Certainly! I can help you with trigonometry. To find the lengths of a triangle and the angles, we typically use the trigonometric ratios: sine, cosine, and tangent. These ratios relate the angles of a right triangle to the lengths of its sides.
To find the lengths of a triangle:
1. If you have one angle and the length of one side, you can use the sine, cosine, or tangent ratio to find the lengths of other sides.2. If you have two sides and the included angle, you can use the Law of Cosines to find the length of the third side.3. If you have two angles and the length of one side, you can use the Law of Sines to find the lengths of the other sides.To find the angles of a triangle:
1. If you have the lengths of two sides, you can use the Law of Cosines to find the measure of the included angle.2. If you have the lengths of two sides and the included angle, you can use the Law of Cosines to find the measure of the third side.3. If you have the lengths of two sides and the measure of the included angle, you can use the Law of Sines to find the measures of the other angles.Remember to use the appropriate trigonometric ratio or trigonometric formula depending on the given information. Also, keep in mind the restrictions and conventions for angles and sides in triangles, such as the Pythagorean theorem and the sum of angles in a triangle.
I hope this helps! Good luck with your exam. If you have any specific questions or examples, feel free to ask.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
-4x^2 + 2x - 5(1+x) which expression is equivalent to the given expression
The given expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5, not -5 - 5x.
To simplify the expression -4x^2 + 2x - 5(1+x), we can distribute the -5 to the terms inside the parentheses:
-4x^2 + 2x - 5(1+x) = -4x^2 + 2x - 5 - 5x
Next, we can combine like terms:
-4x^2 + 2x - 5 - 5x = -4x^2 + (2x - 5x) - 5
Simplifying further, we have:
-4x^2 + (2x - 5x) - 5 = -4x^2 - 3x - 5
Therefore, the expression -4x^2 + 2x - 5(1+x) is equivalent to -4x^2 - 3x - 5.
It's important to note that when we distribute the -5 to the terms inside the parentheses, we multiply each term by -5. So, the expression becomes -5(1) - 5(x). However, -5(1) simplifies to -5, and -5(x) simplifies to -5x. Hence, the expression simplifies to -5 - 5x.
For more such question on equivalent visit:
https://brainly.com/question/2972832
#SPJ8
Compare the functions shown below:
g(x)
f(x) = 7x + 3 tangent function with y intercept at 0, 2 h(x) = 2 sin(3x + π) − 1
Using complete sentences, explain which function has the greatest y-intercept.
Answer: The fuction with the greatest intercept is 0,2
Step-by-step explanation:
Find the area if the following circle circumference = 280cm find r from c
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=280 \end{cases}\implies 280=2\pi r\implies \cfrac{280}{2\pi }=r\implies \cfrac{140}{\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{140}{\pi } \end{cases}\implies A=\pi \left( \cfrac{140}{\pi } \right)^2 \\\\\\ A=\pi \cdot \cfrac{140^2}{\pi^2}\implies A=\cfrac{19600}{\pi }\implies A\approx 6238.87~cm^2[/tex]
Kate is firing off her homemade rockets for a project in physics class. The
maximum height of any of her rockets can be represented by the equation
h = 40t-16t², where h is the height (in feet) of the rocket after t seconds.
Find the domain and range
The domain of the height function is [0, 2.5]
The range of the height function is [0, 25]
How to find the domain and range?We know that the height is given by the quadratic function:
h(t) = 40t - 16t²
First, the domain. This is the set of possible values of t.
We know that we start at t = 0.
The final value of the domain is t such that the rocket returns to the ground, that is when h = 0.
We can rewrite the function as:
h(t) = 40t - 16t² = t*(40 - 16t)
It is zero when t = 0 (we already know) and when 40 - 16t = 0
Solving the second one we get:
40 - 16t = 0
40 = 16t
40/16 = t
2.5 = t
Then the domain is [0, 2.5]
For the range we need to find the maximum height, we know that the minimum height is h = 0.
The maximum one is when t = (2.5 + 0)/2 = 1.25
Evaluating there we get:
h = 40*1.25 - 16*(1.25)²
h = 25
Then the range is [0, 25]
Learn more about quadratic functions:
https://brainly.com/question/1214333
#SPJ1
Decimal operations
22.12 x 0.6 =
The product of 22.12 and 0.6 is indeed 13.272.
