72
x=12
Then the capacity of bigger cooler=5x
=5×12
=60
Hence, if June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60 gallons
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Use the DistributiveProperty to express40 + 56
Answers
Answer:We want to use distributive property to express:
Using distributive property,
[tex]40+56=8\times5+8\times7[/tex]Explanation:
[tex]40+56[/tex]8 is a common factor of 40 and 56, so we can write:
as
[tex]\begin{gathered} 8\times5=40 \\ \text{and} \\ 8\times7=56 \end{gathered}[/tex]S
[tex]40+56=8\times5+8\times7[/tex]What is the square root of the product of m and n
Answers
The square root of the product of m and n is √mn.
What are square roots?The value that, when multiplied by itself, returns the original number is called the square root of any number. The sign "√" is used to denote it. There are two square roots for every number, one of which has a positive value and the other a negative value. For instance, the number 4 has 2 and -2 as its two square roots.Any number's square root is represented as the number raised to the power 1/2. The following is the square root formula for the number x.[tex]\sqrt{x} = x^{1/2}[/tex]
To determine the square root of the product of m and n, find the product of m and n and raise the product to the power 1/2.
Product of m and n = mn
The square root of the product is = [tex](mn)^{1/2} = \sqrt{mn}[/tex]
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given function f(x)=-4x+11, evaluate when f(13)=
Answers
We can evaluate the function as follows:
[tex]f(x)=-4x+11\Rightarrow f(13)=-4\cdot(13)+11\Rightarrow f(13)=-52+11[/tex]Then, the function evaluated in f(13) is equal to -41, f(13) = -41.
Members of a soccer team raised $2143.50 to go to a tournament. They rented a bus
for $888.50 and budgeted $62.75 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Answers
Answer:
Step-by-step explanation:
$2143.5 = $62.75x - $888.5.
Rewrite the following in the form log (c) log(4) + log(3)
Answers
The required logarithm in the form log(c) is log(12).
What are logarithms?The inverse function to exponentiation in mathematics is called the logarithm. If aˣ = n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐ n.
Given:
log(4) + log(3)
Using the product property of logarithms, which states that a product's logarithm is equal to the sum of its logarithms.
log(ab) = log a + log b
Here, a = 4 and b = 3
So, log(12) = log(4) + log(3)
Therefore, the required logarithmic function in the form log(c) is log(12).
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. Length of the rectangular prism is 4 ft. The height and width are both 3 feet. Find the surface area of the prism.
Answers
Ok, so
Here we have a rectangular prism with the following measures:
-Length = 4ft
-Height = 3ft
-Width = 3ft.
Remember that the surface area of a rectangular prism can be found using:
[tex]SA=2lw+2wh+2lh[/tex]Where "l" is the length, "w" is the width, and "h" is the height.
If we replace our values in the equation given, we got that:
[tex]\begin{gathered} SA=2(4)(3)+2(3)(3)+2(4)(3) \\ SA=24+18+24 \\ SA=66 \end{gathered}[/tex]Therefore, the surface area of the prism is 66 ft2.
Olivia bought snacks for her team's practice. She bought a bag of chips for $2.25 and a 8-pack of juice bottles. The total cost before tax was $11.69. Which equation could be used to determine j, how much each bottle of juice costs?
Answers
What is the compound interest earned on a $10,000 investment that earns 6% compounded monthly for 5 years?
Answers
Explain why the value of the sine ratio for an acute angle
of a right triangle must always be a positive value less
than 1.
Answers
The sine is defined as the length of the opposite side divided by the length of the hypotenuse, both of which are positive. Since dividing a positive number by a positive number results in a positive number, the sine must be positive.
Also, since the hypotenuse is the longest side of the triangle, the sine is equal to some positive number less than the length of the hypotenuse being divided by the length of the hypotenuse, resulting in a number less than 1.
Thousandths Chart The students in Ms. Lowell's class wrote a thousandths decimal chart on the board. 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.02 Describe the pattern in the table above for moving across a row from left to right.
Answers
Answer:
the pattern is that the next number in the row is obtained by adding 0.001 to the previous number
Step-by-step explanation:
Difference between consecutive numbers as you go from left to right is an increase of 0.001
So the pattern is that the next number in the row is obtained by adding 0.001 to the previous number