The light bulb should be placed 1 inch from the vertex so that the rays will be reflected parallel to the axis.
The reflector of a flashlight is in the shape of a paraboloid of revolution.
Its diameter is 4 inches and its depth is 1 inch.
To find the distance from the vertex to the light bulb, so that the rays will be reflected parallel to the axis, we will use the following steps:
Step 1: Write the equation of the paraboloid.
For the given paraboloid, the vertex is at the origin (0,0,0) and the axis of symmetry is the z-axis.
Since the paraboloid is symmetric with respect to the z-axis, the equation of the paraboloid can be written as:
[tex]$$z=\frac {x^2+y^2}{4p}$$[/tex]
where p is the distance from the vertex to the focus.
Here, we have to find p.
Step 2: Find the value of p.
We know that the diameter of the reflector is 4 inches.
Since the paraboloid is symmetric with respect to the z-axis, the diameter of the paraboloid is also 4 inches.
Therefore, the radius of the base of the paraboloid is 2 inches.
Since the depth of the paraboloid is 1 inch, the vertex is 1 inch away from the base of the paraboloid.
Hence, the value of p can be found as follows: p = distance from vertex to focus
= [tex]$\frac{1}{4}$[/tex]
distance from vertex to the base
[tex]= $\frac {1}{4}$ (2)[/tex]
[tex]= $\frac{1}{2}$[/tex] inches
Step 3: Find the distance from the vertex to the light bulb.
Since the rays should be reflected parallel to the axis, the light bulb should be placed at a distance of
[tex]2p = 2 $\times$ $\frac{1}{2}$ = 1 inch[/tex] from the vertex.
For similar question on vertex.
https://brainly.com/question/25651698
#SPJ11
Think of a time when you had a question in math class, did you ask it? If so, did it get answered? If you tend to not ask your questions, why do you think you hesitate to ask? Have you ever had someone else ask the same question you had? How did it make you feel? Relief?
Asking questions in math class is crucial for deepening understanding, and teachers strive to create a supportive learning environment for students to feel comfortable seeking help.
Students may hesitate to ask questions in math class for various reasons, such as fear of being judged by peers or the teacher, feeling like their question is not important, or simply not wanting to disrupt the flow of the lesson. However, it's essential to remember that asking questions is an integral part of the learning process and can lead to a deeper understanding of the subject.
When students do ask questions, they may feel relieved to have their doubts clarified, and it can also benefit other students who may have had the same question but were hesitant to ask. Teachers typically encourage questions and strive to create a supportive learning environment where students feel comfortable asking for help.
In summary, asking questions is an essential aspect of learning, and students should feel encouraged to ask them, as it can lead to a deeper understanding of the subject and help their peers who may have had similar questions.
To learn more about math class please click on below link
https://brainly.com/question/10704243
#SPJ1
The following shows a graph of y = x^2+ 5
Can we use this graph to find the solutions of 0 = c^2 + 5? Why or why not?
There are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.
How to find the solutions of y = x²+ 5.To find the solutions of 0 = x² + 5, we need to find the values of x that make the equation true. One way to do this is by solving the equation algebraically using methods like factoring, completing the square, or using the quadratic formula.
We cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, since the graph shows the values of y that correspond to different values of x, not the values of x that satisfy the equation 0 = x² + 5. However, we can use the graph to help us visualize the solution to the equation.
Since 0 = x² + 5 is equivalent to x² = -5, we know that the solutions to the equation must be imaginary numbers, since the square of any real number is always non-negative. Therefore, there are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.
In summary, we cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, but we can use the graph to see that the equation has no real solutions.
To know more about Equation visit:
brainly.com/question/28243079
#SPJ1
how many ways are there to distribute five balls into three boxes if (c) the balls are unlabeled, but the boxes are labeled?
There are 243 ways to distribute five unlabeled balls into three labeled boxes.
Since the balls are unlabeled, we only need to consider the number of balls in each box, rather than which specific ball goes where.
We can use a combination approach to solve this problem. Let's think about distributing the balls one at a time. For the first ball, there are three boxes to choose from. For the second ball, there are also three boxes to choose from. We can continue this process until all five balls have been distributed.
