PLEASE HELP!!!
Can someone help me out with this math problem.(CALCULUS 2)
picture of problem attached below.
Answers
The centre of mass of 40g, (1,3); 30g, (2,-1); 70g, (0,0) and 50g (0,-2) is located at (10/19,-1/19).
The formula to find the coordinates (X,Y) of centre of mass of a discrete particles system is,
X = (m₁x₁+m₂x₂+m₃x₃+m₄x₄)/(m₁+m₂+m₃+m₄)
Y = (m₁y₁+m₂y₂+m₃y₃+m₄y₄)/(m₁+m₂+m₃+m₄)
As we know,
m = 40
m = 30
m = 70
m = 50
Putting all the values in the formula,
for X coordinate,
X = [(40×1)+(30×2)+(70×0)+(50×0)]/(40+30+70+50)
X =(40+60+0+0)/(190)
X = 100/190
X = 10/19
For Y coordinate,
Y = [(40×3)+(30×-1)+(70×0)+(50×-2)]/(40+30+70+50)
Y= (120-30+0-100)/(190)
Y = -10/190
Y = -1/19
So, the centre of mass of the discrete particle system is at (10/19,-1/19)
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Related Questions
Given: m//n
Prove: m2 + m28 = 180
Answers
Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.
If m2 + m28 = 180 then we get ∠2 + ∠8 = 180°
What are the theorems for parallel lines?Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines.
Two lines are said to be parallel if a transversal and two matching angles it forms are congruent.
Verification of Parallel Lines
that which contradicts the alternate interior angles theorem.the opposite of the theorem relating comparable angles.the converse of the same-side interior angles hypothesis.alternative exterior angles theorem's opposite.When two lines are intersected by a transversal and the opposing interior angles line up, the intersected lines are said to be parallel. Two lines are said to be parallel if they are divided by a transversal such that their opposing exterior angles are equivalent.
Therefore,
Given line m is parallel to line m
Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.
Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.
Therefore, ∠2 = ∠6
∠2 + ∠4 = 180° ( Sum of the angles on a straight line is 180°)
∠6 + ∠8 = 180° ( Sum of the angles on a straight line is 180°)
∵ ∠2 = ∠6
∴ ∠6 + ∠8 = 180° ⇒ ∠2 + ∠8 = 180°
∠2 + ∠8 = 180° , Hence Proved.
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On average, Adrian's salary is 1.05 times the previous year's salary.If Adrian initially has $52,000 and n denotes the number of years, which recursive equation gives Adrian's annual income, /(7), as a function ofthe year?
Answers
Given:
Adrian initially has $52,000 and n denotes the number of years
Required:
Adrian's annual income, /(7), as a function of
the year?
Explanation:
Initially has $52,000, therefore
[tex]f(1)=52,000\text{ Exclude B,D}[/tex]The salary is 1.05 times the previous year's salary.
[tex]f(n)=1.05.f(n-1),\text{ for n}\ge2[/tex]Required answer:
Option D
10.Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7. 11.Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2. 12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.) 13. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0. 14. Write a quadratic equation that cannot be factored.
Answers
Explanation
Question 10
We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7
To do so, we will make use of
[tex]y=x^2-(sum\text{ of roots})x+product\text{ of roots}[/tex]So we will follow the steps below
[tex]\begin{gathered} Sum\text{ of roots = 3+}-7=-4 \\ product\text{ of roots =3\lparen-7\rparen=-21} \end{gathered}[/tex]substituting the above, we will have
[tex]\begin{gathered} x^2-(-4)x+(-21)=0 \\ \\ x^2+4x-21=0 \end{gathered}[/tex]Therefore, the quadratic equation is
[tex]x^2+4x-21[/tex]CRITICAL THINKING Find the values of a, b, and c so that the linear system shown has (---1. 2. --3) as its only solution. Explain your reasoning. x + 2y - Bra -r-y +z = b 2x + 3y - 2z=c enter your answer as follows: a=_,b=_,c=__without any spaces. Show Your Work
Answers
1) Let's set the system of linear equations:
x +2y -3z = a
-x -y +z = b
2x +3y -2z =c
2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:
x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4
-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0
2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2
3) Hence, a = 4 b = 0 and c = -2
A cooking for the nursing home is preparing 100 yeast rolls for dinner the dry ingredients needed include 14 1/8 cups of flour 6 3/8 cups of sugar and 3/8 cups of salt how many cups of dry ingredients are in this recipe
Answers
Given the following ingredients
Cups of flour = 14 1/8 = 113/8 cups
Cups of sugar = 6 3/8 cups = 51/8 cups
Cups of salts = 3/8 cups
Calculate the total cups of dry ingredients
[tex]Total\text{ cups}=\frac{113}{8}+\frac{51}{8}+\frac{3}{8}[/tex]Find the LCM
[tex]\begin{gathered} Total\text{ cups}=\frac{113+51+3}{8} \\ Total\text{ cups}=\frac{167}{8} \\ Total\text{ cups}=20\frac{7}{8}cups \\ Total\text{ cups}=19+1\frac{7}{8} \\ Total\text{ cups}=19+\frac{15}{8} \\ Total\text{ cups}=19\frac{15}{8}cups \end{gathered}[/tex]Therefore there are 19 15/8 cups of dry ingredients in this recipe
Jason has 22 strawberry scones and 55 blackberry scones. He wants to make as many identical bags of scones as possible. Each bag should have an equal number of raspberry scones and an equal number of blackberry scones. What is the greatest number of bags Jason can fill? Explain how you know.
