The maximum value of Q was found to be 26.49 subject to the cost constraint K+4L=16.2, and the optimal value of Q decreased by approximately 9.39 when the cost constraint was changed to K+4L=17.
To find the maximum value of Q subject to the cost constraint, we can use the method of Lagrange multipliers. We first define the Lagrangian function:
L(K, L, λ) = 10√(KL) + λ(K + 4L - 16.2)
where λ is the Lagrange multiplier.
∂L/∂K = 5√(L/K) + λ = 0
∂L/∂L = 5√(K/L) + 4λ = 0
∂L/∂λ = K + 4L - 16.2 = 0
K = 3.24, L = 2.16, λ = -2.5
Therefore, the maximum value of Q is:
Q = 10√(3.24*2.16) = 10√7.0224 ≈ 26.49
If the cost constraint is changed to K+4L=17, we can repeat the same process with the new constraint to get:
K = 4.25, L = 0.6875, λ = -2.5
Therefore, the new maximum value of Q is:
Q = 10√(4.25*0.6875) = 10√2.9297 ≈ 17.10
The change in the optimal value of Q is then:
17.10 - 26.49 ≈ -9.39
The optimal value of Q decreases by approximately 9.39 when the cost constraint is changed from K+4L=16.2 to K+4L=17. This indicates that the optimal value of Q is sensitive to changes in the cost constraint.
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Find the maximum value of Q = 10√/KL subject to the cost constraint K+4L=16.
Estimate the change in the optimal value of Q if the cost constraint is changed to K+4L =17. Interpret the meaning of Lagrange multiplier.
Ted invests in an annuity which earns 6.2% annual interest and he contributes $250 per month for 30 years. If Ted wants to perform some calculations to determine his future value, what formula would Ted use?
The future value of Ted's investment after 30 years would be approximately $13,711.86.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
Ted can use the formula for the future value of an annuity to calculate the future value of his investment:
FV = Pmt x (([tex](1 + r)^{n}[/tex]) - 1) / r
Where:
FV = Future Value
Pmt = Payment per period (monthly in this case)
r = Interest rate per period (monthly in this case)
n = Number of periods (in this case, 30 x 12 = 360 months)
Substituting the given values, we get:
FV = $250 x (([tex](1 + 0.062/12)^{360}[/tex] - 1) / (0.062/12)
FV = $250 x (283.8576) / 0.0051667
FV = $13,711.86
Therefore, the future value of Ted's investment after 30 years would be approximately $13,711.86.
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Find the slope of a line perpendicular to the line whose equation is 5x + 6y = - 18.
Fully simplify your answer.
Answer:
m = [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
First, we must rewrite 5x + 6y = - 18 to the form y = mx + b.
5x + 6y = -18
6y = -5x - 18
y = [tex]\frac{-5}{ 6}[/tex]x - 3
The equation of a perpendicular line to y = [tex]\frac{-5}{ 6}[/tex]x - 3 must have a slope that is the negative reciprocal of the original slope.
So, the slope of the perpendicular line is
m = [tex]\frac{6}{5}[/tex]
Answer: 6/5
Step-by-step explanation:
trust me
I have an Amazon account that I pay a flat rate of $8 a month. With it, I get free movies and shows. However, any premium movie I purchase costs me $4 more. If I spent $24 last month, how many premium movies did I buy?
The equation would be set up as shown below:
(Let x represent the amount of premium movies I bought.)
4x + 8 = 24
next: subtract 8 from both sides = 4x = 16
then: divide both sides by 4, which gives us our answer = x = 4
So I purchased 4 premium movies.
What are your examples or equations in your day-to-day life
help mee with this question
Answer: 22
Step-by-step explanation:
The first one is 10.
The other 2 has 6, because 10-4=6
So
10+(6x2)=22
URGENT NEED HELP PLEASE ♥️
Can someone give me the answer and explain how they solved it
log 2 + 1
Answer:
(i) log 1 base 2 = log_{2} 1 =1.30103
Step-by-step explanation:
pl z give me brainliest i don't have any
Select the correct answer. Which expression is equivalent to the given expression? 4 in x + in 3 - in x
Answer:
The expression 4 in x + in 3 - in x can be simplified using logarithmic rules: 4 in x + in 3 - in x = in x^4 + in 3 - in x = in (x^4 * 3 / x) = in (3x^3) Therefore, the expression is equivalent to in (3x^3).
