The cross-section of the reflector in a flashlight is a parabola. Suppose the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.
Assume the vertex is at the origin and that the parabola is concave left (it opens left as depicted in the picture). What is the equation for the cross-section of the reflector?
Answers
The equation of the cross-section of the reflector which is in the form of a parabola is y² = -10x
What is a parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Given that, The cross-section of the reflector in a flashlight is a parabola, the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.
We know that, the equation of the parabola turned to the left i.e. to the negative side of the coordinate system is:
y² = -2px
where p is the parameter of the parabola
The relationship between the parameter and the focus is.
p = 2 f
p = 2×2.5 = 5 cm
Since, the equation of the parabola is:
y² = -2p
Therefore, put p = 5
y² = - 2×5x = -10x
y² = -10x
Hence, the equation is y² = -10x
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Related Questions
4 (w+1) =-6 gsdfnvbsfgbsdfbsdfb
Answers
Answer: Hello There!!
w = -5/2
Step-by-step explanation:
4(w+1)=−6
Step 1: Simplify both sides of the equation.
4(w+1)=−6
(4)(w)+(4)(1)=−6(Distribute)
4w+4=−6
Step 2: Subtract 4 from both sides.
4w+4−4=−6−4
4w=−10
Step 3: Divide both sides by 4.
4w/4 = -10/4
Answer:
-10/4
Step-by-step explanation:
4(w+1)=−6
Step 1: Simplify both sides of the equation.
4(w+1)=−6
(4)(w)+(4)(1)=−6(Distribute)
4w+4=−6
Step 2: Subtract 4 from both sides.
4w+4−4=−6−4
4w=−10
Step 3: Divide both sides by 4.
4w/4 = -10/4
): If (6x-3)(6x+3)=ax^2-b, what is the value of a? What is the value of b?
Answers
Explanation:
(6x-3)(6x+3)
= 36x² - 18x - 18x - 9
= 36x² - 9
(6x-3)(6x+3) = ax² - b
36x² - 9 = ax² - b
a = 36 and b = 9
Hope it helps!
The accompanying specific gravity values describe various wood types used in construction. 0.32 0.35 0.36 0.36 0.37 0.38 0.40 0.40 0.40 0.41 0.41 0.42 0.42 0.42 0.42 0.42 0.43 0.44 0.45 0.46 0.46 0.47 0.48 0.48 0.49 0.53 0.54 0.54 0.55 0.58 0.61 0.66 0.66 0.67 0.68 0.76 Construct a stem-and-leaf display using repeated stems. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Stem
Answers
Answer:
Follows are the responses to the given question:
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]Stem\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Leaf\\\\[/tex]
[tex]3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5,6,6,7,8\\\\4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0,0,0,1,1,2,2,2,2,2,3,4\\\\4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5,6,6,7,8,8,8\\\\5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1,4,4\\\\[/tex]
[tex]5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5,8\\\\6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6,6,7,8\\\\7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ NONE\\\\7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\[/tex]
The stem & leaf show demonstrates that 0.55 for both the data is indeed a reasonable value.
The probable outlier is the data value 0.76.
The variability of the techniques is relatively large.
It show isn't symmetrical and seems to be optimistic.
Using traditional methods, it takes 8.1 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 23 students and observed that they had a mean of 8.2 hours with a standard deviation of 1.2. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answers
Answer:
The value of the test statistic is 0.4.
Step-by-step explanation:
The value of the test statistic is given by:
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Using traditional methods, it takes 8.1 hours to receive a basic flying license.
This means that [tex]\mu = 8.1[/tex]
A researcher used the technique with 23 students and observed that they had a mean of 8.2 hours with a standard deviation of 1.2.
This means that [tex]n = 23, X = 8.2, \sigma = 1.2[/tex]
Find the value of the test statistic.
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{8.2 - 8.1}{\frac{1.2}{\sqrt{23}}}[/tex]
[tex]t = 0.4[/tex]
The value of the test statistic is 0.4.
Convert the angle from radians to degrees.
Answers
Answer:
first go to a diffrent site
Step-by-step explanation:
A pair of shoes costs $50. What is the total cost of the shoes after 7.25% tax is added? Round the tax to the nearest cent.
Answers
Answer:
Step-by-step explanation:
50(1+7.25/100)
50(107.25/100)
50(1.0725)
53.625
$53.63
help please...
Which graph represents a proportional relationship?
Answers
Answer:
Graph C.
Step-by-step explanation:
The graph which illustrates a proportional relationship is graph c because as the value on the Y-axis increases, the values on the X-axis increases consequently.