So, for each ball, there are three choices of which box to put it in. Therefore, the total number of ways to distribute the five balls into the three labeled boxes is
3 x 3 x 3 x 3 x 3 = 3^5 = 243
Learn more about combination here
brainly.com/question/28720645
#SPJ4
Determine the area and perimeter of the figure below. Note that each square is 1 unit in length.
Answer:
area = 127[tex]units^{2}[/tex]
perimeter = 46 units
Step-by-step explanation:
count them
Given f(x)=5x+7 and g(x)=2x+2, find g(g(1-3w))
Enter as the final value or expression without parentheses
As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).
Which of these are they known as?When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).
We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).
We must first determine g(1-3w):
Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.
g(1-3w) ≈ 2 - 6w + 2 (distribute the 2)
g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)
We can again again enter the result of g(1-3w) into g(x):
If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2
g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)
g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)
To know more about parentheses visit:
https://brainly.com/question/28146414
#SPJ1
If ΔDEF is similar to ΔPRY, what is the measure of PY?
A 12 centimeters
B 21 centimeters
C 24 centimeters
D 48 centimeters
PLEASE HELP MEEEEEEEEEEE!
What is the measure of the unknown angle?
A straight angle divided into a fifty-eight-degree angle and an unknown angle.
100°
112°
120°
122°
Therefore , the solution of the given problem of angles comes out to be the right response is option d 122°.
An angle meaning is what?Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.
Here,
180 degrees is the length of a straight circle. It has been split into a 58-degree angle and an unidentified angle, as far as we are aware. So that we can determine the size of the undetermined angle, let's use subtraction:
=> Angle unknown = 180 degrees minus 58 degrees
=> Angle unknown = 122 degrees
As a result, the undetermined angle is 122° in size.
The right response is (d) 122°.
To know more about angles visit:
https://brainly.com/question/14569348
#SPJ1
The players of a travel volleyball team have no more than a combined total of 385
shirts and hats to sell for a fundraiser to fund a trip. The shirts sell for $12
each, and the hats sell for $25
each. The players must make a combined total of at least $7,450
from the fundraiser. If s
represents the number of shirts sold during the fundraiser, and h
represents the number of hats sold during the fundraiser, which system of inequalities represents the scenario?
system of inequalities represents the scenario: The differences are 12s + 25h 7450 and s + h 385.
When expressions or values do not have an equal relationship to one another, this relationship is referred to in mathematics as an inequality. Inequality is the product of an unbalanced system. The symbol "=" denotes equality between two quantities, and the symbol denotes inequality between them.
The maximum count of hats and shirts sold in this case is 385 if s stands for the quantity of shirts sold during in the fundraiser and h for the amount of hats sold during in the campaign.
=> s +h 385
And the players must make a combined total of at least $7, 450 from the fundraiser, then shirts sell for $12 each, and the hats sell for $25 each then,
=> 12*s+25*h 7450
=> 12s + 25h 7450
Hence the inequalities are, s +h 385 and 12s + 25h 7450.
To know more about Inequality click here.
brainly.com/question/30228778
#SPJ4
when we use 5.66 standard deviations, what is this minimum guarantee, as a percentage of the data? use one decimal place in reporting your answer in percent, but don't use the % sign. %
using 5.66 standard deviations provides a minimum guarantee of 99.85% of the data being covered.
When we use 5.66 standard deviations, we can guarantee at least 99.9% of the data falls within that range.
This is based on the empirical rule, which states that for a normal distribution, approximately 99.7% of the data falls within 3 standard deviations of the mean. Therefore, 5.66 standard deviations would cover a greater percentage of the data, which can be calculated as:
99.7% + [(100% - 99.7%) / 2] = 99.85% (rounded to one decimal place)
So, using 5.66 standard deviations provides a minimum guarantee of 99.85% of the data being covered.
Learn more about data here
https://brainly.com/question/14893265
#SPJ4
a line that passes through (3,5) and (4,13)
Answer:
y = 8x-19
Step-by-step explanation:
The first step is to find the slope.
m= ( y2-y1)/(x2-x1)
= ( 13-5)/(4-3)
= 8/1
= 8
Then we can use the slope intercept formula.
y = mx+b
y = 8x+b
Substitute a point to find the intercept.
5 = 8*3+b
5 = 24+b
-19 = b
The formula is
y = 8x-19
Answer:
y = 8x - 19
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 5 ) and (x₂, y₂ ) = (4, 13 )
m = [tex]\frac{13-5}{4-3}[/tex] = [tex]\frac{8}{1}[/tex] = 8 , then
y = 8x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 5 )
5 = 8(3) + c = 24 + c ( subtract 24 from both sides )
- 19 = c
y = 8x - 19 ← equation of line
In the figure below, find the exact value of z. (Do not approximate your answer.)
Answer:
z=8
Step-by-step explanation:
Considering the triangle on the RHS,
Let the Unknown side be "x"
from pythagora's theorem,
x ^ 2 = 4 ^ 2 - 2 ^ 2 x = √(4 ^ 2 - 2 ^ 2)
x = √(16 - 4)
x = √12
cos alpha = 2/4 , alpha = arccos(2/4)
alpha = 60°
< ABC + theta + alpha = 180°
theta = 180 - alpha - <ABC
theta = 180 - 60 - 90
theta = 30°
Now Considering the triangle on the LHS,
tan 30 = (√12)/y
y = (√12)/(tan 30°)
y = 6
z = y + 2
z = 8
what percent of light bulbs can last within one standard deviation of the mean, between 57.6 hours and 66.4 hours?
About 68% percent of light bulbs can last within one standard deviation of the mean, between 57.6 hours and 66.4 hours.
To determine the percentage of light bulbs that can last within one standard deviation of the mean, between 57.6 hours and 66.4 hours, you can follow these steps:
1. Identify the range of values:
In this case, the range is between 57.6 hours and 66.4 hours.
2. Recognize that this range represents one standard deviation from the mean.
In a normal distribution, approximately 68% of values fall within one standard deviation of the mean.
So, about 68% of light bulbs can last within one standard deviation of the mean, between 57.6 hours and 66.4 hours.
for such more question on percent
https://brainly.com/question/24877689
#SPJ11
what is the probability of getting a tail on the coin and at least a 5 on the die? round your answer to four decimal places, if necessary.
The probability of getting a tail on the coin and at least a 5 on the die is 0.1667 rounded to four decimal places.
How are probabilities determined?The probability is frequently stated as a ratio between the total number of outcomes in the sample space and the number of positive outcomes. This is how it is written: Number of Favorable Outcomes P(E) = Probability of an Event (Sample space).
If a coin is fair and impartial, the likelihood of getting a tail is equal to half.
On a six-sided dice, the likelihood of getting at least a 5 is 2/6, or 1/3. Either rolling a 5 or rolling a 6 will result in a 5 or a 6 on the die. The likelihood of rolling at least a 5 is 2/6 or 1/3 because there are a total of six possible results.
You can multiply the probabilities of the two occurrences to determine the likelihood that they will occur simultaneously (assumed to be independent events). As a result, the likelihood of getting at least a 5 on the die and a tail on the coin is:
1/2 * 1/3 = 1/6
Thus, there is a 1 in 6 possibility of rolling at least a 5 on the die and getting a tail on the coin in a single trial. Another way to say this is as a percentage:
1/6 * 100% = 16.67%
Thus, rounded to four decimal places, the likelihood of receiving a tail on the coin and at least a 5 on the die is 0.1667.
To know more about probability visit:
https://brainly.com/question/30719832
#SPJ1
Add the additive inverse to the product of - 1 and - 4
The answer to this question is 0.
To add the additive inverse to the product of - 1 and -4, we must first find the product of -1 and -4. The product of -1 and -4 is 4. Now that we have found the product of -1 and -4, we can add the additive inverse to it. The additive inverse of 4 is -4, so we add -4 to 4. 4+ (-4) is equal to 0. Therefore, the answer to this question is 0.
For more questions on additive inverse
https://brainly.com/question/28525250
#SPJ11
A total of 646 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
64 im pretty cxsure
Step-by-step explanation:
Aright cone has radius 5 ft and slant height 9 ft. The radius and slant height are both multipliedby 1/2. Which of the following correctly describes the effect on the surface area?a. The surface area is multiplied by 4b. The surface area is multiplied by 1/2.c. The surface area is multiplied by 2d. The surface area is multiplied by 1/4
The effect on the surface area is best described by the statement "the surface area is multiplied by 1/4." The correct option is D.