Allison uses 3
inches of fabric to make a bookmark. She buys 412
feet of fabric.
How many bookmarks can Allison make with 412
feet of fabric?
Allison can make 1648 bookmarks with 412 feet of fabric.
First of all, the total length of fabric, and the length of each bookmark have different units.
Therefore, we convert fabric length into inches.
∵ 1 foot = 12 inches
∴ 412 feet = 412 × 12 inches
= 4944 inches.
Now,
length of each bookmark = 3 inches (given)
Total length of fabric in inches = 4944 inches
∴ Total number of bookmarks = 4944 ÷ 3
= 1648
Hence we find that the total number of bookmarks that Allison can make from 412 feet of fabric is 1648.
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help real quick! brainliest to the correct answer
Answer:
[A] Multiply the bottom equation by -3/2, then add the equations.
[C] Multiply the top equation by -3, then add the equations.
Step-by-step explanation:
You want to know a suitable "elimination" strategy for the two equations ...
2x -6y = 66x -4y = 2EliminationThe result of an elimination strategy is that one of the variables in the combined equations has a coefficient of 0. If we add the equations as a final step, the coefficients must be opposites for that to happen.
RatiosThe ratios of variable coefficients in the top equation to those in the bottom equation are ...
x: 2/6 = 1/3y: -6/-4 = 3/2A suitable elimination strategy will multiply one of the equations by a value that makes this ratio -1. Let's look at the choices.
A. Bottom by -3/2Multiplying the bottom equation by -3/2 makes the ratio of x-coefficients be ...
[tex]\dfrac{1}{3}\times\dfrac{1}{\left(-\dfrac{3}{2}}\right)}=-\dfrac{2}{9}\ne -1[/tex]
Multiplying the bottom equation by -3/2 makes the ratio of y-coefficients be ...
[tex]\dfrac{3}{2}\times\dfrac{1}{\left(-\dfrac{3}{2}\right)}=-\dfrac{6}{6}=-1[/tex]
This is a suitable strategy for eliminating the y-variable.
B. Bottom by 3, then subtract itThis strategy is equivalent to multiplying the bottom equation by -3, then adding. This will make the x-coefficient ratio be ...
[tex]\dfrac{1}{3}\times\dfrac{1}{\left(-3}\right)}=-\dfrac{1}{9}\ne -1[/tex]
Multiplying the bottom equation by -3 makes the ratio of y-coefficients be ...
[tex]\dfrac{3}{2}\times\dfrac{1}{-3}=-\dfrac{3}{6}\ne-1[/tex]
Not a suitable strategy for elimination.
C. Top by -3Multiplying the top equation by -3 makes the ratio of x-coefficients be ...
[tex]\dfrac{1}{3}\times\dfrac{-3}{1}}=-\dfrac{3}{3}= -1[/tex]
This is a suitable strategy for eliminating the x-variable.
Choices A and C are suitable strategies for eliminating a variable.
A swimmer dives into a lake and swims to the surface in a parabolic path. path of the swimmer can be modeled by the equation
h (t) = t - 4t-where h is the height in
feet, and t is the time in seconds.
Complete the statement.
The diver will reach the surface of the water
after seconds.
Answer:
the diver will reach the surface of the water after 1/4 seconds.
Step-by-step explanation:
To find when the swimmer reaches the surface of the water, we need to set h(t) to zero since the surface of the water is at a height of zero feet.
0 = t - 4t^2
Simplifying the equation, we get:
4t^2 = t
4t^2 - t = 0
t(4t - 1) = 0
So, either t = 0 (which corresponds to the initial time when the swimmer is at the surface) or 4t - 1 = 0. Solving for t, we get:
4t - 1 = 0
4t = 1
t = 1/4
Therefore, the diver will reach the surface of the water after 1/4 seconds.
select the correct answer from each drop-down menu. a bag contains five tiles numbered 1 through 5. savannah randomly selects a tile from the bag, replaces the tile, and then draws a second tile. when savannah selects her tiles, selecting the first tile and selecting the second tile are (options on drop down. independent or dependent) events. the probability that the numbers on both tiles are even is (choices on drop down. 20, 40, 10, 16)%.