A direct proportion implies that the values of the quantities on both sides are increasing at a constant rate. Critically looking at graph c, you will notice or observe that the values both intersect at specific intervals or points on the graph.
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
o
A. They must be diameters.
B. They must be parallel.
C. They must be congruent.
D. They must be perpendicular.
SNBMIT
Answers
The true statement the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What is the condition for two chords to be congruent?If the two chords are congruent, then they must be equidistant from the center of the circle.
A is rejected because the chord might not pass through the center of the circle.
B is rejected because the chords are not obligated to be parallel.
C is rejected because it is not compulsory for the chords to be perpendicular.
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Answer: C. They must be congruent.
Step-by-step explanation:
Two points are located on a graph, Point A is (-1, 10), and Point B is (4,3). What is the
distance between Point A and Point B?
A) 8.6
B)13.3
C) 10
D)3
Answers
Answer:
10
Step-by-step explanation:
como puedo resolver 5 anos en in minuto
Answers
what two numbers multiple to -24 and add up to 2
Answers
Answer:
-4 and 6
Step-by-step explanation:
HELP ME I WILL GIVE BRAINLIEST I PROMISE!!!!!!!!!
Answers
the ratio of the angle measures of a triangle are 3:3:4 what angle measures the triangles classification
Answers
Step-by-step explanation:
sum of the ratio=3+3+4=10
now,
angle I = 3/10×180=54
angle II= 3/10×180=54
angle III=4/10×180=72
that shows th given triangle is isoceles
I need help please.
Answers
Answer:
A) c(x)=2x+60
$74
Step-by-step explanation:
A) c(x)=2x+60
$74
solve
2. y+0.4=2
what is y?
Answers
The answer is,
[tex]y = 1.6[/tex]
Answer:
Y = 1.6
Step-by-step explanation:
Y = 2 - 0.4
Y = 1.6
The hypotenuse of a triangle is one foot more than
twice the length of the shorter leg. The longer leg IS
seven feet longer than the shorter leg. Find the
dimensions of the triangle.
Answers
Answer:
y uwu
Step-by-step explanation: i think
Compare the fractions using >, < or=.
9/10 and 78/100
Answers
Answer:
9/10 > 78/100
Step-by-step explanation:
We can make 9/10 into 90/100, and since they now have the same denominator (Bottom number in fraction), we can now compare the numerators (Top number in fraction). 90 is greater than 78 so we can say that 9/10 > 78/100 (9/10 is greater than 78/100).
Which expression is equivalent to 3x + 6y
A: 3(x + 2y)
B: 3(x + 3y)
C: 9xy
D: 18xy
Answers
option a as 3 is outside of bracket it will be multiplied by what is in bracket sot the answer will equivalent to question
The equivalent expression for the given expression is 3(x+2y). Therefore, the correct answer is option A.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 3x+6y.
Here, the common factor of two terms 3x and 6y is 3
Now, 3(x+2y)
Therefore, option A is the correct answer.
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need help solving this
Answers
Answer:
For this question, subtract 5 on both sides to get [tex]\frac{m}{3}[/tex]=7. Then, multiply 3 on both sides to get m=21.
Answer:
M=21
Hope this helps, and happy valentines day :D
A boat can travel 77 9/16 nautical miles in 8 1/2 at how many knots is the boat traveling
Answers
Divide miles by time:
77 9/16 miles / 8 1/2 hours =
Rewrite as I’m proper fractions:
1241/16 / 17/2
Flip the second fraction over and multiply:
1241/16 x 2/17 = (1241x2)/(16x17) =
2482/272 = 9 1/8 miles per hour
Hi there!
Simplify each terms:
[tex]77\frac{9}{16}*8\frac{1}{2}=77\frac{9}{16}*8\frac{8}{16}[/tex]
Divide each terms:
[tex]77\frac{9}{16}*8\frac{8}{16}=9\frac{2}{16}[/tex]
Simplify terms:
[tex]9\frac{2}{16}=9\frac{1}{8}[/tex]
Final Result:
[tex]9\frac{1}{8}[/tex]
h(t)= 50- t/5
h(35)=
Answers
Answer:
h(35) = 43
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
h(t) = 50 - t/5
h(35) is t = 35
Step 2: Evaluate
Substitute in t: h(35) = 50 - 35/5Divide: h(35) = 50 - 7Subtract: h(35) = 43Vhat is the value of a in the equation 3 a+b=54, when b = 9?
O 15
O 18
O 21
0 27
Answers
U can rewrite
a= 54-9
So a=45
3a + (9) = 54
-9. -9
3a= 45
\3 \3
A= 14
The value of “a” is 15
A number that adds with 2/3 substrate 1/3 will be 8.What should be the number??