Given that the radius of a right cone is 5 ft and the slant height is 9 ft. If the radius and slant height of the cone are both multiplied by 1/2, then the new radius of the cone will be:5 × (1/2) = 2.5 ft
New slant height of the cone will be:9 × (1/2) = 4.5 ft. The surface area of a cone can be given by the formula:
S = πrl + πr² Where r is the radius of the base, l is the slant height of the cone, and π is a constant (3.14). The surface area of the original cone can be calculated as:
S1 = π × 5 × 9 + π × 5² = 141.37 ft². Now, if we multiply the radius and slant height by 1/2, the new surface area of the cone will be:S2 = π × 2.5 × 4.5 + π × 2.5² = 17.67 ft².
Therefore, the ratio of the new surface area to the original surface area will be:S2/S1 = 17.67/141.37 = 0.125Thus, the new surface area is 1/8th (0.125) of the original surface area or multiplied by 1/8th (1/2 × 1/4). So, the surface area is multiplied by 1/4.
To know more about surface area, click on the link below:
https://brainly.com/question/23877107#
#SPJ11
A two-sided t-test for a population mean is conducted of the null hypothesis H0 : μ = 100. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of a = 0.10 ?A. The p-value is less than 0.10, and H0 should be rejected.B. The p-value is less than 0.10, and H0 should not be rejected.C. The p-value is greater than 0.10, and H0 should be rejected.D. The p-value is greater than 0.10, and H0 should not be rejected.
Option D is correct, the p-value is greater than 0.10, and H₀ should not be rejected.
What is Null hypothesis?The null hypothesis is denoted as H₀, is a statement or assumption that suggests there is no significant or meaningful relationship between two variables in a statistical hypothesis test.
If a 90 percent t-interval constructed from the sample data contains the value of 100, it means that the sample mean is within the confidence interval.
Since the null hypothesis H₀: μ = 100 is also assuming that the population mean is 100, this suggests that the sample data is consistent with the null hypothesis.
Given a significance level of α = 0.10, we compare the p-value with this significance level to make a conclusion.
If the 90 percent confidence interval contains the hypothesized value (100 in this case), it suggests that the p-value is likely to be greater than 0.10.
There is insufficient evidence to reject the null hypothesis at a significance level of 0.10.
Therefore, the p-value is greater than 0.10, and H₀ should not be rejected.
To learn more on Null hypothesis click:
https://brainly.com/question/30821298
#SPJ6
1. Copy this table into your notebook and complete it. Lines l1 l2 correspond to the
two equations in a linear system. Predict the number of solutions to the system. (PLEASE HELPPPP)
Answer: 1.5
Step-by-step explanation:
Winston is baking a pie. The diameter of the pie is 12 inches. What is the area of the pie? Use 3. 14 for pi and round your answer to the nearest tenth
If the diameter of the pie is 12 inches, then the area of pie is 113.04 in² and 113 in² after rounding to the nearest tenth.
The formula for the area of a circle is: A = π × r²
where A is the area, pi is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In this case, we are given the diameter of the pie, which is 12 inches. To find the radius, we need to divide the diameter by 2:
r = 12 / 2
= 6 inches
Now we can use the formula for the area of a circle to find the area of the pie:
A = π × r²
A = 3.14 × 6²
A = 113.04 square inches
Rounding to the nearest tenth gives:
A ≈ 113.0 square inches
Therefore, the area of the pie is approximately 113.0 square inches.
To learn more about area of a circle click here
brainly.com/question/28642423
#SPJ4
the fact that the overall frequency of an event can be determined by multiplying together the frequencies of the independently occurring factors related to that event is called what?
The fact that the overall frequency of an event can be determined by multiplying together the frequencies of the independently occurring factors related to that event is called a frequency multiplier. Also called as multiplication rule.
What is the multiplication rule?
The multiplication rule states that the overall probability of a sequence of events happening jointly is the product of the probabilities of the individual events.
In probability, the multiplication rule is used to calculate the joint probability of two independent events that occur together.
What are the factors in a probability scenario?In probability scenarios, the factors are the set of conditions that influence the probability of a certain occurrence, event, or outcome.
These factors are used to calculate the probability of an event. The likelihood of the occurrence of an event is based on these factors.
The multiplication rule can be used to calculate the overall frequency of an event by multiplying the frequency of each factor independently related to the event.