Selecting the first tile (1st) and selecting the secοnd tile (2nd) are independent events.
The prοbability οf selecting an even number οn a single draw is 2/5 οr 0.4, as there are twο even numbers (2 and 4) οut οf a tοtal οf five pοssible numbers.
Since the events are independent, the prοbability οf selecting an even number οn bοth draws is the prοduct οf the prοbabilities οf selecting an even number οn each draw:
P(bοth even) = P(even οn first) × P(even οn secοnd) = 0.4 × 0.4 = 0.16
Sο the prοbability that the numbers οn bοth tiles are even is 16%.
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Please answer this somebody that’s good at math I have been posting this and nobody answered:(
Answer: 30 inches
Step-by-step explanation:
Length x Width x Height
Your length is 2, your height is 3 and your width is 5. So this means 2x3x5.
2 times 5 equals 10. 10 times 3 equals 30. Your answer is 30! Hope this helps you!
one paycheck is $250 less than another. The sum of the two checks is &1628. how much is each check written for.?
Answer: $939 and $689
Step-by-step explanation:
We can create a system of equations to help us solve. Let x be one and y be the other paycheck.
y = x - $250
y + x = $1,628
Next, we can solve the system of equations by graphing. The point of intersection is our solution. See attached. This gives us (939, 689), so one check was written for $939 and one was written for $689.
Which of the following are the next three terms in the sequence (1, 2, 3, 9, -27, 81, ..}?
The next three terms are:
-243, 729, -2187
The equation y32.92-572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, z, in degrees Fahrenheit (F)
Complete the statements
When the outside temperature is 30°F, the sales are estimated to be
When the outside temperature is [DROP DOWN 21, the sales are estimated to be $1,993.33
When the outside temperature is 30°F, the sales are estimated to be $414.73.
The outside temperature is approximately 78.03°F, the sales are estimated to be $1,993.33.
Define temperatureIt refers to a physical property of matter that reflects how hot or cold an object is relative to other objects or a standard scale. Temperature is typically measured in units such as Celsius (°C), Fahrenheit (°F), or Kelvin (K).
When the outside temperature is 30°F, the sales are estimated to be:
y = 32.92(30) - 572.87
y = 987.60 - 572.87
y = $414.73
Therefore, when the outside temperature is 30°F, the sales are estimated to be $414.73.
When the outside temperature is x, the sales are estimated to be $1,993.33, we can solve for x as follows:
1,993.33 = 32.92x - 572.87
2,566.20 = 32.92x
x ≈ 78.03°F
Therefore, when the outside temperature is approximately 78.03°F, the sales are estimated to be $1,993.33.
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One square has a side 3 cm greater than the side of a second square. What are lengths of the sides if the sum of their areas is 1017 cm2. (Make sure to foil your product on the squares)
Using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.
What are squares?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.
It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.
The square's four sides are equal to one another or congruent.
The square's opposing sides run parallel to one another.
The square's diagonals form a 90° angle with one another.
The square's two diagonals are equal to one another.
Area: s²
s² + (s+3)² = 1017
s² + s² + 9 = 1017
2s² = 1017 - 9
2s² = 1,008
s² = 1008/2
s² = 504
s = ²504
s = 22.44
Round off: 22 cm
Then, (s+3) = 22 + 3 = 25 cm
Therefore using the area formula, the length of the sides of the two squares are 22 cm and 25 cm respectively.
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Y varies inversley with x. If y = -2 when x = 6, find the value of y when x = -12.
The value of y for the inverse variation when x = -12 is derived to be equal to 1.
What is inverse variationInverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.
when x = 6 and y = -2, then k is derived as:
-2 = k/6
k = -12 {cross multiplication}
when x = -12, y is derived as:
y = -12/-12
y = 1
Therefore, the value of y for the inverse variation when x = -12 is derived to be equal to 1.