Answers
Answer:
The number is [tex]\frac{23}{3}[/tex]
Step-by-step explanation:
I am going to call the number x.
A number that adds with 2/3 subtract will 1/3 will be 8.
As an equation, this is:
[tex]x + \frac{2}{3} - \frac{1}{3} = 8[/tex]
Now we solve the equation to find x. So
[tex]x + \frac{2-1}{3} = 8[/tex]
[tex]x + \frac{1}{3} = 8[/tex]
[tex]x = 8 - \frac{1}{3}[/tex]
[tex]x = \frac{24}{3} - \frac{1}{3}[/tex]
[tex]x = \frac{24-1}{3}[/tex]
[tex]x = \frac{23}{3}[/tex]
The number is [tex]\frac{23}{3}[/tex]
The Roller family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park. The Coaster family
spends $146 on 3 adult tickets and 2 youth tickets at the same park. Find the price of adult and youth tickets,
Answers
Answer:
34 adult ticket and 22 youth tickets
Step-by-step explanation:
Let the price of adult be x
Let the price of youth tickets be y
If the Roller family spends $134 on 2 adult tickets and 3 youth tickets at an amusement park, then;
2x+3y = 134 .... 1
Also if the Coaster family spends $146 on 3 adult tickets and 2 youth tickets at the same park then;
3x+2y = 146 ..... 2
Solve simultaneously
2x+3y = 134 .... 1 * 3
3x+2y = 146 ..... 2 * 2
_____________
6x+9y = 402
6x+4y = 292
Subtract
9y-4y = 402-292
5y = 110
y = 110/5
y = 22
Substitute y =22 into 1;
From 1;
2x+3y = 134
2x+3(22) = 134
2x+66 = 134
2x = 134-66
2x = 68
x = 34
Hence there are 34 adult ticket and 22 youth tickets
Which of these expressions are equivalent to 225 3/2? Select all that apply.
Answers
Answer:
C.
Step-by-step explanation:
it could also be written as (sqrt225)^3
C is correct because sqrt225 is equivalent to 225^1/2
using exponent rules, 3 mutiplies to the 1/2 making it 225^3/2
If a shirt selling for $18 is marked upto $20 then the % increase is
equal to
a. 11%
b. 10%
c. 12%
d. 9%
Answers
Answer:
11%
Step-by-step explanation:
it is a simple question, whenever you need to find % increase or % decrease.
always divide the increase as in this case $2 by the original amount which is $18 and multiply it by 100 as you need to take the %.
so,
2/18*100 gives you 11.11% * is multiply
Step-by-step explanation:
$20 - $18 = $2
to get % of increase we need to know what % of $18 the $2 are.
$2 ÷ $18 = 0.11111111........
Multiply this number by 100 and you will get the percentage.
0.111111111111........ x 100 = 11.1111111111....%
PLEASE HELP I WILL GIVE BRAINLIEST
Is RST = XYZ? If so, name the postulate that applies.
A. Might not be congruent
B. Congruent - SSS
C. Congruent - ASA
D. Congruent - SAS
Answers
Answer:
D
Step-by-step explanation:
two sides are congruent and in between is an angle
PLEASE SOMEONE HELP, I WILL FAIL IF I DONT GET THIS DONE, IVE GOTTEN NO HELP AND I ONLY HAVE 30 MINS FR REAL
Answers
Answer:
18m³ + 2m² - 1m
Step-by-step explanation:
For perimeter you add up all the side lengths.
Cubed term:
5m³+5m³+8m³
10m³+8m³
18m³
Squared term:
3m²+3m²+ (-4m²)
6m² - 4m²
2m²
Regular term:
-2m + (-2m) + 3m
-4m + 3m
-m
The Venn diagram below represents the students in a particular high school.
How many female students have a part-time job and a driver's license?
Female
Part-time job
74
111
56
45
92
38
137
89
Driver's license
No
Answers
Answer:
C. 45
Step-by-step explanation:
Since the question is asking how many females have both a driver's license and a part-time job. So you need to find the number that reoresents all three of these categories. This category is shown in the very center with the number 45.
Hope it helps!
Answer:
C. 45
Step-by-step explanation:
Because its inside all three circles that you want.
Mark the best answer.
1. The grid map shows the location of
some places on a college campus.
What are the coordinates of the
dormitory? (8-1)
Library
Gymnasium
12 Student
Center
5 4 3 2
Dormitory
I.XI
10
2013
Academic
Hall
A (2.1)
B 12)
CK1-2)
D (2.1)
Answers
Answer:
it makes sense
Step-by-step explanation: