On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles in order to make renting from Company B a better deal
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so, we have -
Company A charges = $35 per day
plus = $0.45 per mile.
Company B charges = $60 per day
plus = $0.25 per mile.
McCall would need to drive 126 miles in order to make renting from Company B a better deal
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Alberto, bill, candela and diana are four friends
Here is some information about the height of each of these friends
Albertos height is 158 cm
bills height is 175cm
candelas height is greater than dianas height
the median height of these four friends is 160 cm
the range of the heights of these four friends is 21cm
work out candelas height and dianas height
Answer:
Candelas - 154cm
Dianas - 162 cm
Step-by-step explanation:
Median is the mean of the two middle numbers when the numbers are arranged in an ascending order.
We will first have to workout the order when they are placed in ascending order.
Note: Everything here is in ascending order.
Albertos cannot be the shortest as if that happened, the median will not be 160 (Dianas will have to be 179cm as the given range is 21 cm and the mean of Candelas and Bill can never be 160 cm.)
Albertos will have to be second as it cannot be third.( The median will not be 160 when the third number is greater than the second number.)
Now, Dianas will have to be third. ( It can't be first, nor it can be fourth as the median of the height will not be possible to be 160 again without changing the order.)
So, next, obviously, Candelas is first.
So, the order is,
Candelas, Albertos, Dianas, Bill
or,
Candelas , 158, Dianas, 175cm.
Dianas is 162 cm if the mean of 158 cm and Dianas's height is 160 cm.
Candelas's height is 175 - 21 = 154 cm
So the height of Candelas is 154 and height of Dianas is 162.
Which equation represents the function on the graph?
ANSWER CHOICES
A: f(x)= cos 1/4x
B: f(x)= sin 4x
C: f(x)= cos 4x
D: f(x)= sin 1/4x
The equation represents the function on the graph is f(x)= cos 4x.
What is the function on the graph?
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.
We have given,
A: f(x)= cos 1/4x
B: f(x)= sin 4x
C: f(x)= cos 4x
D: f(x)= sin 1/4x
To find the equation represent the function on the graph:
f(x) = cos 4x
let take the values on the x-axis of the graph,
x = п/2, п, 3п/2, 2п, 5п/2
For cos 360 degrees, the angle 360° lies on the positive x-axis. Thus cos 360° value = 1
Since the cosine function is a periodic function, we can represent cos 360° as, cos 360 degrees = cos(360° + n × 360°), n ∈ Z.
⇒ cos 360° = cos 720° = cos 1080°, and so on.
so, cos 4( п/2) = cos 4( 3п/2) = cos 4( 2п) = cos 4( 5п/2) = 1.
Hence, the equation represents the function on the graph is f(x)= cos 4x.
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quadrilateral abcd , was dilated to produce the image, quadrilateral A′B′C′D′ . The length of the side between vertices A and B is 5 inches. What is the length of the side between the vertices A′ and B′? Enter your answer as a fraction in simplest form by filling in the boxes. k12
Answer:Dilation is the increase or decrease in the size of a figure by a factor k. If a figure is dilated to produce an image, they are similar, hence the ratio of the corresponding sides are proportional. The length of the side between the vertices A′ and B′ is 16/7 units. Find out more on transformation at: brainly.com/question/1548871 Advertisement
Step-by-step explanation:
Find at least three different sequences starting with 1. 2, 4 where the terms are generated by a simple rule.
Here are three different sequences starting with 1, 2, and 4, where the terms are generated by a simple rule:
1, 2, 4, 8, 16, 32, ...
The rule for this sequence is to multiply the previous term by 2.
1, 2, 4, 7, 11, 16, 22, ...
The rule for this sequence is to add the previous two terms.
1, 2, 4, 8, 14, 24, ...
The rule for this sequence is to multiply the previous term by 2 and then subtract it from the previous term.
Note that there is an infinite number of different sequences that can be generated by simple rules.
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Please Help Soon
Simplify each of 10−8 and 8−10 to determine if the commutative property applies to subtraction. State your findings
Answer:
The communicative property does not apply to subtraction.
10 - 8 = 2
8 - 10 = -2
We do not get the same answer. 2 and -2 are not the same number.
Step-by-step explanation:
z is a standard normal random variable. the p(z ≥ 2.11) equals
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
To calculate the p(z ≥ 2.11), you can use a z-table to look up the z-score. This z-score falls in the area of the tail of the distribution, which means it is the area to the right of 2.11.
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
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PLEASE HELP ASAP!!!!! CORRECT ANSWER GETS BRAINLY
Answer:
(c) pr +ps +qr +qs
Step-by-step explanation:
You want to identify an expression that can be factored by grouping.
Factor by groupingThis method of factoring involves grouping terms that have a common factor, then factoring that out. If the entire expression can be factored by grouping, then the result of this first round of factoring is expressions that also have a common factor.
One expression that can be factored by grouping is ...
pr +ps +qr +qs
= p(r +s) +q(r +s) . . . . . . . each pair of terms is factored
Now we notice that the factor (r+s) is common to both terms, so we can factor this further:
= (p +q)(r +s)
The expression that can be factored by grouping is ...
pr +ps +qr +qs . . . . choice C
<95141404393>
If j = h and k = m, then which expression represents the value of g? triangle acb, point e is on segment ac between points a and c and point d is on segment bc between points b and c, creating segment ed, ce equals h, ea equals j, cd equals k, db equals m, ed equals g, and ab equals f g equals f over 2 g = 2f g equals j over h g equals k over m
By using The Pythagoras theorem, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A), i.e. g = 1/2 is correct.
Pythagoras theorem:
The Pythagorean Theorem, also known as the Pythagorean Theorem, describes the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides of the triangle. If AB and AC are the sides and BC is the hypotenuse of the triangle then BC2 = AB2 + AC2 .where AB is the base, AC is the height or altitude and BC is the hypotenuse.
The area of the square formed by the longest sides (hypotenuses) of right-angled triangles is equal to the sum of the areas. The number of squares formed by the other two sides of a right triangle. In a right triangle, the formula for the Pythagorean theorem is expressed as:
c² = a² + b²
where
'c' = hypotenuse of a right triangle
'a' and 'b' are the other two legs.
In the question:
It is given that:
If j = h and k = m
From the given question, C is a right-angle triangle as j = h and k = m
From the definition of the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides
h² +k²= g²
From the triangle ΔABC
(j + h)² +(m + h)² = f²
⇒ (h + h)² +(k+ k)² = f²
⇒ (2h)² +(2k)²= f²
⇒ 4h²+ 4k² = f²
⇒ 4(h²+k²) = f²
⇒ 4×g² = f²
⇒ (2g)² = f²
⇒ 2g = f
⇒ g = f/2
Thus, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A) is correct.
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Help me please yall id appreciate it
Is used to estimate the concentration of viable microorganisms in a sample by means of replicating liquid broth growth in ten-fold dilutions.
Find the measure of <IMN?According to the Side Angle Side (SAS) postulate, two sides and the included angle of one triangle must be congruent to two sides and the included angle of another triangle in order for these two triangles to be considered congruent.
A is measured at a 40° angle. Measurement in mathematics refers to the quantification of a variety of quantities, including length, weight, capacity, and volume. Any amount is measured and expressed in two parts: a numerical value and the particular unit.
The most often measured quantities are the following: Length. Measurement units can be expressed in writing as symbols, words, or abbreviations. Use the following words for fundamental measuring units: 25 pounds, 12 inches. Use the following symbols to denote derived units of measurement: 38 mph, 27 ft/s2.
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4
Complete each congruency statement, and name the rule used.
If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "CanNot Be Determined" in place of the rule.
Chapter Reference
b
M is the midpoint of
CI
△CAM ≅ △____ by ____
A
M
I
C
Answer:
△C AM ≅△
By rule
△TAN ≅ △LEF, by the SSS congruence theorem.
What is the SSS congruence theorem?The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.
From the triangles given by the image presented at the end of the answer, the congruent sides are given as follows:
NT and LE.TA and EF.AN and FL.(the congruence of each side is represented by the |, || and ||| notations).