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What is the diameter of a hemisphere with a volume of 62617 cm³, to the nearest tenth of a centimeter?
The diameter of the hemisphere to the nearest tenth of a centimeter is 62.1 cm.
What is hemisphere?
A hemisphere is a three-dimensional geometric shape that consists of a half-sphere, which is a curved surface that is shaped like the surface of a ball, and a flat circular base that lies on a plane perpendicular to the sphere's axis of symmetry. A hemisphere can be thought of as the three-dimensional analogue of a circle.
The volume of a hemisphere is given by the formula:
V = (2/3)π[tex]r^3[/tex]
where V is the volume and r is the radius of the hemisphere.
We are given the volume of the hemisphere as 62617 [tex]cm^3.[/tex]
So, we have:
62617 = (2/3)π[tex]r^3[/tex]
Multiplying both sides by 3/2π, we get:
[tex]r^3[/tex] = 62617 * (3/2π)
Simplifying, we get:
[tex]r^3[/tex] = 29897.4152
Taking the cube root of both sides, we get:
r ≈ 31.04
The diameter of the hemisphere is twice the radius, so:
d = 2r ≈ 62.08
Rounding to the nearest tenth, we get:
d ≈ 62.1
Therefore, the diameter of the hemisphere to the nearest tenth of a centimeter is 62.1 cm.
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Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
tan θ / sec θ
if correct brainest! look at picture
Answer:
x = 47
Step-by-step explanation:
All angles in a triangle ALWAYS add up to 180 degrees, so to find a missing angle, subtract what is already given. It will be 180 - (102+31), which is the same as 180-133 which equals 47. The basic rule is to subtract given angels from 180 to find the missing side.
Translate the argument to symbols and use a truth table to determine whether the argument is valid or invalid.
If it rains, then I will watch the Real World marathon.
It did not rain.
.. I did not watch the Real World marathon.
Let p="It rains," and let q="I will watch the Real World marathon."
Part: 0/4
Part 1 of 4
(a) Write the argument in symbols.
Translated into symbols:
If it rains, then I will watch the Real World marathon.
It did not rain.
.. I did not watch the Real World marathon.
The argument to symbols of the logic expression is shown below
Translating the argument to symbolsFrom the question, we have the following parameters that can be used in our computation:
If it rains, then I will watch the Real World marathon.It did not rain.I did not watch the Real World marathon.The argument in symbols can be expressed as:
p -> q
~p
Therefore, ~q
Where:
p = "It rains."
q = "I will watch the Real World marathon."
"->" denotes "implies".
"~" denotes "not".
So the argument can be read as "If it rains, then I will watch the Real World marathon. It did not rain.
Therefore, I did not watch the Real World marathon."
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Mr. Campbell has just purchased supplies for his classroom. He bought 76 markers, 31 rulers, and one projector. The markers cost 0.90 each, the rulers 1.60 each, and the projector 97.95 . What was the total amount that he spent?
Answer:
215.95
Step-by-step explanation:
68.4+49.6+97.95
the diameter of each tire on a vehicle is 32 inches. if the tires are moving at a rate of 800 revolutions per minute, find the linear speed of the vehicle in miles per hour.
Answer:
The linear speed of the vehicle is approximately 0.798 miles per hour.
Step-by-step explanation:
The circumference of a tire is given by the formula C = πd, where d is the diameter of the tire. So, the circumference of each tire is:
C = πd = π(32 inches) ≈ 100.53 inches
Now, to find the distance that the vehicle travels in one revolution of each tire, we use the circumference formula again:
distance traveled in one revolution = circumference of the tire = 100.53 inches
Since the tires are rotating at a rate of 800 revolutions per minute, the vehicle travels a distance of:
distance traveled in one minute = distance traveled in one revolution × number of revolutions per minute
= 100.53 inches/revolution × 800 revolutions/minute
= 80424 inches/minute
To convert this to miles per hour, we need to divide by the number of inches per mile and the number of minutes per hour:
speed = (80424 inches/minute) × (1 mile/63360 inches) × (60 minutes/1 hour)
≈ 0.798 miles/hour
Therefore, the linear speed of the vehicle is approximately 0.798 miles per hour.