Learn more about the overall frequency of an event at: https://brainly.com/question/15171176
#SPJ11
please help !!!
math hw
Answer: they all include a variable, an "x" in parentheses, and they all have the number 2 in it.
Step-by-step explanation:
a pizza that is 12 in diameter is cut into six slices. find the length of each arc intercepted by each slice (length of the crust). find the area of each slice.
The length of each arc intercepted by each slice is 2.09 inches.
The area of each slice 18.85 square inches .
To find the length of each arc intercepted by each slice and the area of each slice of a pizza that is 12 inches in diameter, follow the steps below. Length of each arc intercepted by each slice
The formula to find the length of each arc is given by:
L = θ/360 * 2πr
WhereL = length of arc
θ = angle of arc in degrees
r = radius of circle (diameter/2)
Given, diameter of pizza = 12 inches
So, radius of pizza = 12/2 = 6 inches
Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.
Now, substituting the given values in the formula:
L = 60/360 * 2π* 6L = 1/6 * 12πL = 2π/3 ≈ 2.09 inches
The formula to find the area of each slice is given by:
A = θ/360 * πr²
Given, diameter of pizza = 12 inches
So, radius of pizza = 12/2 = 6 inches
Since the pizza is cut into 6 equal slices, each slice will have an angle of 360/6 = 60 degrees.
Now, substituting the given values in the formula:
A = 60/360 * π* 6²A = 1/6 * 36π
A = 6π ≈ 18.85 square inches
Thus, the length of each arc intercepted by each slice is approximately 2.09 inches and the area of each slice is approximately 18.85 square inches.
You can learn more about circular area at
https://brainly.com/question/10645610
#SPJ11
Helppppppppppppppppp
your neighborhood fast food restaurant only sells chicken nuggets in packs of five or seven. what is the largest number of nuggets that is impossible to order?
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven. This is because the restaurant only sells nuggets in packs of five and seven. This means that if you wanted to order eleven nuggets, it would not be possible.
To explain this mathematically, eleven can be written as 5+5+1, 7+4, or 3+3+3+2. As none of these can be made with just five and seven packs of chicken nuggets, it is impossible to order eleven.
If the restaurant sold chicken nuggets in packs of three and seven, then it would be possible to order eleven nuggets (3+3+3+2).
In conclusion, the largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.
See more about the largest number at: https://brainly.com/question/19267346
#SPJ11
rahquez and trinidad both leave the park at the same time, but in opposite directions. if trinidad travels 6 mph faster than rahquez and after 8 hours they are 288 miles apart, how fast is each traveling?
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
For more details about propensity click here:
https://brainly.com/question/28766632#
#SPJ11
you may need to use the appropriate table ( (standard normal table) ) to answer this question. the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. what is the probability of completing the exam in one hour or less?
The probability of completing the exam in one hour or less is 0.0228.
We are given that the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. We need to find the probability of completing the exam in one hour or less, i.e., in 60 minutes or less.
Now, we need to convert this value into the standard normal variable z, by using the formula
z = (x - μ) / σ
where, x is the given value, μ is the mean and σ is the standard deviation. Putting the given values in the formula, we get
z = (60 - 80) / 10z = -2
We need to find the probability of completing the exam in 60 minutes or less. This can be represented as P(X ≤ 60). We know that P(Z ≤ z) can be found out from the standard normal table. Therefore, we need to look at the standard normal table to find the probability P(Z ≤ -2). From the standard normal table, we get
P(Z ≤ -2) = 0.0228
Therefore, the probability of completing the exam in one hour or less is 0.0228 (rounded to four decimal places).
To learn more about probability refer :
https://brainly.com/question/29291264
#SPJ11
how to do this.............
Answer:
The one selected is correct
Step-by-step explanation:
to meet the required weight specification, a total of 30 yards of material must be used for each frame. what is the optimal solution? if ati purchase the professional grade for $8 per yard will optimal solution change?
The optimal solution would be to use $240 worth of professional grade material for each frame.
Describe Optimal Solution?An optimal solution is a solution that provides the best possible outcome for a problem or situation, given a set of constraints or requirements. In mathematical optimization, an optimal solution is the solution that maximizes or minimizes an objective function while satisfying a set of constraints.
In other words, an optimal solution is the solution that is most efficient, effective, or desirable according to a certain set of criteria. It is the solution that achieves the best possible outcome, given the available resources and limitations.