Answers
11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.
In this question we have been given Jason has 22 raspberry scones and 55 blackberry scones.
We need to find the maximum number of bags Jason can fill with equal number of raspberry scones and blackberry scones.
We will be using Greatest common factor (GCF) for knowing the number of bags.
22 = 2 × 11
and 55 = 5 × 11
So, the greatest common factor of 22 and 55 is 11
GCF(22, 55) = 11
Therefore, 11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.
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Does our data provide enough evidence to prove that New York police are racially biased (in terms of use of force)? Why or why not?
Answers
We want to proof for this case if there is enough evidence to conclude that the New York police are racially biased in terms of force
From the info given is possible to see that the proportion with High level of force used is higher for Black people compared to White people. A difference of 6.3-5.8% = 0.5%.
In the other hand, we can see that for the Hands up force level, there is a significant difference between the two proportions, higher for Black compared to White with a difference of 15.1-9.7%= 5.4%
And finally when we analyze the case for No force used, we can see that there is a higher percentage for White (84.4%) compared to Black (78.7%) with a difference of 5.7%.
Based on this results we can conclude that in general the New York police is partially biased since is possible to see that for any level of force used the records are in favor of the White people.
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 70
grams of an alloy that contains 12% copper with 90 grams of pure copper.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?
Answers
a)There is 160 grams of copper are in the resulting mixture
b) There is 61.5% percentage of the resulting mixture is copper.
What are mathematics operations?
• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.
• The operation's arity is determined by the number of operands.
• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.
• A zero-arity operation, also known as a nullary operation, is a constant.
• The mixed product is an example of an arity 3 operation, also known as a ternary operation
From the question:
a) Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.
The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams
b) 70 grams of an alloy that contains 12% copper = 70 × 12%
= 70 grams × 0.12
= 8.4 grams
The number of grams of copper in the resulting mixture = 160 grams
The percentage of the resulting mixture that is copper is
=( 8.4 grams + 90 grams of pure copper/160) × 100
= 98.4/160 × 100
= 61.5%
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Hey can someone help me for q2 and onwards with step by step working out on paper so that I can understand them better. Thank u!!!
Answers
Answer:
f
Step-by-step explanation:
what is the answer of this problem ? help me to find
Answers
Given:
Total invested amount = $9000
One account = 5%
Another account = 6%
Find-:
Invested amount of each equation
Explanation-:
Let in 5% account invested amount is x
then amount in 6% account is (9000-x)
Then,
[tex]5\%\text{ of }x+6\%\text{ of }(9000-x)=510[/tex]Then the value of "x" is:
[tex]\begin{gathered} \frac{5}{100}\times x+\frac{6}{100}\times(9000-x)=510 \\ \\ 0.05x+0.06(9000-x)=510 \\ \\ 0.05x+(0.06\times9000)-0.06x=510 \end{gathered}[/tex]The "x" is:
[tex]\begin{gathered} 0.05x-0.06x+540=510 \\ \\ -0.01x=510-540 \\ \\ -0.01x=-30 \\ \\ x=\frac{-30}{-0.01} \\ \\ x=3000 \end{gathered}[/tex]The value of x is 3000 the mean amount in 5% invested amount is 3000.
