A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 10 cm.
(a) Find an equation of the parabola.
(b) Find the diameter of the opening CD, 11 cm from the vertex.
Answers
The equation and diameter CD of the parabola are x=1/10 y^2and 2√110
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
a(x – h)2 + k
Where:(h, k) - The vertex of the parabola.
a - Least distance between the vertex and the focus of the parabola.
Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.
Given;
Vertex is at origins (0,0) and latus rectum = 10 and the graph open right so a is positive and the equation is:
x=a (y-k)^2+h.
To write the equation we need to find a using the latus rectum equation.
We substitute the values.Then inverse place of a with 10
Latus rectum=|1/a|
10=|1/a|
a=1/10
The equation:
x=a (y-k)^2+h
x=1/10(y-0)^2+0
x=1/10 y^2
-Assume the distance between C and the center is EC. If E is (11,0) and C is (11, y).
-EC=y
-The equation of the parabola is x=1/10 y^2
Now, Substitute the value of C coordinate, which
x=1/10 y^2
Substitute the value of C coordinate, which is (11, y).
11×10=1/(10×10) y^2
√(y^2 )=√110
y=EC=√110
Because the distance of EC = ED
CD=EC×2
CD=√110×2
CD=2√110
Therefore, the equation of parabola and CD will be x=1/10 y^2 and 2√110
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Related Questions
Suppose a and b are independent events. if p(a) = .5 and p(b) = 0.45 what is p(a^b)
Answers
If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.
What are independent events?Independent events are events such that the occurrence of one event won't affect the other.
Therefore,
P(a) × P(b) = P(a ∩ b)
Hence,
P(a) = 0.5
P(b) = 0.45
Therefore,
P(a ∩ b) = 0.5 × 0.45
P(a ∩ b) = 0.225
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Solve for m
-7+4m+10=15-2m−7+4m+10=15−2mminus, 7, plus, 4, m, plus, 10, equals, 15, minus, 2, m
m=
Answers
The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2
Algebra-7 + 4m + 10 = 15 - 2m
collect like terms4m + 2m = 15 + 7 - 10
6m = 12
divide both sides by 6m = 12/6
m = 2
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The water park charges a $45 fee plus $5 per student for a field trip. The
bowling alley charges a $35 fee plus $7 per student. The lines in the graph
represent the cost of each field trip.
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
Cost ($)
100
90
80
70
60
50
40
30
20
10
Field Trip Costs
y = 35+ 7x
y = 45 + 5x
1 2 3 4 5 6 7 8 9 10
Number of students
Answers
Using linear functions, the cost will be the same, of $70, when there are 5 students.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the functions are:
y = 45 + 5x.y = 35 + 7x.The costs are the same when:
45 + 5x = 35 + 7x
2x = 10
x = 5.
The cost is:
y = 45 + 5 x 5 = $70.
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Assuming a normal distribution, families spends an average of $500 on their monthly cell phone bills with a standard deviation of $75. What is the probability a random families' bill is between $350 and $400
Answers
There is a 0.02275 to 0.0968 chance that a random family's bill will be between $350 and $400.
Calculating the probabilityProvided that,
Mean of the population = 500
The standard deviation(S.D) of the population = 75
Assume,the variable in normal distribution = X
Z= (x- mean)/ S.D
Provided , x = $350 - $400
Z= 350-500/75 = -2(when x=$350)
Z= 400-500/75 = -1.3 (taken x= $400)
The probability that a household will spend between $350 and $400 monthly
P(350>X<400) = P( -2>Z<-1.3)
= 0.02275 to 0.0968 (from probability table)
Therefore, the final answer is 0.02275 to 0.0968.
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which relation is a function
Answers
a function is a relationship between inputs where each input is related to exactly one output.
The relation in option B is a function.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given are 4 relations, A, B, C, D.
From the definition of function, it is clear that, no input value have more than one output value.
A : The value of x = -2 is mapping to 2, 1, 0, -1.
That is, an input value is having more than one output values.
So this is not a function.
B : Here the input values, 0, 1, 2 and 3 maps to -2.
Here the input values are distinct. No input values are mapping to more than one output value.
So this is a function.
C : Here 1 is mapping to -2 and 3. So not a function.
D : For x = 0, there are two y values, 3 and -3.
So this is not a function.
Hence option B is a function.
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What value, written as a decimal, should lena use as the common ratio? 1.0 1.5 2.5 2.0
Answers
The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0
According to the question,
1.0 1.5 2.5 2.0
a = 1.0
r = 1.5/1 = 1.5
r = 2.5/1.5 = 1.6667
r = 2/2.5 = 0.8
common ratio is different, so given sequence is not geometric sequence.