To compute the product of 22.12 and 0.6, we can perform the multiplication using the standard algorithm for decimal multiplication.
Multiply the decimal part (the digits after the decimal point) first.
0.12 x 0.6 = 0.072 (Multiply 12 by 6, which gives 72, and then move the decimal point two places to the left.)
Multiply the whole numbers.
22 x 0.6 = 13.2 (Multiply 22 by 6, which gives 132, and then move the decimal point one place to the left.)
Add the results from Step 1 and Step 2.
0.072 + 13.2 = 13.272
Therefore, when multiplying 22.12 by 0.6, the result is 13.272.
To verify the calculation, we can check by using estimation. 22.12 is approximately 22 and 0.6 is approximately 0.6. Multiplying 22 by 0.6 gives 13.2, which is close to our calculated result of 13.272. This further confirms that our multiplication is correct.
Hence, the product of 22.12 and 0.6 is indeed 13.272.
for such more question on product
https://brainly.com/question/847241
#SPJ8
in a party everyone present received 2 gifts from each of the other people present. If 480 gifts were exchanged,how many people attended the party
Answer:240
Step-by-step explanation:
divide 480 by the amount of gift everybody gets . 2
Answer:
I think the answer would be 240 people that received a gift.
Step-by-step explanation:
If there were 240 people at the party that received gift then we would check by dividing 480 and 2.
Why?
Simply because if there was 480 gifts and 2 were given to each person then it would only make sense that , that’s as the amount.
(2 persons would have 4 gifts, and if there was 240 people then there would be 480 gift brought to the party)
in ABC,A=38° 18', a = 300m, b=150m. solve the triangle Completely
Using sine law and cosine law, the value of the missing sides are
B = 17.94°, C = 124.03° and c = 403.57m
What is the value of the missing sides?To solve the missing side, we have to use the sine angle formula.
The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
The formula is given as;
a / sin A = b / sin B
A = 38° 18' = 38.03°
Substituting the values into the formula
300 / sin 38.03 = 150 / sin B
sin B = 150 * sin 38.03 / 300
sin B = 0.3080
B = sin⁻¹(0.3080)
B = 17.94°
From the sum of angles in a triangle;
A + B + C = 180°
38.03 + 17.94 + C = 180
C = 124.03°
Using cosine rule;
c² = a² + b² - 2(a)(b)cos C
c² = 300² + 150² - 2(300)(150)cos 124.03°
c² = 162866.422
c = √162866.422
c = 403.57m
Learn more on sine rule here;
https://brainly.com/question/4372174
#SPJ1
A state offers specialty license plates that contain 3 letters followed by 2 numbers. License plates are assigned randomly. All license plates are equally likely. Find the number of possible license plates that can be issued using this system.
There are 17,576,000 possible license plates that can be issued using this system.
To calculate the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.
For the first character, there are 26 letters in the English alphabet. Therefore, we have 26 options for the first character.
Similarly, for the second and third characters, we also have 26 options each.
For the fourth character, there are 10 possible numbers (0-9).
And for the fifth character, we again have 10 possible numbers.
To find the total number of possible license plates, we multiply the number of options for each character together:
Number of possible license plates = Number of options for the first character × Number of options for the second character × Number of options for the third character × Number of options for the fourth character × Number of options for the fifth character
Number of possible license plates = 26 × 26 × 26 × 10 × 10
Calculating this expression gives us:
Number of possible license plates = 17,576,000
Therefore, there are 17,576,000 possible license plates that can be issued using this system.
for such more question on total number
https://brainly.com/question/25109150
#SPJ8
Please help
Factor
f(x) = 2×2 - 9x- 18
(2x + [?])(x - [ ])
Step-by-step explanation:
The quadratic expression f(x) = 2x^2 - 9x - 18 can be factored as (2x + 3)(x - 6). So, the missing values in the given expression (2x + [?])(x - [ ]) are 3 and 6, respectively.
Answer:
(2x + 3)(x -6)
Step-by-step explanation:
2x² -9x -18
2 × -18 = -36
Find factors of -36 which you multiply will give -36 but when same factors are added will give -9.
-12 × 3 = -36
-12 + 3 = -9
2x²-12x +3x -18
2x(x - 6) + 3(x -6)
(2x + 3)(x -6)
Find the area, i have a lot of problems finding the area in general. and i spent a lot of time trying to figure this out?