6% invested amount is:
[tex]\begin{gathered} =9000-3000 \\ \\ =6000 \end{gathered}[/tex]So each account invested amount is:
[tex]\begin{gathered} 5\%\rightarrow3000 \\ \\ 6\%\rightarrow6000 \end{gathered}[/tex]Which relation is a function?
Answers
let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function. Check the picture below.
A very easy way to find out if a graph is a function is to use the vertical line test.
Look at each graph and mentally draw a vertical line that goes through each of its points.
If that line goes through more than one point (2, 3, 4...) then that graph is not a function.
That's because a function, is an equation for which each input (x value) has exactly one output (y value). There cannot be two points of the same x value, with two different y values.
The temperature in the morning was –2º F. The temperature in the evening was 9º F higher than it was in the morning. What was the temperature in the evening?
Answers
Answer:
Step-by-step explanation:
-2f
Find the perimeter and area of
the figure if each unit on the
graph measures 1 centimeter.
Round answers to the nearest
tenth, if necessary.
A(2, 1)
B(8, 6).
C(10, 1)
Answers
The figure's perimeter and area would be as follows.
Perimeter = 21.19 cm
Area = 25.501 cm²
What is coordinate system?A Cartesian coordinate system in some kind of a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular lines that are aligned to the point and are both measured in the same length.
According to the given data:point of the coordinates are as follows:
A(2, 1)
B(8, 6).
C(10, 1)
We know that the formula for finding for the distance is:
d=√((x2 – x1)² + (y2 – y1)²).
For Point AB:
X₁ = 2
Y₁ = 1
X₂ = 8
Y₂ = 6
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((8 – 2)² + (6 – 1)²).
d=√((6)² + (5)²).
d=√(36 + 25).
d=√(61).
AB =7.81
For Point BC:
X₁ = 8
Y₁ = 6
X₂ = 10
Y₂ = 1
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((10 – 8)² + (1 – 6)²).
d=√((2)² + (-5)²).
d=√(4 + 25).
d=√(29).
BC = 5.38
For Point CA:
X₁ = 10
Y₁ = 1
X₂ = 2
Y₂ = 1
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((2 – 10)² + (1 – 1)²).
d=√((-8)² + (0)²).
d=√(64 + 0).
CA = 8
The perimeter of the given figure is:
Sum of all the sides.
AB + BC + CA
7.81 + 5.38 + 8
21.19 cm
Now finding the area of the tringle we use Pythagoras formula:
H² = P² + B²
P² = H² - B²
P² = (7.81)² - (5.38)²
P = 9.4837
We know that the area of the triangle is: = 1/2(base * Hight).
= 1/2(5.38 * 9.48)
= 25.501 cm²
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What is the measure
Answers
Here, we want to get the measure of the angle marked A
We are going to use the sides given
The trigonometric ratio that links the adjacent to the hypotenuse is the cosine
The cosine is the ratio of the adjacent to the hypotenuse
Mathematically;
[tex]\begin{gathered} \cos \text{ m}\angle CAB\text{ = }\frac{12}{15} \\ \\ m\angle CAB\text{ = }\cos ^{-1}(\frac{12}{15}) \\ \\ m\angle CAB\text{ = 36.87} \end{gathered}[/tex]Fin tends to exaggerate. He says if he stacked all the quarters he's ever spent on gumball machines, they would reach to the moon. The distance to the moon is about [tex]3.85 \times {10}^{8} [/tex]m and the width of a quarter is about[tex]1.75 \times {10}^{ - 3} [/tex]m. If Fin's claim were true, how many quarters has he spent on gumball machines?
Answers
For this problem we were given the distance to the moon and the width of a quarter in meters. We need to determine how many quarters we would need to stack in order to reach the moon.
In order to solve this problem, we need to divide the distance from the surface of the Earth to the moon by the width of each quarter. Notice that both numbers are presented in scientific notations, therefore we need to divide the coefficients and subtract the exponents. This is done below:
[tex]\begin{gathered} n=\frac{3.85\cdot10^8}{1.75\cdot10^{-3}} \\ n=2.2\cdot10^{8-(-3)} \\ n=2.2\cdot10^{8+3} \\ b=2.2\cdot10^{11} \end{gathered}[/tex]If Fin's claim were true, he'd need to stack a total of 2.2*10^11 quarters.