Hence, the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.
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Look at the image below.
Find the area of the parallelogram.
Answers
Answer: 80 square units
Step-by-step explanation:
[tex]A=(8)(10)=80[/tex]
Juan needs to rewrite this difference as one expression. First he factored the denominators. What step should Juan take next when subtracting these expressions
Answers
The next step Juan will take is to multiply the second fraction by (x-2)/(x-2).
Given that Juan needs to rewrite this difference as one expression (3x/(x²-7x+10))-(2x/(3x-15)) and factor the denominator as (3x/(x-2)(x-5))-(2x/3(x-5)).
An algebraic expression in mathematics is an expression composed of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.
The given expression is (3x/(x²-7x+10))-(2x/(3x-15))
Firstly, we will factored the denominator as
(3x/(x-2)(x-5))-(2x/3(x-5)).
Now, we will multiply and divide the second fraction by (x-2), we get
(3x/(x-2)(x-5))-((2x(x-2))/3(x-5)(x-2)).
Hence, the next step when subtracting these expressions (3x/(x-2)(x-5))-(2x/3(x-5)) is multiply the second fraction by (x-2)/(x-2).
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N
Mason is creating a design using a straightedge and compass. He wants to construct a segment FG, which is congruent to segment BE in the
given figure.
A. the distance from B to E
To what width should Mason set his compass when constructing segment FG?
OB.
O C.
O D.
the distance from D to F
The distance from F to c
A
the distance from A to C
F
A
D
Answers
The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.
WidthFG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.
Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.
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Answer:
b to e
Step-by-step explanation:
plato
Which of the following equations will produce the graph shown below?
Answers
The equation that will produce the given graph is; 6x² + 6y² = 144
What is the equation of the Circle?The standard equation of a circle can be expressed as:
(x + a)² + (y - b)² = r²
where;
(a, b) is the center of the circle
r is the radius of the circle.
From the diagram, we can see that the radius of the circle is between 4 and 5. Thus, the correct equation must have a radius between these values.
From the option, we can see that the only equation that will have a radius between 4 and 5 is;
6x² + 6y² = 144
Divide through by 6 to get;
x² + y² = 24
x² + y² = √24
Thus r = √24 which is greater than 5
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In total, 2 baseballs and 3 footballs cost $67. a football is $4 more than 3 times the cost of a baseball. find the cost of a baseball
Answers
The cost of the Baseball is $5.
Lets take football cost as "x"
And taking baseball cost as "y"
According to given conditions,
2y + 3x = 67
x= 3y + 4
Lets put the values of x in equation (1):
2y + 3 (3y+4) = 67
=> 2y + 9y + 12 = 67
=> 11y = 55
y = 5
x = 3(5) + 4
x = 19
Hence the cost of the Baseball is $5.
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Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
Answers
The theorem that would be included in the proof is: CPCTC theorem.
What is the CPCTC Theorem?CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.
To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:
1. angle D ≅ angle F [given]
2. angle DBE ≅ angle ECF [given]
3. side DE ≅ side EF [given]
4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]
5. DB ≅ FC [by the CPCTC theorem]
With the given proof, we can state that side DB is congruent to side FC.
Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.
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Statement
The wastes from
nuclear power plants
are very toxic.
Nuclear power plants
produce less air
pollution than power
plants that use fossil
fuels.
Nuclear power plants
are safe.
The benefits of nuclear
power outweigh the
risks.
How my answer changed
Part of the lesson or other evidence that
changed my mind supported my original
answer
H
Answers
The new statement will be:
The nuclear power plants wastes are very toxic.Air pollution from Nuclear power plants is much lower that from powerplants that make use of fossil fuels.Power plants that are Nuclear are regarded as safe.The risks of nuclear power is much more lower than the benefits.What changed my mind in the above?Nuclear energy is known to be one that produce a lot of radioactive waste and this tends to pose a threat to human health and the environment.
Hence, The new statement will be:
The nuclear power plants wastes are very toxic.Air pollution from Nuclear power plants is much lower that from powerplants that make use of fossil fuels.Power plants that are Nuclear are regarded as safe.The risks of nuclear power is much more lower than the benefits.Learn more about nuclear power from
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
Answers
The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;
2.3p – 10.1 = 6.49p – 4 and230p – 1010 = 650p – 400 – pWhich equations have the same solution as the given equation?It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.
The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.