As the three sides are congruent, we have that triangles TAN and LEF are congruent by the Side - Side - Side congruence theorem.
Missing InformationThe two triangles are given by the image presented at the end of the answer.
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a sumbmarine dives 300 feet every 2 minutes, and 6/750 feet every 45 minutes. find the constant rate at which the sumbmarine dives. give our answer in feet per minute and in feet per hour.
the constant rate at which the submarine dives is 30 feet per minute and 1,800 feet per hour.
feet per minute: 30 feet per minute
feet per hour: 1,800 feet per hour
We can calculate the rate of descent of the submarine by dividing the total distance it dives each time by the total time it took to dive.
For the first scenario where it dives 300 feet every 2 minutes, the rate of descent is 300/2 = 150 feet per minute.
For the second scenario, it dives 6/750 feet every 45 minutes so the rate of descent is 6/750 * 60/45 = 30 feet per minute.
Therefore, the constant rate at which the submarine dives is 30 feet per minute and 1,800 feet per hour.
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calculer la longueur dun cercle de diametre 78mm
Answer:
La circunferencia es 245.044 mm
Pham burgers has beginning net fixed assets of $684,218, ending net fixed assets of $679,426, and depreciation expense of $48,859. What is the net capital spending for the year if the tax rate is 21 percent?.
If Pham burgers has beginning net fixed assets of $684218 , ending net fixed assets of $679426 and depreciation expense of $48859 , then the net capital spending for the year is $44067 .
For the Pham burgers , the Beginning Net Fixed Assets is = $684218 ;
the ending net fixed assets for Pham burgers is = $679426 ;
the depreciation expense for Pham burgers is = $48859 ;
the tax rate is 21% , which is not relevant for this question ;
The Net capital Spending for the year can be calculated using the formula :
[tex](Ending \; Net \; Fixed \;Assets - Beginning \; Net\; Fixed \; Assets) + Depreciation[/tex] ;
substituting the required values ,
we get ;
Net Capital Spending for year is = ($679426 - $684218) + $48859 ;
On simplifying ,
we get ;
= $44067 .
Therefore , the Net Capital Spending for the year is $44067 .
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A map has a scale of 1 : 500.
Martha measures a distance of
5 cm on the map. What actual
distance in m does this
correspond to?
Answer: it is 0.05 m
seniors at a certain high school took a survey regarding future plans. all plan to attend college some time; however, 77% plan to go to college immediately following high school. of those who plan to attend college immediately following high school, 17% plan to major in math. of those who do not plan to attend college immediately following high school, 11% plan to major in math. what is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in math.
The probability that a randomly chosen senior does not plan to attend college right away and majors in math is 12.5%.
Step 1: Calculate the probability of not attending college immediately after high school:
100% - 77%
= 23%
Step 2: Calculate the probability of majoring in math among those who do not attend college right away: 11%
Step 3: Calculate the probability of not attending college right away and majoring in math:
11% / 23%
= 0.125
The probability of a randomly chosen senior not attending college immediately following high school and majoring in math can be calculated by first determining the probability of not attending college right away. This can be done by subtracting the percentage of seniors who plan to attend college immediately from 100%. This yields 23%. Then, the probability of majoring in math among those who do not attend college right away can be determined by taking the percentage of those who plan to major in math among this group, which is 11%. Lastly, the overall probability of not attending college right away and majoring in math can be calculated by taking the probability of majoring in math among those who do not attend college right away and dividing it by the probability of not attending college right away. This yields 11% / 23%, or 0.125.
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you are treating a 50-year-old man that was involved in a fire. he suffered 25% 2nd-3rd degree burns to the anterior chest, neck and face. he has singed nasal hairs, and you identify stridor on your primary survey. pulse oximetry is 88% on a 100% non-rebreather mask. a burn center is 45 miles away. the next most appropriate step prior to transfer is:
A 100% non-rebreather mask has a pulse oximetry reading of 88%. There is a burn centre 45 miles distant. the best course of action to do after transferring a serious burn side.