A company that teaches self-improvement seminars is holding one of its seminars in Wildgrove. The company pays a flat fee of $164 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $8 to purchase books and supplies. Each attendee will pay $49 for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take? What will be the company's total expenses and revenues?
The company's total expenses and revenues will both be $196 when 4 attendees register.
What is Algebraic expression ?
In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.
Let's assume that the company's goal is to break even, which means that their total revenue should be equal to their total expenses.
Let's represent the number of attendees by "x." For the company to break even, the total revenue earned from x attendees must be equal to the total expenses incurred.
Total Expenses = Fixed Cost + Variable Cost
Fixed cost = Facility rent fee = $164
Variable cost = Books and supplies per attendee = $8
Total Expenses = $164 + $8x
Total Revenue = Price per attendee x Number of attendees = $49x
To find the break-even point, we set the total revenue equal to the total expenses and solve for x:
$49x = $164 + $8x
$41x = $164
x = 4
Therefore, the company needs to have 4 attendees to break even.
To calculate the total expenses and revenues, we can substitute x = 4 into the equations we derived above:
Total Expenses = $164 + $8(4) = $196
Total Revenue = $49(4) = $196
Therefore, the company's total expenses and revenues will both be $196 when 4 attendees register.
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Solve for x. Please due soon
The value of x for measure a base angle for the isosceles trapezoid is equal to 25°.
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
angle C is equal to angle D so;
3x + 1 = 76°
3x = 76° - 1 {subtract 1 from both sides}
3x = 75°
x = 75°/3 {divide through by 3}
x = 25°
Therefore, the value of x for measure a base angle for the isosceles trapezoid is equal to 25°.
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Need to find x using the Pythagorean Theorem
Answer:
1. 15
2. 26
3. ≈ 7.62
4. 8
5. ≈ 23.24
6. √2
7. ≈ 19.42
8. 18
9. x≈10.29 y≈5.83
Step-by-step explanation:
Use a²+b²=c² throughout the problems and plug in the given sides and hypothenuse.
1. 9²+12²=c²
81+144=225
√225 = 15
2. 10²+24²=c²
100+576=676
√676=26
3. 7²+3²=c²
49+9=58
√58 ≈ 7.62
4. a²+6²=10²
a²+36=100
a²=64
x=8
5. a²+6²=24²
a²+36=576
a²=540
x≈ 23.24
6. 1²+1²=c²
1+1=2
x=√2
7. a²+8²=21²
a²+64=441
a²=377
x≈ 19.42
8. a²+24²=30²
a²+576=900
a²=324
x=18
9. for x:
9²+5²=x²
81+25=106
√106 ≈10.29
x ≈10.29
for y:
5²+3²=y²
25+9=34
√34 ≈5.83
y ≈5.83
boom shakalaka
Suppose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. Also, suppose that the distribution's mean is 470 and its standard deviation is 10.
This information can be used to understand the performance of the students and Evaluate their scores in relation to the overall group.
Suppose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. In this scenario, the distribution's mean is 470 and its standard deviation is 10.
A normal distribution, also known as a Gaussian distribution or bell curve, is a symmetric distribution where the majority of the data falls around the mean value. In this case, the mean score is 470, which represents the average intelligence score for the 1,000 students. The standard deviation, which is 10 in this case, measures the dispersion or spread of the data around the mean.
To interpret the scores, we can use the empirical rule, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Applying this rule:
- About 68% of the students scored between 460 (470-10) and 480 (470+10).
- Approximately 95% of the students scored between 450 (470-2*10) and 490 (470+2*10).
- Around 99.7% of the students scored between 440 (470-3*10) and 500 (470+3*10).
This information can be used to understand the performance of the students and evaluate their scores in relation to the overall group.
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2. the new principal is $58,254.26. For payment 329, find the following:
a) The interest on $58,254.26
$
b) The payment to principal
$
c) The new principal
$
The interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.