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Answer:
B & C
Step-by-step explanation:
edge 2023
Which choice is equivalent to the quotient below? √16 OA. A OB. N/హ / OC. 2 D. √√2
Answers
Answer:
C
Step-by-step explanation:
Please refer to the attached photo for step by step solutions.
Note: Square roots and squares will always cancel out each other.
A data value is considered _______ if its z-score is less than 2 or greater than 2.
Answers
A data value is considered significantly low or significantly high if its z-score is less than -2 or greater than 2.
What does it mean if z-score is 2?
A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean. A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.What does a standard deviation of 2 mean?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.Learn more about standard deviation
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The correct question is -
A data value is considered _______ if its z-score is less than minus−2 or greater than 2.
Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the descriptions.
Answers
The tiles to match the descriptions are;
Hull house - Neighbourhood assistance.
Muckrakers - Investigative journalists.
Protestants - Temperance movement.
Women's suffrage - Nineteenth amendment.
What is Progressive time period?The Progressive Era, which encompassed the years between the 1890s and the 1920s in US history, was one of intense social and political reform with the goal of advancing the creation of a better society.
Case 1: The settlement home that welcomed newly arrived European immigrants to the United States in 1889 is known as Hull House. There were also social, educational, and artistic initiatives for immigrants in this building.
Case 2: Muckrakers A name used to describe a group of North American journalists in the early 20th century who made public criticisms of: government corruption, abuse of labor is destructive to society and is committed by influential people or institutions of the time.
Case 3: Third, the term "Protestantism" is used to describe a variety of 16th-century religious movements. Because the Catholic Church had a different understanding of the Bible's holy texts, this movement was distinguished by its break with it.
Case 4: The 19th Amendment to the United States Constitution, which was adopted in June 1919, guaranteed every American woman the right to vote.
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The complete question is-
Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the
descriptions
Tiles;
Hull House
Muckrakers
Protestants
Women's Suffrage
Pairs;
Investigative journalists
Temperance Movement
Neighbourhood assistance
Nineteenth Amendment
What is 8 11/12 + 9 5/18
Answers
Step-by-step explanation:
The picture is the full explanation for this question answer.
18.19 is the solution for the given improper function.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To add 8 11/12 and 9 5/18, we need to first find a common denominator. The smallest number that both 12 and 18 divide evenly is 36.
Converting 8 11/12 to an improper fraction:
8 11/12 = (8 × 12 + 11) / 12 = 107/12
Converting 9 5/18 to an improper fraction:
9 5/18 = (9 × 18 + 5) / 18 = 167/18
Now that we have a common denominator of 36, we can add the two fractions:
107/12 + 167/18 = (107 × 3) / (12 × 3) + (167 × 2) / (18 × 2)
= 321/36 + 334/36 = 655/36
So 8 11/12 + 9 5/18 = 655/36 or approximately 18.19.
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Find the product of X^2 (4x - 3).
A. 5x^3
B. 5x^3 - 3x^3
C. 4x^3 - 3x^2
D. X^2 + 4x - 3
Answers
x² ( 4x - 3)
Apply the multiplicative law of distribution.
x² × 4x - x² × 3Multiply the monomial
4x³ - x² × 3Multiply the monomial
4x³ - 3x² ==> AnswerTherefore, the correct option is "C".
The probability of picking an ace at random out of a
deck of 52 cards is What would be the probabil-
13
ity of picking an ace at random if 2 aces were
removed from the deck?
Answers
Answer:
2/50=1/25
Step-by-step explanation:
2 aces are removed hence 2 aces are left out of 50 cards
Find the volume of a pyramid with a square base, where the side length of the base is
18.7 ft and the height of the pyramid is 8.8 ft.
Answers
Answer:
1025.76
Step-by-step explanation:
Formula for a right rectangular pyramid is (l*w*h)/3
The length and width are both 18.7, so we can plug that in. The height is 8.8.
It becomes:
(18.7*18.7*8.8)/3, which equals the answer above.
The diagram below shows a logo formed by removing a semicircle with diameter AB and a
rhombus DEFG from an isosceles trapezium ABCE where AE = BC.
Find the area of the logo.