A 50-year-old man who was injured in a fire is being treated by you. He sustained 25% 2nd–3rd degree burns to his face, neck, and anterior chest. He has burned nasal hairs, and your initial survey reveals stridor.
Any damage that exceeds 10% in size should be treated in a similar manner, although significant burns are classified as those that encompass 25% or more of the total body surface area. Rapid evaluation is essential. Any blaze can be managed using the general strategy for a significant burn. The most crucial things are to take a thorough history.
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A can of motor oil weighs 31 ounces. When one half of the oil in the can has been poured
out of the can and the remaining can and oil weighs 16 ounces how much does the can
weigh?
The value weight of the can is 1 ounce
What is subtraction?To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less. The minuend, subtrahend, and difference are parts of a subtraction problem.
The total weight of the can and oil is 31 ounces .
When ½ of the the oil is poured the weight of the can and oil is 16 ounces.
Therefore the weight of ½ of oil is 31-16 = 15 ounces
if ½ of the oil weighs 15 ounces
full oil will weigh 15× 2 = 30 ounces
the weight of the can = 31-30 = 1ounce
Therefore the weight of the can is 1 ounce
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1. Write the explicit formula for the sequence below
The explicit formula for the arithmetic sequence 40, 37, 34, 31 is given as follows:
[tex]a_n = 40 - 3(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In the sequence, each term is the previous term subtracted by three, hence the common difference is given as follows:
d = -3.
The first term is of:
[tex]a_1 = 40[/tex]
Hence the explicit formula is given as follows:
[tex]a_n = 40 - 3(n - 1)[/tex]
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please help me answer this question
Check the picture below.
notice, times where he stops, is time where distance is not added however time elapses, meaning we get a straight line, when chatting with his friend, it went from 10 minutes to 15 minutes over the same 800 meters, in other words, he never moved, time kept on going for 5 minutes. When he gets back home, distance goes from 2000 meters to 0 meters, 0 meters because he's back at 0 distance after 90 minutes.
An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29º. Her clinometer is 28 meters from the base of the tree and is on a tripod making it 1.5 meters above ground level. How tall is the tree? Show all your work.
An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29º, The height of the tree is 17.03 meters
What is the height?Generally, To find the height of the tree, we can use the tangent function and some basic trigonometry. The tangent of an angle is the ratio of the opposite side (the height of the tree) to the adjacent side (the distance from the base of the tree to the clinometer).
tan(29) = opposite / adjacent
We know that the distance from the clinometer to the base of the tree is 28 meters, and that the clinometer is 1.5 meters above ground level.
So we can use the Pythagorean theorem to find the adjacent side:
adjacent = √(28^2 + 1.5^2)
= 28.03 meters
Now we can use the tangent function to find the opposite side:
opposite = tan(29) * adjacent
Using a calculator we can get the opposite = 15.53 meters
The height of the tree is opposite + 1.5 (the clinometer height) '
= 15.53 + 1.5
= 17.03 meters
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a) we roll 50 dice to find the distribution of the number of spots on the faces. b) howlikelyisitthatinagroupof120themajority may have type a blood, given that type a is found in 43% of the population? c) we deal 7 cards from a deck and get all hearts. how likely is that? d) we wish to predict the outcome of a vote on the school budget, and poll 500 of the 3000 likely voters to see how many favor the proposed budget. e) a company realizes that about 10% of its packages are not being sealed properly. in a case of 24, is it likely that more than 3 are unsealed?
We can use probability to find the answers to the questions - the final answers are given below.
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
We will answer each part in detail.
Part (a)
No, there are more than 2 outcomes in this particular scenario.
Part (b)
Yes, there are two outcomes (Type A or not).
Part (c)
No, probability changes as the cards are dealt.
Part (d)
No, the trials are not independent.
Part (e)
Yes, two outcomes (more than 3 or not)
These are the final answers:
(a): No
(b): Yes
(c): Yes
(d): No
(e): Yes
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Janine is getting a new phone. She needs to purchase her phone, which
is $850. Then each month will be $65.
Write an equation for total cumulative cost (C) per month (m).