The total area of the composite figure is 51.5 square yards
Calculating the area of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The total area of the composite figure is the sum of the individual shapes
So, we have
Surface area = 9 * 2 + 2 * 3 + 1/2 * (3 + 8) * 5
Evaluate
Surface area = 51.5
Hence. the total area of the figure is 51.5 square yards
Read more about area at
brainly.com/question/26403859
#SPJ1
You pick two digits 0 through 9 at random without replacement and write them in the order picked what is the probability that you have written the first two digits of your phone number assume there are no repeats of digits in your phone number give your answer as a fraction
Alright, so let's assume your phone number has no repeated digits. The first task is to select the first digit of the two-digit number. Since phone numbers don't start with zero, you have 9 choices (1 through 9).
The next task is to select the second digit. Because we've already used one digit, and we're assuming there are no repeats in the phone number, we have 9 choices left (0 and the 8 digits that were not selected first).
That gives us a total of 9 * 9 = 81 possible two-digit numbers.
Now, your phone number has a specific first two digits, right? There's only one such combination that matches your phone number.
So the probability that the two-digit number you've selected matches the first two digits of your phone number is 1 in 81, or 1/81.
Think of it this way, my friend: Imagine you have a bag with 81 marbles, each marble has a unique two-digit number on it. You close your eyes and reach into the bag to pick a marble. The chance that you'll pick out the marble with your phone number's first two digits is just like finding one special marble in a bag of 81. It's quite the quest, isn't it? But that's what makes the game of probability so interesting!
Find the x- and y-intercepts of the graph.
Answer:
see explanation
Step-by-step explanation:
the x- intercepts are the values of x where the graph crosses the x- axis
these occur at x = - 2 and x = 2
then x- intercepts are x = - 2 , x = 2
the y- intercept is the value of y where the graph crosses the y- axis
this occurs at y = 4
then y- intercept is 4
x intercept of a graph is the point(s) of the graph that intersects x-axis , y intercept of a graph is the point(s) of the graph that intersects y-axis .
x and y intersepts vary from graph to graph , a graph may have various x and y intersepts , a graph may have one x and y intersepts , or may don't have none of them , or may have only one of the intersepts
_______________________
In this graph
there are two x intersepts and one y intersept
x intersepts :
( 2 , 0 )
( -2 , 0 )
y intersept :
( 0 , 4 )
The probability distribution below represents the probability of x number of males in a group who have a form of
color blindness.
X. P(x)
0 0.641
1 0.287
2 0.048
3 0.014
4 0.007
6 0.003
a.) Find the probability of exactly 1 male has a form of color blindness.
b.) Find the probability that 1 gr less males have a form of color blindness.
c.) Find the probability that more than 3 males have a form of color blindness.
Answer:
a
Step-by-step explanation:
i did it
Which statement about the points (0, 3), (2, 8), (8, 2), and (0, 1) is true?
All but one of the points is on the x-axis.
The points (0, 3) and (0, 1) are located on the same axis.
All but one of the points are in Quadrant I.
The point (8, 2) is the closest to the x-a
The statement about the points (0, 3), (2, 8), (8, 2), and (0, 1) that is true is All but one of the points are in Quadrant I. Option C
How to determine the statementThe first quadrant, positioned at the upper-right area of the Cartesian plane, involves coordinates that have favorable values for both x and y.
The coordinates (0,3), (2,8), and (0,1) all fall under quadrant I since their x and y values are positive.
The point located in Quadrant IV can be identified as (8, 2) due to its positive x-coordinate and negative y-coordinate.
Hence, it can be said with precision that Quadrant I contains all but one point.
Learn more about quadrants at: https://brainly.com/question/863849
#SPJ1
3
X-4
What is the center of f(x)?
Let f(x)
=
+2.
None of the answer choices (2,4), (2,-4), (4,2), or (4,-2) are applicable to the function f(x) = 3/(x-4) + 2. The function does not have a center point in the traditional geometric sense. Option E.
he function f(x) = 3/(x-4) + 2 does not have a center in the traditional sense. The concept of a center is typically associated with geometric figures such as circles or ellipses.
The function f(x) = 3/(x-4) + 2 represents a rational function. It does not have a central point or location like a circle, which has a center at (h, k). In this case, we are dealing with a rational expression involving x.
The equation f(x) = 3/(x-4) + 2 describes a vertical shift of the graph of the function 3/(x-4) by 2 units upward. However, this vertical shift does not correspond to a center point.
