PLEASE HELP
The filament of a car headlight is a thin wire that glows when electricity passes through it. Parabolic reflectors with a filament at the focus send light out in a straight beam. The cross section of a 2 inch deep headlight reflector has the equation y2=6x.
A. Draw a sketch of this situation. Include the location of the focus in your drawing.
B. How wide is the beam of light projected from the headlight's reflector? Show all work and give your answer as a decimal rounded to hundredths place.
Answers
Answer:
A. Please find attached the drawing of the reflector showing the location of the focus created with Microsoft Excel
B. The width of the beam of light projected from the headlight's reflector is approximately 6.93 inches
Step-by-step explanation:
The given equation representing the cross section of the headlight reflector is y² = 6·x
The shape of the reflector = Parabolic
The general equation of a parabola is (y - k)² = 4·p·(x - h)
The focus of the parabola, Focus = (h + p, k)
By comparison to the general equation of a parabola, from the equation of the reflector, we have;
k = 0, h = 0, 4·p = 6
∴ p = 6/4 = 3/2 = 1.5
∴ The focus of the parabola = (1.5, 0)
A. Please find attached the graph of the equation of the cross-section of the reflector, showing the filament at the focus, created with Microsoft Excel
B. The depth of the reflector is x = 2 inches
A vertical or horizontal parabola has two x-values for a given y-value or two y-values for a given x-value respectively
For the given horizontal parabola, the width of a parabola at a point is the difference between the two y-values at the point
At x = 2, we have;
y² = 6 × x = 6 × 2 = 12
∴ y = ±√(12)
The two y-values at x = 2 are y₁ = √(12) and y₂ = -√(12)
The width of the parabola, w = y₁ - y₂
The width of the parabola at x = 2, w = √(12) - (-√(12))
∴ w = √(12) +√(12) = 4·√3
The width of the parabola at x = 2, w = 4·√3 inches
The width of the parabola at x = 2 = The width of the beam of light projected from the headlight's reflector = 4·√3 inches
By giving the answer as a decimal and rounded to the hundredths place, we have;
The width of the beam of light projected from the headlight's reflector ≈ 6.93 inches.
Related Questions
6. The height distributions of two different classes at Dover Elementary School are shown below. Both groups have the same interquartile range (IQR). Dover Elementary School Class Heights Third grade Fourth grade + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 54 '55 which class has the greater median height?
Answers
Answer:
G.fourth grade
Step-by-step explanation:
The media is the line inside the box that’s the middle
In third grade the median is 50 but in fourth grade the median is 52 so therefore your answer is fourth grade
And the reason I know this is because I’m in 7th and have the exact same question
Whoever helps me will be lucky for the rest of your life
Answers
Answer:
A) 3.5
16 shovels full
Step-by-step explanation:
9x + 13 = 17x - 15
8x = 28
x = 3.5
20 + 5x = 32 + 4.25x
0.75x = 12
x = 16
Mikel gave a $1.32 tip for an order that cost $8.80.
Determine whether or not each tip below is proportional to Mikel's tip.
Proportional to Mikel's tip
Not proportional to Mikel's tip
$2.22 tip for a $14.80 order
$1.86 tip for a $10.50 order
ООО
$0.78 tip for a $5.20 order
Answers
Answer:
Step-by-step explanation:
Multiple the numbers one by one and the answers you’ll get u can choose to divide multiple plus or minus and u will get the answer
FIRST ONE TO AWNSER AND IF CORRECT GETS BRAINLYIST AND 50 POINTS!!!!!
Malik asked his teacher if there was a way to check his answer after writing equivalent expressions. What should be his teacher’s response?
A. Choose a number to substitute for the variable. Find the value of each expression. If the values are even, the expressions are equivalent.
B. Substitute a number for the variable. If the simplified expressions have the same value, the expressions are equivalent.
C. Multiply each expression by the same number. If the expressions are equal, the expressions are equivalent.
D. Add a number to each expression. If the simplified expressions are equal, the expressions are equivalent.
Answers
Answer:
the answer would be A ? ig
HEY THERE! PLS HELP ME WITH THIS MATH QUESTION- AN EXPLANATION WOULD BE GREAT! THE CORRECT ANSWER SHALL BE MARKED AS BRAINLIEST AND ACHIEVE POINTS! THANKS :)
xoxo
Answers
Answer:
105
Step-by-step explanation:
To find area, you have to multiple the width by the height.
15*7=105.
Answer:
Area = 2307.9 cu.cm
Step-by-step explanation:
Height of the cylinder (h) = 15cm
radius (r) = 7 cm
we know ,
[tex]area \: of \: cyliner = \pi {r}^{2} \times h \\ \: \: \: \: = 3.14 \times {(7cm)}^{2} \times 15cm \\ \: \: = (3.14 \times 49 \times 15) {cm}^{3} \\ = 2307.9 {cm}^{3} [/tex]
Susana has four identical square gems. She wants to arrange them to form a larger quadrilateral with four right angles and two pairs of parallel sides. Susana’s assistant says that the quadrilateral must be a square, as shown. Do you agree? If so, explain your reasoning. If not, draw a quadrilateral to support your answer.