Answers
The area of the logo is 136. 14 cm²
Determining the area
First, let's find the area of the semicircle
Area of semicircle = 1/2(πr²)
radius = 8/2 = 4cm
Substitute into the formula
Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²
Now, let's find area of trapezium
Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]
Area = [tex]\frac{12 + 10. 2}{2} * 10[/tex]
Area = [tex]11. 1 * 10[/tex]
Area = 111 cm²
Area of logo = Area of trapezium + area of semicircle
Area of logo = 111 + 25. 135
Area of logo = 136. 14 cm²
Thus, the area of the logo is 136. 14 cm²
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Describe the following expressions in words: x+4
Answers
Hope this helped :)
What is the recursive formula for the geometric sequence with this explicit
formula?
a^n=9(-1/3)^(n-1)
Answers
You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area
Answers
The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.
Dimensions to Minimize the Surface Area of the Box
It is given that the box is square based with an open top.
⇒ The box has one square and 4 rectangles
Thus, the total surface area of the box is given as,
S= a²+ab+ab+ab+ab
S= a²+4ab ______________ (1)
Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.
This equation is later used for minimization of the surface area.
Also, the volume, V = a²b
It is also given that volume of the box is 184 in³.
⇒ 184 = a²b _____________ (2)
Forming a One-Variable Equation
From equation (2), b=184/a²
Now, substitute this value of b in equation (1) to get,
S = a² + 4a(184/a²)
S = a² + 4(184/a)
S = a² + 736/a
Minimization of Surface Area to find the Dimension
We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0
dS/da = 2a -736/a²
0 = 2a -736/a²
⇒ 0 = 2a³- 736
2a³ = 736
a³ = 736/2
a³ = 368
a = ∛368
a= 7.17 in
∵V = a²b
184 = (7.17)²b
b = 184/7.17²
b = 184/51.4089
b = 3.58 in
Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..
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3 m
8 m
12 m
9m
6 m
Find the total surface area of the trapezoidal prism in the figure.
Answers
The total surface area of the trapezoidal prism is 180m². Option C
Total surface area of a trapezoidal prism
The formula for the total surface area of a trapezoidal prism is;
Total surface area = h (b + d) + l (a + b + c + d)
Where
b and d are parallel sides = 3, 9
h is the distance = 8
l is the length of the trapezoidal prism. = 12
Substitute into the formula
Total surface area = [tex]8(3 + 6) + 12(3 + 6)[/tex]
Total surface area = 72 + 108
Total surface area = 180 m²
Thus, the total surface area of the trapezoidal prism is 180m². Option C
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Destiny bags 3 grocery bags a minute. how long will it take her to bag 150 bags?
Answers
Answer: I believe its 50 because you would have to see 3 x what equals 150
Step-by-step explanation:
The time taken to her to bag 150 bags is 50 minutes.
What is grocery?Grocery Items are any of the items listed that are offered only for off-premises consumption are as follows:-
(1) packaged or fresh fish, meat, or poultry.
(2) packaged or fresh plants or vegetables.
(3) packaged or fresh dairy goods (other than ice cream, frozen yogurt, or other confection/dessert items).
According to the given question, Three grocery bags are packed every minute. So, the time taken to 150 bag the time taken is computed as follows:-
Time Taken = Total number of bags/Number of bags per minute
= 150 / 3
= 50 minutes
Therefore, it can be concluded that the time taken for her to bag 150 bags is 50 minutes.
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EXTRA POINTS, AND ILL GIVE YOU BRAINLIEST
1 x/3 - 3/4 = 5/12 solve for x!
Answers
The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
x/3 - 3/4 = 5/12
Hence:
x/3 = 5/12 + 3/4
x/3 = 7/6
x = 7/2
The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2
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can someone please help me
Answers
Based on definition of unit circle and angle properties on Cartesian plane, we find the following results: A: π/5, B: 3π/7, C: 4π/3.
How to determine angles in a unit circle
Units circles are commonly used to understand angles and trigonometric functions in a simple way. Vectors in a unit circle are ordered pairs of polar form: (x, y) = (cos θ, sin θ).
To solve this problem, we must take these tips into account:
Angles in the first quadrant are within 0 < θ < π/2.Angles in the second quadrant are within π/2 < θ < π.Angles in the third quadrant are within π < θ < 3π/2.Angles in the fourth quadrant are within 3π/2 < θ < 2π.Then, we have the following results: A: π/5, B: 3π/7, C: 4π/3.
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This question is down below. Please solve in detail if you know how to solve.
Answers
Answer:
8.4 meters tall ( one decimal place)
Step-by-step explanation:
See diagram below:
find distance 'd' as tan 68 = opp / adj = d/6
then d = 6 tan 68 = 14.85 m
Then find h as tan 9 = h / d
d tan 9 = h
14.85 tan 9 = h = 2.35 m tall
add the 6 m height of the house 8.4 m tall