The function f(x) = 3/(x-4) + 2 does not have a center point. The concept of a center is not applicable in this context as it is commonly associated with geometric figures rather than rational functions. Option E is correct.
For more such question on function. visit :
https://brainly.com/question/11624077
#SPJ8
cinetica?
Un automóvil de 800 kg se desplaza a 50km/h cuál será su energía cinética.
The kinetic energy of this car is equal to 77160.49 Joules.
How to calculate the kinetic energy of this car?In Mathematics, the kinetic energy of a physical object can be calculated by using the following equation (formula):
K.E = 1/2 × mv²
Where:
K.E represent the kinetic energy.m represent the mass.v represent the speed or velocity.Note: 50 km/h to m/s = 50 × 1000/3600 = 13.89 m/s
By substituting the given parameters into the formula for the kinetic energy of a physical object, we have the following:
Kinetic energy, K.E = 1/2 × 800 × 13.89²
Kinetic energy, K.E = 400 × 192.90
Kinetic energy, K.E = 77160.49 Joules.
Read more on kinetic energy here: https://brainly.com/question/25959744
#SPJ1
Complete Question:
An 800 kg car travels at 50 km/h, what will its kinetic energy be?
for a data set of 98,67,100,88,90, the range is
Answer:33
Step-by-step explanation:Range=maximum minus minimum in data set
100 - 67 = 33
Answer:
33
Step-by-step explanation:
67, 88, 90, 98, 100 is the set in order from least to greatest.
Range is the largest number (100) minus the smallest number (67).
100 - 67= 33.
Thus, your answer is 33.
3. What is the slope of a line that is parallel to the line shown?
(0, 3) (3,2)
1/3
-1/3
-3
3/2
Answer:
slope m = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, 2) ← 2 points on the line
m = [tex]\frac{2-3}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]
• Parallel lines have equal slopes
then parallel line will have a slope of - [tex]\frac{1}{3}[/tex]
Rent for a 3 bedroom apartment is regularly $936 per month. Apartment management is offering one month free. If you sign a one year lease and apply the free month equally across months, how much is your new, monthly lease amount
Answer:
$858
Step-by-step explanation:
You are paying 11 months of rent for 1 year.
11 × $936 = $10,296
The total rent paid in 1 year for 11 months of rent is $10,296.
Divide the total by 12:
$10,296/12 = $858
The monthly amount averages to $858.
PLEASE HELPPPPPPPPPP
Answer:
Step-by-step explanation:
The degree is 4 the leading coefficient is even/positive. There are 3 distinct real 0's and 3 relative extreme values
Explanation:
4th degree. Degree is the highest exponent. The number of 0's (times it hits the curve)tells you the degree. The curve goes through the x 2 times, which means 2 x's. Then it bounces off x 1 time which means there are 2 x's there too but because this one bounces off it means it's not a distint solution it's a multiplicity ex (x-3)². So that accounts for 4 solutions
Even/positive coefficient. That's the first number in the equation. Because it's facing up it's a positive but all the ends are both facing up so that tells you it's even. Think of a parabola that is an even function, this follows those rules too.
3 distinct zeroes. This is explained in 4th degree. Zeroes are solutions, when it hits x axis. Goes through x 2 times and bounces once. So there are 3 distinct zeroes
3 relative extreme values. This is how many "mini" max and mins you have.
Identify the solution for this system of equations
{4x + y = 7
{2y + 3= 3x - 16
A. (1,3)
B. (3,-5)
C. (7,-1)
D. No solution
The solution for the system of equations is (x, y) = B. (3, -5).
The correct option is B. (3, -5).
To find the solution for the system of equations:
{4x + y = 7
{2y + 3 = 3x - 16
We can solve it using the method of substitution or elimination. Let's use the method of elimination:
First, let's multiply the second equation by 2 to eliminate the variable y:
2(2y + 3) = 2(3x - 16)
4y + 6 = 6x - 32
Rearranging this equation, we get:
6x - 4y = 38 ----(1)
Now we have the system of equations:
4x + y = 7 ----(2)
6x - 4y = 38 ----(1)
Next, let's multiply equation (2) by 4 to eliminate the variable y:
4(4x + y) = 4(7)
16x + 4y = 28
Now we have the system of equations:
16x + 4y = 28 ----(3)
6x - 4y = 38 ----(1)
Adding equations (3) and (1) eliminates the variable y:
(16x + 4y) + (6x - 4y) = 28 + 38
22x = 66
x = 66/22
x = 3
Substituting the value of x into equation (2), we can solve for y:
4(3) + y = 7
12 + y = 7
y = 7 - 12
y = -5
for such more question on system of equations
https://brainly.com/question/12526075
#SPJ8
If your grocery bills over the last four weeks were &203,&195,$180 and &238, what was the average bill?