Answers
Answer: i agree u are right it makes sence
Step-by-step explanation:
Answer: I do not agree
Step-by-step explanation: The picture below meets all the requirements, four right angles, and two parallel lines
Help this is due in 2 minutes
Answers
Answer:
The value of the machinery after 5 years is $236.20
Step-by-step explanation:
Generally, we have the depreciation exponential expression as;
V(t) = I (1 - r)^t
V(t) is the value of the machinery at a point in time
I is the initial value or the cost of the machinery when bought which is $400
r is the rate of decrease which is 10% and is same as 10/100 = 0.1
t is the time which is 5 years
Substituting these values;
V(5) = 400( 1 - 0.1)^5
V(5) = 236.196
to the nearest vent, this is $236.20
Tell whether this equation has no solution, one solution, or infinitely
many solutions.
2x+5=5x-1
O no solution
Oone solution
O infinitely many solutions
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
please please answer and dont put any links :)
Answers
15x+7=98
15x=105
x=7
hope this helps :)
which of the following points are in the solution set to the inequality below? Select all that apply.
y<-4x+6
a: (4,3)
b: (-4,1)
c: (5,-2)
d: (-3,5)
e: (1,6)
f: (3,-6)
Answers
Step-by-step explanation:
a) 3<-4*3+6
3<-12+6
3<-6
which is false
b)1<-4*(-4)+6
1<16+6
1<22
which is true
c) -2<-4*5+6
-2<-20+6
-2<-14
which is false
d) 6<-4*1+6
6<10
which is true
f)-6<-4*3+6
-6<-12+6
-6<-6
which is false
I hope this helps.
which is the correct input-output table for the function g(x)=-1/2(4x+6)
Answers
Answer: The third choice.
Step-by-step explanation: To find the first output, start with your first input. In this case, it's -2, so your equation would be g(-2)= -1/2(4(-2)+6). Start by solving inside the parenthesis. 4x-2=-8 and -8+6=-2. -1/2x-2= 1, so your first output should be 1. The only choice that has this is the third one, so that is your answer. Hope I could help :)
what is the probability of a chance event is 0.05, it to happen when compared to a chance event with a probability of 0
Answers
Answer:
I can't understand
Step-by-step explanation:
I will just try to rewrite your question so someone lese can answer it.
"What is the probability of a chance event, with a probability of 0.05, to happen when compared to a chance event with a probability of 0."
or just what is the probability(how high or low are the chances) of an event with a very low chance of happening when compared to an event that can never happen.
need help
problem/question in image below
Answers
Answer:
Option A would be the correct answer
I don't have an explanation to type but you can trust me :)
Please mark as brainliest for further answers :)Which point on the number line best represents the location of 78?
F Point M
G Point N
H Point P
J Point O
Answers
because if you simplify 78 it’ll give you about 8.831...
help plzzzzz! it's math and I'll give 30 points
Answers
Answer:
[tex]\sqrt{45}[/tex]
Step-by-step explanation:
Hi there,
In order to solve this problem, you have to know the Pythagorean Theorem:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
We can see from the graph that line segment ML and LN are 6 and 3 units respectively. Since we know the lengths of two sides of the triangle, we can use the theorem above to find the hypotenuse (MN).
⇒ [tex]6^{2}[/tex] + [tex]3^{2}[/tex] = [tex]c^{2}[/tex]
⇒ 45 = [tex]c^{2}[/tex]
⇒ c = [tex]\sqrt{45}[/tex]
Hope this explanation helps. Cheers.
Find the area of the given shape
Answers
Answer:
Step-by-step explanation:
15 * 9=135
135 + 37.5 = 172.5
Situation:
Find the age of the spear head to the nearest
year.
An archaelogist in Turkey discovers a
spear head that contains 32% of its
original amount of C-14.
Enter the correct answer.
DONE
N = Noekt
No - inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answers
John Burroughs $6.50 from his friends to pay for snacks and $11. 75 from sister to go to the movies. How much money does he need to repay
Answers
Answer:
18.25
Step-by-step explanation:
......ur welcome.............
(9x + 4) - (-5x2 - 5x + 7)
Answers
Answer:
44 I think
Step-by-step explanation:
i don't know I'm not too sure
Can someone help me figure this out I'm completely lost and this is due in like an hour, the question is "Use the diagram to find the length of GH."
Answers
Answer:
GH = 4
Step-by-step explanation:
GH = AB due to congruency markings therefore
5y - 8 = 3y
-8 = =2y
4 = y
Answer:
GH=12
Step-by-step explanation:
You use what this other solution to the answer was. However, they did not include that GH is 3y, so while one y=4, 3y=12. Therefore, GH=12
Evaluate the expression when m=3. m 2 - 5m + 7
Answers
Answer:
-2
Step-by-step explanation:
Substitute 3 for m: (3)2 - 5(3) + 7
Simplify: 6 - 15 + 7
Follow PEMDAS and subtract 6 from 15: -9 + 7
Add: -2
Hope this helps ^-^
You said m = 3.