Can someone help with 16,17 and 18 ! thank you !
Answers
In questions 16, 17 and 18 we have a right triangle and in the three cases you know the measues for 2 sides, except for hipotenuse.
We can use the following relation to solve the problem:
[tex]tg(x)=\frac{\text{Opposite side}}{Adjacent\text{ side}}[/tex]16)
[tex]\begin{gathered} tg(x)=\frac{\text{1}7}{7}=2.4285 \\ tg(x)=2.4285 \\ x=tg^{-1}(2.4285) \\ x=68\degree \end{gathered}[/tex]17)
[tex]\begin{gathered} tg(x)=\frac{8}{10}=0.8 \\ x=tg^{-1}(0.8) \\ x=39\degree \end{gathered}[/tex]18)
[tex]\begin{gathered} tg(x)=\frac{\text{1}1}{8}=1.375 \\ x=tg^{-1}(1.375) \\ x=54\degree \end{gathered}[/tex]18 is how many times more then 6
Answers
Answer: 3 times more
Step-by-step explanation:
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.3 years, and standard deviation of 1.1 years.If you randomly purchase one item, what is the probability it will last longer than 10 years?Use the normal table and round answer to four decimal places
Answers
We want to find the following probability:
[tex]P(X>10)[/tex]where X is a normal random variable with mean 13.3 and standard deviation 1.1. To find this probability let's normalize the random variable; to do this we use the z-score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, in this case, we have:
[tex]P(X>10)=P(z>\frac{10-13.3}{1.1})=P(z>-3)[/tex]Using the standard normal table, we have:
[tex]P(X\gt10)=P(z\gt(10-13.3)\/1.1)=P(z\gt-3)=0.9987[/tex]Therefore, the probability of purchasing an item with a lifespan greater than 10 years is 0.9987
PLEASE SOLVE THIS IM GIVING 40 POINTS
Answers
The coordinates of the point P lying between AB is found as (7, -2/5).
What is termed as the section formula?The Section formula is used to calculate the coordinates of a point that separates a line segment either internally or externally into a certain ratio. When a point separates a line segment in some ratio, we just use section formula to determine the coordinates of the that point.For the given question;
The two end coordinates are;
(x₁, y₁) = (8, 0)
(x₂, y₂) = (3, -2)
The ratio of the division is;
AP/PB = 1/4
OR
m:n = 1:4
The Formula for finding the coordinates of P for internally crossing is;
x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Put the values;
x = (mx₂ + nx₁)/(m + n)
x = (1×3 + 4×8)/(1 + 4)
x = (3 + 32)/5
x = 7
Now for y coordinates.
y = (my₂ + ny₁)/(m + n)
y = (1×(-2) + 4×0)/(1 + 4)
y = -2/5
Thus, the coordinates of the point P lying between AB is found as (7, -2/5).
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10) Given that a=4 b=2 and C=-1
find the value of:
1) a - b + c
11) 20
Answers
Answer:
1 is the answer
Step-by-step explanation:
a-b+c Substitute values into the equation
4-2+(-1)
2+(-1)
2-1
1 Answer
The value of: 1) a - b + c is, 1 is the solution.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
a=4 b=2 and C=-1
now,
a-b+c
Substitute values into the equation
we get,
4-2+(-1)
=2+(-1)
=2-1
=1 (Answer)
Hence, The value of: 1) a - b + c is, 1 is the solution.
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A used car dealership is interested in the age of a used car and the price of the vehicle. The manager collects a simple random sample of vehicles as shown in the table.
The equation of the least-squares regression line is
ŷ = 19.2 – 0.868x, where ŷ is the price of the vehicle (in thousands of dollars) and x is the age (in years). Which shows the residual plot?
ANSWER: A
Answers
Answer:
The Answer is A
Step-by-step explanation: Edge
Jordan looks at the line plot. He says the difference between the most capacity and the least capacity is 1/4 gallon. He says he knows the difference without subtracting. Explain Jordan’s mistake and find actual difference between measurements.
Answers
In a line plot the maximum value is the rightmost mark in the line plot; in this case the maximum capacity is 2 1/2. On the other hand the minimum value is the leftmost mark in the line plot, here the minimum is 1 1/2. Let's calculate the difference between them:
[tex]2\frac{1}{2}-1\frac{1}{2}=1[/tex]Therefore, the difference between the maxiimum and minimum capacity is 1.