Answer: $204
Step-by-step explanation:
203 plus 195 plus 180 plus 238 equals 816
816 divided by 4 equals 204
203+195=398
398+180=578
578+238=816
816/4=204
What is the area of a right triangle with a height of six and one fourth yards and a base of 22 yards?
34 yds2
sixty eight and three fourths yds2
132 yds2
one hundred thirty seven and one half yds2
Answer:
68.75 square yards (rounded to the nearest hundredth).
Step-by-step explanation:
To find the area of a right triangle, we can use the formula:
Area = (1/2) * base * height
Given the height of 6 and one fourth yards (6 1/4) and a base of 22 yards, we can calculate the area as follows:
Area = (1/2) * 22 * (6 1/4)
To simplify the calculation, we can convert the mixed fraction 6 1/4 to an improper fraction:
6 1/4 = (4 * 6 + 1) / 4 = 25 / 4
Now we can substitute the values into the area formula:
Area = (1/2) * 22 * (25/4)
Next, we can simplify the expression by multiplying the numbers:
Area = (11/1) * (25/4)
Multiplying the numerators and denominators:
Area = (11 * 25) / (1 * 4)
= 275 / 4
To convert the fraction to a mixed number, we can divide the numerator by the denominator:
275 ÷ 4 = 68 remainder 3
Therefore, the area of the right triangle is:
Area = 68 3/4 square yards or 68.75 square yards (rounded to the nearest hundredth).
Among the options provided, the closest match is "sixty-eight and three fourths yds2".
Answer:
68.75 square yards
Step-by-step explanation:
Megan says "when you square root a number, the answer is always smaller."
Show she is wrong.
Megan is wrong because the square root of a number can be either smaller or larger, depending on whether the number is less than or greater than 1.
Megan's statement that "when you square root a number, the answer is always smaller" is incorrect.
In fact, the square root of a number can be either smaller or larger than the original number, depending on the value of the number.
To demonstrate that Megan is wrong, let's consider a few examples:
Square root of 4:
The square root of 4 is 2.
In this case, the square root is smaller than the original number.
Square root of 1:
The square root of 1 is also 1.
Here, the square root is equal to the original number.
Square root of 9:
The square root of 9 is 3.
In this case, the square root is larger than the original number.
Square root of 16:
The square root of 16 is 4.
Again, the square root is larger than the original number.
From these examples, we can see that the square root of a number can be smaller, equal to, or larger than the original number.
It depends on the specific value of the number.
Megan's statement oversimplifies the relationship between a number and its square root.
In general, the square root of a number is a value that, when multiplied by itself, gives the original number.
It is not always smaller but rather a value that satisfies the mathematical relationship.
For similar question on square root.
https://brainly.com/question/3617398
#SPJ8
similarly in right triangles
The value of y for the right triangle is equal to 48, which makes the first option correct.
How to evaluate for the values of y for the triangleThe perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.
60/x = 36/60 {opposite/hypotenuse}
x = (60 × 60)/36 {cross multiplication}
x = 100
by Pythagoras rule the unlabeled side of the entire triangle is calculated as:
√(100² - 60²) = 80
so;
y/80 = 60/100 {opposite/hypotenuse}
y = (60 × 80)/100 {cross multiplication}
y = 48
Therefore, the value of y for the right triangle derived to be 48.
Read more about right triangle here:https://brainly.com/question/2920412
#SPJ1
I need some help on my exam reveiw for my math class, can someone please help me so i get a good grade and know how to do my exam?
A preimage includes a line segment with a length of x units and a slope of munits. The preimage is dilated by a scale factor of n.
The length of the corresponding line segment in the image is nx units. The slope of the corresponding line segment in the image is m.
What is slope?The slope or gradient of a line is described as a number that describes both the direction and the steepness of the line.
The is very important and tells you how steep a line is, or how much y increases as x increases.