To find the optimal solution, we need more information about the specific weight specification and the cost of different types of materials.
However, if we assume that there is only one type of material available, and that it costs $x per yard, we can set up an equation to find the optimal solution:
30x = cost per frame
If the professional grade material costs $8 per yard, then the equation becomes:
30(8) = $240 per frame
So, the optimal solution would be to use $240 worth of professional grade material for each frame, assuming that it meets the weight specification. If the weight specification requires a different amount of material, or if there are other materials available at different prices, the optimal solution would be different.
To know more about equation visit:
https://brainly.com/question/545403
#SPJ1
SHOW YOUR WORK BELOW! PLEASE SOMEONE
80 POINTS
The equation to the given graph is y= (1/2) * 2ˣ. So correct option is B.
Describe Parabola?A parabola is a type of curve that results from the intersection of a cone with a plane that is parallel to one of its sides. It is a conic section, which means it is a geometric shape that can be formed by cutting a cone with a plane.
The shape of a parabola is similar to that of a U-shaped curve, but it is symmetric around a vertical line called the axis of symmetry. The point where the axis of symmetry intersects the parabola is called the vertex.
The equation of a parabola can be written in different forms, but the most common form is:
y = ax^2 + bx + c
where "a", "b", and "c" are constants that determine the shape, position, and orientation of the parabola. If "a" is positive, the parabola opens upward, and if "a" is negative, it opens downward.
We can observe that the given graph passes through the points (-1,1), (0,2), (1,4), (2,8). This suggests that the graph is a parabola that opens upwards.
We can use the general form of a quadratic equation to write the equation of the parabola in the form y = ax² + bx + c, where a, b, and c are constants. Since the parabola opens upwards, we know that the coefficient of the x² term is positive.
To find the values of a, b, and c, we can substitute the coordinates of the given points into the equation and solve the resulting system of equations.
Using the point (-1,1), we get:
1 = a(-1)² + b(-1) + c
1 = a - b + c
Using the point (0,2), we get:
2 = a(0)² + b(0) + c
2 = c
Using the point (1,4), we get:
4 = a(1)² + b(1) + c
4 = a + b + c
Using the point (2,8), we get:
8 = a(2)² + b(2) + c
8 = 4a + 2b + c
Substituting c = 2 from the second equation into the third and fourth equations, we get:
4 = a + b + 2
8 = 4a + 2b + 2
Simplifying these equations, we get:
a + b = 2
2a + b = 3
Solving for a and b, we get:
a = 1
b = 1
Therefore, the equation of the parabola is y = x² + x + 2.
To check which of the given options matches this equation, we can simplify the equation:
y = x² + x + 2
y = (x + 1/2)² + 7/4
This shows that the given parabola is a vertical shift of the standard parabola y = x² by 7/4 units upward.
Out of the given options, the only equation that matches this form is option B, y = (1/2) * 2ˣ. Therefore, the answer is B) y= (1/2) * 2ˣ.
To know more about equation visit;
https://brainly.com/question/4074088
#SPJ1
Find the inverse of the function below and sketch by hand a graph of both the function and it’s inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. F(x)=x^2+2 with the domain x>0
The inverse function is as follows: f-1(x) = (x - 2) with y > 0 as the domain as limit the range of the inverse function to y > 0 .
what is function ?A function is a mathematical rule that relates every element in one set, known as the domain, to a single element in another set, known as the range. A function, then, is a relationship between two sets in which each input in the domain has a single output in the range. Equations, tables, graphs, and symbols can all be used to express it. Consider the function f(x) = 2x + 1 as an illustration. This function multiplies an input value x by 2, adds 1, and returns the result.
given
The steps listed below can be used to determine the inverse of the function f(x) = x2 + 2:
Step 1: Substituting y for f(x)
[tex]y = x^2 + 2[/tex]
Switch x and y in step 2:
[tex]x = y^2 + 2[/tex]
Step 3: Calculate y
[tex]x - 2 = y^2[/tex]
y = ± √(x - 2) (x - 2)
Since we want the inverse to be a function as well, we may limit the range of the inverse function to y > 0 because the original function's domain is x > 0.
The inverse function is as follows: f-1(x) = (x - 2) with y > 0 as the domain.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