C(m) = 850 + 65m is the formula for the total cumulative cost (C) per month (m).
Word problems involving linear equationsLinear equations are equations that has a leading degree of 1. An example of a linear equation is y = mx + b
where:
m is the slopeb is the y-interceptAccording to the given question, Janine is getting a new phone. She needs to purchase her phone, which is $850.
Amount paid monthly = $65
If she completes the payment in 'm' months, the equation for total cumulative cost (C) per month (m) is C(m) = 850 + 65m
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In the first table of values, how does n differ from f(n)? in other words, what do n and f(n) mean?
N and f(n) is totally different by their own circumstances.
how does n differ from f(n)?N is independent variables
And f(n) is dependent variable
These are the main difference about n and f(n),You can typically depend on f(n) to represent the value of the function f at n. fn might mean f(n), especially when the domain is natural numbers, but it usually denotes the nth function in a sequence of functions.
F(a,b) would mean that the function takes two values, a and b. Your function takes one argument, n.
For example, f(n) might be the number of eggs in n packages, where each package has a dozen eggs. That would be f(n) = 12n, so f(3) = 12 * 3 = 36.
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(2x + 4) ( x- 4)
I need help
need to be 20 character long so the answer is 2x²+12x-16 the answer is C
(Graphing Linear Equations MC)
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $120, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 100
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 120 through the point 2 comma 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 140
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 120 through the point 2 comma negative 100
Answer:
"going from the point 0 comma negative 120 through the point 2 comma negative 100"
Step-by-step explanation:
Let y be the total income from the homecoming dance, and x the number of students who purchase tickets (at $10 each). We are told that it costs $120 for the decorations.
The income from ticket sales would be:
1) the number of tickets sold times $10/ticket, or $10
2) Less the expenses of decorating (-$120)
We can write the total income as:
y = $10x - $120
The graph of this function would be a straight line that has a y-intercept of -$120. Before any ticket is sold, the cost of decorations must be considered. If no tickets are sold (x=0), the total income is -$120.
Using the equation, we can calculate the income when 2 tickets are sold (x=2):
y = $10x - $120
y = $10*(2) - $120 [two tickets sold]
y = -$100
Summary
y = $10x - $120
(0,-$120)
(2,-$100)
This matches the statement "going from the point 0 comma negative 120 through the point 2 comma negative 100" provided in the answer options.
See the attached graph.
karen collected data from a random sample of 1200 homeowners in her state asking whether or not they use electric heat. based on the results, she reports that 50% of the homeowners in the nation use electric heat. why is this statistic misleading?
The statistic is misleading because the sample is biased.
The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
Thus, the statistic is misleading because the sample is biased.
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I WILL MARK YOU AS BRAINLIEST IF YOU SOLVE THIS FOR ME
Consider the line -7x - 5y = -1
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
Slope of a parallel line : [tex]\boxed{-\frac{7}{5}}[/tex]
Slope of a perpendicular line: [tex]\boxed{\frac{5}{7}}[/tex]
Step-by-step explanation:
Parallel lines have same slope
Perpendicular line will have a slope which is the negative of the reciprocal of the line. In other words, the product of the two slopes should be - 1
[tex]\textrm{First convert the line equation to slope-intercept form } y = mx + b\\\\-7x - 5y = -1\\\\\textrm{Add 7x to both sides }\\\\-5y = 7x -1\\\\\textrm{Divide both sides by -5}\\\\y = -\dfrac{7}{5} x+ \dfrac{1}{5}\\\\[/tex]
The slope of this line is
[tex]-\dfrac{7}{5}[/tex]
which is the coefficient of x
A parallel line will also have the same slope of
[tex]-\dfrac{7}{5}[/tex]
ANSWER 1
A perpendicular line will have slope
[tex]- \dfrac{1}{-\dfrac{7}{5}} = \dfrac{5}{7}[/tex]
ANSWER 2
Check by multiply both slopes to see if it results in - 1
[tex]-\dfrac{7}{5} \times \dfrac{5}{7} = -1[/tex]
Step-by-step explanation:
always bring the equation into the form
y = ...
in that case the slope is simply the factor of x.