Replace every m you see with 3.
m^2 - 5m + 7
(3)^2 -5(3) + 7
9 - 15 + 7
-6 + 7 = 1
Answer is 1.
44% of what number is 11?
Answers
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What is mpo?
128°
O 1730
O 1920
O 256°
Answers
Answer:
it's the 2nd one because
Step-by-step explanation:
have a nice day
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answers
Answer:
Columbian exchange. Tell a story in chronological order of the changes that the community undergoes as it and the communities around it make contact with Europeans over a span of roughly 50 to 100 years.
This section is worth 20 points. See the scoring rubric for more details on how you
will be graded
Use the evidence you gathered to tell the story of a hypothetical indigenous
community in the Americas and its experience involving the Columbian Exchange.
Come up with a community whose circumstances are typical of many in Central
America, the West Indies, or another part of the Americas that had direct contact with
Europeans. Tell the story in chronological order, but feel free to skip whole years or
decades so that you can cover each of the important topics related to the activity: the
availability of goods, the effects of disease, and the impact of European culture
(language and religion, for example), at the very least.
Think of your story as more of a summary than a work of fiction; you must cover a
large span of time in few words. Base the details of the story on factual evidence and
cite your sources, but keep in mind that the text should be written as a story, not as
an essay with a conventional introduction, body, and conclusion. Aim for about 700
to 1,200 words.
free body diagram can be used to help work out the net force acting on an object. True or, false?Columbian exchange. Tell a story in chronological order of the changes that the community undergoes as it and the communities around it make contact with Europeans over a span of roughly 50 to 100 years.
This section is worth 20 points. See the scoring rubric for more details on how you
will be graded
Use the evidence you gathered to tell the story of a hypothetical indigenous
community in the Americas and its experience involving the Columbian Exchange.
Come up with a community whose circumstances are typical of many in Central
America, the West Indies, or another part of the Americas that had direct contact with
Europeans. Tell the story in chronological order, but feel free to skip whole years or
decades so that you can cover each of the important topics related to the activity: the
availability of goods, the effects of disease, and the impact of European culture
(language and religion, for example), at the very least.
Think of your story as more of a summary than a work of fiction; you must cover a
large span of time in few words. Base the details of the story on factual evidence and
cite your sources, but keep in mind that the text should be written as a story, not as
an essay with a conventional introduction, body, and conclusion. Aim for about 700
to 1,200 words.
free body diagram can be used to help work out the net force acting on an object. True or, false?
Step-by-step explanation:
where my brainlest
What is the factored form of 8y2 + 12y?
a 4 (4y2 + 8y)
b 8y(y + 4)
c 4y (2y + 3)
d 8y (y2 + 4)
Answers
Answer:
Hi! The answer to your questions is C. 4y (2y+3)
Step-by-step explanation:
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☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Someone pleaseee help this is my second time I’ve asked the same question please help I need the last one
Answers
Answer:
yes,congruent
reflect about x=-2
translate up 4 and 3 to left
Step-by-step explanation:
same area so they're congruent
help please thank you
Answers
Answer:
C
Step-by-step explanation:
Take sides AD and MP.
6 in. in ADCB is 3/2 * 4 in. in MPON
What value of b will make the equation a true statement? Explain how you arrived at your solution. (−34 + 43)+ b = 0
Answers
Answer:
b = -9
Step-by-step explanation:
Given the equation (−34 + 43)+ b = 0
We are to find the value of b
First solve for the value in parenthesis
(−34 + 43)+ b = 0
9+b = 0
Subtract 9 from both sides
9+b-9 = 0 - 9
b+0 = -9
b = -9
Hence the value of b will make the equation a true statement is -9
Tell whether the angles are complementary or supplementary. Then find the value of $x$ . A ray intersects two other rays forming a right angle. The angles formed after the intersection is x degrees and left parenthesis x minus 20 right parenthesis degrees.
Answers
The measure of the value of x is 55°.
We have,
Complementary angles are two angles that add up to 90 degrees.
Supplementary angles are two angles that add up to 180 degrees.
Now,
The ray intersects two other rays forming a right angle.
This means,
It is a complementary angle.
i.e
x + (x - 20) = 90
x + x - 20 = 90
2x = 90 + 20
2x = 110
x = 55°
Thus,
The measure of the value of x is 55°.
Learn mroe about complementary angles here:
https://brainly.com/question/15380971
#SPJ12
Directions: Solve for x.
Answers
Answer:
x = 6
Step-by-step explanation:
From the given picture,
ΔABC and ΔADE are the similar triangles.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
[tex]\frac{x+18}{x}=\frac{28}{(28-21)}[/tex]
7(x + 18) = 28x
7x + 7×18 = 28x
28x - 7x = 126
21x = 126
x = [tex]\frac{126}{21}[/tex]
x = 6