PLEASE HELP!!!
Simplify the expression to a polynomial in
standard form:
(3x² + x − 5) (2x² + x + 3)
Answers
The standard form is 6x⁴+5x³-2x-15.
Here the term polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as subtraction, addition, division, and multiplication. the standard form of a polynomial is :
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ +aₙ₋₂xⁿ⁻² + ………………. + a₁x + a₀
Where aₙ, aₙ₋₁, aₙ₋₂, ……………………, a₁, a₀ are the coefficients of xⁿ, xⁿ⁻¹, xⁿ⁻², ….., x and are to a real number.
The polynomial given to us is (3x² + x − 5) (2x² + x + 3)
=3x²(2x² + x + 3) + x (2x² + x + 3) − 5 (2x² + x + 3)
= 6x⁴ + 3x³+9x²+2x³+x²+3x-10x²-5x-15
= 6x⁴+3x³+2x³+9x²+x²-10x²+3x-5x-15
= 6x⁴+5x³-2x-15
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Which relation IS a function?
Answers
Answer: B.
Step-by-step explanation: A function relates an input to an output.
The relation which is a function is: function 1.
Option A is correct.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
A relation is a function when each input have only one output.
Function 1 have one output to each corresponding output.
Function 2 have two output for input x= 2.
Function 3 have two output for input x= 3.
Function 4 have two output for input x= 1.
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Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)a. -33b. -36c. -63d. -69
Answers
Given:
[tex]a_n=3-6(n-1)[/tex]Find-: 12th term of the sequence is
Sol:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \end{gathered}[/tex]Where,
[tex]\begin{gathered} n=\text{ term.} \\ \\ n=12 \end{gathered}[/tex]Put the value then:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \\ n=12 \\ \\ a_{12}=3-6(12-1) \\ \\ a_{12}=3-6(11) \\ \\ a_{12}=3-(6\times11) \\ \\ a_{12}=3-66 \\ \\ a_{12}=-63 \end{gathered}[/tex]So 12th term is -63
Answer:
-63
Step-by-step explanation:
How many graduates in the sample came from University A?
Answers
The number of graduates in the sample that came from University A is:
35 + 90 + 35 = 160 graduates
P(t) models the number of people on a beach, t hours past midnight on a certain day.What does P(10) = N mean?Group of answer choicesThere were an equal number of people on the beach at 10:00 AM and at N hours past midnight.There were N people on the beach at 10:00 AM.There were 10 people on the beach at N hours past midnight.
Answers
Since P(t) models the number of people on a beach, t hours past midnight, hence P(10)=N means that there were N people on the beach at 10 am
What is the value of the Missing angle
Answers
Answer: 120
Step-by-step explanation:
All angles in a triangle add up to 180. The third angle in the triangle is 60. A straight line is always 180, and line TU intersects it. So, subtract 60 from 180 and you get 120.
Answer:
120 degrees
Step-by-step explanation:
70 + 50 = 120 (exterior angle of a triangle)
The sum of the interior angles of a polygon with 10 sides can be expressed as 360n. What is the value of n? O 2 04 O 6 08
Answers
The sum of the interior angle of a polygon with 10 sides is equal to 1440°
If it can be expressed as 360n, then n is
[tex]\begin{gathered} 360n=1440 \\ \\ \text{Divide both sides by 360} \\ \frac{360n}{360}=\frac{1440}{360} \\ \frac{\cancel{360}n}{\cancel{360}}=\frac{1440}{360} \\ n=4 \\ \\ \text{Therefore, }n\text{ is equal to }4 \end{gathered}[/tex]with a vertex of (-7,-2) and directrix of x=-1, is this a vertical or horizontal parabola?
answer step by step please
Answers
Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola
What is directrix of a parabola?The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.
The directrix does not touch the parabola
How to determine if a parabola is vertical or horizontal using the directrixA parabolic equation is also called quadratic equation.
Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:
when the directrix is given at x, the directrix runs in the vertical direction and the parabola is a horizontal parabolawhen the directrix is given at y, the directrix runs in the horizontal direction and the parabola is a vertical parabolaThe axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:
the y direction the parabola is a vertical parabolathe x direction the parabola is a horizontal parabolaIn the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola
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