-7x - 5y = -1
-5y = 7x - 1
y = (-7/5)x + 1/5
so, the slope is -7/5.
a parallel line must have the same slope : -7/5.
a perpendicular slope turns the original y/x slope upside-down and flips the sign :
5/7
Let a function
of 2 variables be defined by h(x, y) = x² + 3xy-(y-x), what is the value of h(5,4)
The value of h(5,4) is 86 in the given function h(x, y) = x² + 3xy-(y-x)
What is a function ?
function can be defined as the relation in which it relates an input to the output.
Given ,
Let a function of 2 variables be defined by
h(x, y) = x² + 3xy-(y-x),
So, the value of h(5,4)
put x = 5 and y = 4 in the function h(x, y) = x² + 3xy-(y-x)
h (5,4) = 5*5 + 3*5*4 - (4-5)
h(5,4) = 25 + 60 - (-1)
h(5,4) = 25+60+1
h(5,4) = 86
Hence, The value of h(5,4) is 86
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a norma window has the shape of a rectangle surmounted by a semicircle of diameter equal to the width of the rectangle. if the perimeter of the window is 10m what is the dimension will admit the most lighT
The dimensions that will admit the most light are, the breadth of the rectangular window is [tex]2b = \frac{20+10\pi }{4+3\pi }[/tex], the length of the window is [tex]2l = \frac{40}{4+3\pi }[/tex] and the radius of the semicircular arc is [tex]l= \frac{20}{4+3\pi }[/tex].
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. "Composite figures" or "composite shapes" are shapes created by combining two or more simple shapes. To determine the area of a composite form, we must add up the areas of all the shapes that make up the figure.In the given question,
Let the length and breadth of the rectangular part of the window be 2l and 2b respectively. So the radius of the semicircular arc will be l.
The total perimeter of the window will be 1 length of the rectangle, 2 breadths of the rectangle, and the length of the semicircular arc.
l+2b+πl = 10
(1+π)l+2b = 10
[tex]b = \frac{1}{2} [10-(1+\pi )l][/tex]
To admit maximum light through the window implies that the area of the window is maximized.
The area of the window will be:
[tex]A = (2l)(2b)+\frac{\pi l^{2} }{2}[/tex]
[tex]= 4lb+\frac{\pi l^{2} }{2} \\= 2l[10-(1+\pi )l] +\frac{1}{2} \pi l^{2}[/tex]
[tex]= 20l-2l^{2} -2\pi l^{2} +\frac{1}{2} \pi l^{2}[/tex]
[tex]= 20l-2l^{2} - \frac{3}{2} \pi l^{2}[/tex]
For the area to be maximum,
[tex]\frac{dA}{dl} =0\\20 -4l -3\pi l = 0\\l= \frac{20}{4+3\pi }[/tex]
[tex]b = \frac{1}{2} [10-(1+\pi )\frac{20}{4+3\pi }\\b = \frac{10+5\pi }{4+3\pi }[/tex]
Therefore, the breadth of the rectangular window is [tex]2b = \frac{20+10\pi }{4+3\pi }[/tex], the length of the window is [tex]2l = \frac{40}{4+3\pi }[/tex] and the radius of the semicircular arc is [tex]l= \frac{20}{4+3\pi }[/tex].
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Show all work to identify the asymptotes and state the end behavior of the function f of x is equal to 4x divided by the quantity of x minus 16 end quantity.
Answer:
Step-by-step explanation:
The function f(x) = 4x/(x-16) has two vertical asymptotes at x = 16. This can be seen by taking the limit of the function as x approaches 16 from the left and right sides.
On the left side, as x approaches 16 from the left, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach -∞. This results in a limit of -∞, indicating a vertical asymptote at x = 16.
On the right side, as x approaches 16 from the right, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach +∞. This results in a limit of +∞, also indicating a vertical asymptote at x = 16.
The end behavior of the function is that as x approaches +∞, the function will approach +∞, and as x approaches -∞, the function will approach -∞.