In conclusion, the slope is constant (the same) anywhere on the line.
Learn more about slope at:
https://brainly.com/question/3493733
#SPJ1
answer all three ASAP!!!!!!!!
The answers to the questions to one significant figure are
a. 4000
b. 2000
c. 10,000
How to find the answersThe problem can be solved using calculator
a
= 24 * 65 / 0.37
= 1608 / 0.37
= 4345.946
= 4000 to one significant figure
b. 71 * 8.2 / 0.22
= 2646.364
= 2000 to one significant figure
c. 49.3 * 11.1 / 0.053
= 10325.094
= 10000 to one significant figure
Learn more about significant figure at
https://brainly.com/question/24491627
#SPJ4
The estimation of the following numbers rounded to one significant figure are:
a. 4,000
b. 3,000
c. 10,000
How to estimate to one significant figures?[tex] \frac{24 \times 65}{0.37} [/tex]
[tex] = \frac{1560}{0.37} [/tex]
= 4216.216216216216
= 4000 to one significant figure.
[tex] \frac{71 \times8.2 }{0.22} [/tex]
[tex] = \frac{582.2}{0.22} [/tex]
[tex] = 2646.363636363636[/tex]
= 3,000 to one significant figure
[tex] \frac{49.3 \times 11.1}{0.053} [/tex]
[tex] = \frac{547.23}{0.053} [/tex]
[tex] = 10325.09433962264[/tex]
= 10,000 to one significant figure
Significant figures are digits 1 to 9
Read more on significant figures:
https://brainly.com/question/24491627
#SPJ1
total surface area of a cuboid is 112^2 find x
1, 3, 9, 27, 81, 243, ?
Find pattern
Answer:
You're multiplying each of those numbers by 3.
Step-by-step explanation:
1 * 3 = 3
3 * 3 = 9
9 * 3 = 27
27 * 3 = 81
81 * 3 = 243
Each number is multiplied by 3.
1 x3=3 -> 3x3=9 -> 9x3=27 -> 27x3=81 and so on.
Happy to help; have a great day! :)
PART A
A manufacturer is designing a flashlight. For the flashlight to emit a focused beam, the bulb needs to be on the central axis of the parabolic reflector, 3 centimeters from the vertex. Write an equation that models the parabola formed when a cross section is taken through the reflector’s central axis. Assume that the vertex of the parabola is at the origin in the xy coordinate plane and the parabola can open in any direction.
answer: y= 1/12(x-0)^2+0
Find the equation of the directrix of the parabola found in part A.
The equation of the directrix of the parabola found in part A is [tex]x^2 = -2cy + c^2.[/tex]
The equation of the parabola formed when a cross section is taken through the reflector's central axis is
[tex]y = (1/12)(x - 0)^2 + 0.[/tex]
In this equation, the vertex is at the origin (0, 0) and the coefficient 1/12 determines the shape of the parabola.
The equation implies that the parabola opens upward because the coefficient of [tex]x^2[/tex] is positive.
To find the equation of the directrix, we can use the distance formula. The directrix is a horizontal line that is equidistant from the vertex as any point on the parabola.
Since the parabola is symmetric with respect to the y-axis, the directrix will also be symmetric with respect to the y-axis.
Let's assume that the directrix is a horizontal line with the equation y = c, where c is a constant.
To find the value of c, we need to consider a point (x, y) on the parabola. The distance from the point (x, y) to the directrix y = c should be equal to the distance from the point (x, y) to the vertex (0, 0).
Using the distance formula, the distance from (x, y) to the directrix y = c is given by |y - c|, and the distance from (x, y) to the vertex (0, 0) is given by [tex]\sqrt{(x^2 + y^2)}[/tex]
Setting these distances equal, we have:
[tex]|y - c| = \sqrt{(x^2 + y^2)}[/tex]
Squaring both sides of the equation, we get:
[tex](y - c)^2 = x^2 + y^2[/tex]
Expanding and simplifying the equation, we have:
[tex]y^2 - 2cy + c^2 = x^2 + y^2[/tex]
Simplifying further, we obtain:
[tex]-2cy + c^2 = x^2[/tex]
Rearranging the terms, we get:
[tex]x^2 = -2cy + c^2[/tex]
This equation represents the equation of the directrix of the parabola formed by the reflector.
For more questions on parabola
https://brainly.com/question/29635857
#SPJ8