What is payment?Payment is the transfer of funds from one party to another in exchange for goods, services, or to fulfill a legal obligation. Payment can take various forms, including cash, check, credit card, money order, or electronic transfer. Payment can be made in person, over the phone, or online. The most important aspect of payment is that it is a legally binding contract between two parties. Payment is an important part of the economic system that facilitates the exchange of goods and services and helps to ensure that all parties involved receive what they expect from the transaction.
The interest on $58,254.26:
To calculate the interest on $58,254.26, we first need to determine the interest rate. Assuming that the interest rate is 3%, we can calculate the interest owed as follows:
Interest = Principal x Interest Rate x Time
Interest = $58,254.26 x 0.03 x 1/12
Interest = $146.38
b) The payment to principal:
To calculate the payment to principal, we need to subtract the interest from the total payment amount.
Payment to Principal = Total Payment – Interest
Payment to Principal = $329 - $146.38
Payment to Principal = $182.62
c) The new principal:
To calculate the new principal, we need to subtract the payment to principal from the original principal.
New Principal = Original Principal – Payment to Principal
New Principal = $58,254.26 - $182.62
New Principal = $58,071.64
In conclusion, the interest on $58,254.26 was calculated to be $146.38, the payment to principal was calculated to be $182.62, and the new principal was calculated to be $58,071.64.
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complete the square to determine all solutions for x^2-4x=2
Answer: To complete the square, we need to add and subtract the square of half the coefficient of x:
x^2 - 4x = 2
x^2 - 4x + 4 = 2 + 4 (adding and subtracting 4)
(x - 2)^2 = 6
Now we take the square root of both sides:
x - 2 = ±√6
Adding 2 to both sides gives:
x = 2 ± √6
So the solutions are:
x = 2 + √6, 2 - √6
Step-by-step explanation:
which number line shows the solotion to one fourth r plus one < five
After looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.
What is a number line?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics.
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A number on the left of a number line is always smaller than a number on the right.
A number to the right is always greater than a number to the left, too.
So, the inequality we have is:
1/4 + 1 < 5
Now, after observing the given lines, we can easily tell that the number line (B) represents 1/4 + 1 < 5 perfectly.
Therefore, after looking at the provided number lines, it is clear that the number line (B) accurately reflects 1/4 + 1 < 5.
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Complete question:
Which number line shows the solution to 1/4 + 1 < 5
use double angle identity to simplify the following expression
tan 12 degrees/1-tan^2 12 degrees
Answer: We can use the double angle identity for tangent, which states that:
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
to simplify the expression.
Let θ = 6 degrees, then we have:
tan(2θ) = tan(12 degrees)
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
tan(12 degrees) = 2tan(6 degrees) / (1 - tan²(6 degrees))
We can use the tangent half-angle identity to find tan(6 degrees), which states that:
tan(θ/2) = sin(θ) / (1 + cos(θ))
Letting θ = 12 degrees, we get:
tan(6 degrees) = sin(12 degrees) / (1 + cos(12 degrees))
We can then use the double angle identity for sine, which states that:
sin(2θ) = 2sin(θ)cos(θ)
to simplify sin(12 degrees). Letting θ = 6 degrees, we get:
sin(12 degrees) = 2sin(6 degrees)cos(6 degrees)
We can use the half-angle identity for cosine to find cos(6 degrees), which states that:
cos(θ/2) = √((1 + cos(θ)) / 2)
Letting θ = 12 degrees, we get:
cos(6 degrees) = √((1 + cos(12 degrees)) / 2)
Substituting these values into the original expression, we get:
tan(12 degrees) = 2tan(6 degrees) / (1 - tan²(6 degrees))
tan(12 degrees) = 2(sin(12 degrees) / (1 + cos(12 degrees))) / (1 - (sin²(12 degrees) / (1 + cos(12 degrees))²))
tan(12 degrees) = 2(2sin(6 degrees)cos(6 degrees) / (1 + cos(12 degrees))) / (1 - (4sin²(6 degrees)cos²(6 degrees) / (1 + cos(12 degrees))²))
tan(12 degrees) = (4sin(6 degrees)cos(6 degrees)) / (1 + cos(12 degrees) - 4sin²(6 degrees)cos²(6 degrees))
This is the simplified expression using the double angle identity.
Step-by-step explanation: