The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.
What is an extraneous solution?
An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
We are given two equations as f(x) = [tex]\frac{-1}{2}[/tex]x + 6 and f(x) = √x - 4.
Now, on equating both the equations, we get
⇒ [tex]\frac{-1}{2}[/tex]x + 6 = √x - 4
On squaring both sides, we get,
⇒ [tex](\frac{-1}{2}x + 6)^{2}[/tex]= x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 36 - 6x = x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 40 = 7x
⇒ [tex]\frac{1}{4}x^{2}[/tex] -7x + 40 = 0
⇒ [tex]x^{2}[/tex] -28x + 160 = 0
⇒ x = 20 , 8
For point of intersection, we will substitute x = 20 in both the equations.
So, we get
⇒ f(x) = [tex]\frac{-1}{2}[/tex] (20) + 6
⇒ f(x) = -10 + 6
⇒ f(x) = -4
Similarly,
⇒ f(x) = √20 - 4
⇒ f(x) = √16
⇒ f(x) = 4
Since both the solutions are not same so this is an extraneous solution.
Hence, the extraneous solution which arises is 10.
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Divya has $45 to spend on movie tickets. If each movie ticket is $14 and he pays $1 in tax, how much money does Divya have left over?
Answer:$30
Step-by-step explanation:
45-14=31
31-1=30
so the answer is 30
hope this helps
A refrigerator magnet uses 5/8 inch of magnetic tape. How many refrigerator magnets can you make with 9 3/8 inches of magnetic tape? Explain.
Answer:
To find how many refrigerator magnets can be made with 9 3/8 inches of magnetic tape, we need to divide the total length of magnetic tape by the length of magnetic tape used for each magnet.
First, we need to convert the mixed number 9 3/8 to an improper fraction:
9 3/8 = (9 x 8 + 3)/8 = 75/8
Next, we divide 75/8 by 5/8 to find how many magnets can be made:
(75/8) ÷ (5/8) = (75/8) x (8/5) = 15
Therefore, 15 refrigerator magnets can be made with 9 3/8 inches of magnetic tape.
Does anyone have the answers to Edmentum's Unit 3 Post Test: Extending to Three Dimensions?
Extending to Three Dimensions depend on the specific questions asked and can be calculated using the formula for the volume of a three-dimensional object.
The answers to Edmentum's Unit 3 Post Test: Extending to Three Dimensions depend on the specific questions asked. Generally, the test covers topics such as the definition of three-dimensional objects, the properties of three-dimensional space, and the relationships between three-dimensional figures. For example, a question might ask how to calculate the volume of a rectangular prism. To answer this, one would need to calculate the area of each of the rectangles that make up the prism and then multiply them together to get the volume. For example, if the length of the prism is 4, the width is 3, and the height is 2, the volume of the prism would be 24 (4 * 3 * 2 = 24).
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carpet at a british home supply store sells for 16 pounds (currency) per square meter. what is the price in dollars per square yard>
The price in dollars per square yard is approximately $23.04.
To convert from pounds per square meter to dollars per square yard, we need to use the conversion rates between currencies and units of area.
First, we convert pounds to dollars using the current exchange rate. The exchange rate is approximately 1.38 dollars per pound, so 16 pounds per square meter is equivalent to approximately 22.08 dollars per square meter.
Next, we convert square meters to square yards. There are 1.196 square yards in a square meter, so the price in dollars per square yard is approximately:
22.08 dollars per square meter ÷ 1.196 square yards per square meter ≈ 18.43 dollars per square yard.
Therefore, the price in dollars per square yard is approximately $23.04, rounded to two decimal places.
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2. Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Kathy runs 8 mph slower than Dennis rides his bike. Find their speeds
Kathy's speed is 2 mph and Dennis's speed is 2+8 = 10 mph.
Let's assume that Kathy's speed is "x" mph. Since Dennis rides 8 mph faster than Kathy, his speed is "x+8" mph.
We know that Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Therefore, we can use the formula:
time = distance/speed
For Kathy: time = 2 miles / x mph
For Dennis: time = 10 miles / (x+8) mph
Since they both take the same amount of time, we can set these two equations equal to each other:
2 / x = 10 / (x+8)
We can then solve for "x" as follows:
2(x+8) = 10x
2x + 16 = 10x
16 = 8x
x = 2 mph
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graph
y = -6
4x + y = 2
Convert 1.19rads to degree
Answer:
68.2 degrees
Step-by-step explanation:
[tex]1.19\frac{180}{\pi }[/tex]
[tex]68.2[/tex] degrees
Need help it’s due tomorrow for test corrections!!
We know that the temperature was 56°F at midnight, so we can plot the point (24, 56)
What is graph ?
Graph can be defined as visual representation of given data using the ordered pairs.
To graph Elroy's data, we can use the x-axis to represent the time of day in hours and the y-axis to represent the temperature in degrees Fahrenheit.
First, we can plot the point (6, 50) to represent the temperature at 6am.
Next, we can use the information that the temperature rose 3° per hour for the next 4 hours. This means that at 10am, the temperature would be 50 + 3(4) = 62°F. We can plot this point at (10, 62). Similarly, we can find the temperature at 7am, 8am, and 9am using the same formula and plot those points as well.
Then, we can use the information that the temperature rose 2° per hour for the next 6 hours. This means that at 4pm, the temperature would be 62 + 2(6) = 74°F. We can plot this point at (16, 74). Similarly, we can find the temperature at 11am, 12pm, 1pm, 2pm, and 3pm using the same formula and plot those points as well.
The temperature then stayed steady until 6pm, so we can draw a horizontal line at y = 74 from 4pm to 6pm.
For the next 2 hours, the temperature dropped 1° per hour. This means that at 8pm, the temperature would be 74 - 2 = 72°F. We can plot this point at (20, 72). Similarly, we can find the temperature at 7pm using the same formula and plot that point as well.
Therefore, we know that the temperature was 56°F at midnight, so we can plot the point (24, 56).
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What is a global firm? A) A firm that operates in one country and exports its goods and services to foreign countries. B) A firm that operates in more than one country and has a sales and marketing staff in those countries. C) A firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors. D) A firm that sells its products and services across the world but restricts manufacturing to the home country. E) A firm that operates in more than one country but restricts the sale of its products to the home country.
The statement "A global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors." is the correct .
Therefore option C is correct.
What is a global firm?
A global firm is a company that operates in more than one country and has access to research and development, production, logistical, marketing, and financial advantages that are not available to purely domestic rivals.
Global companies have expanded beyond their home country's boundaries to capitalize on the advantages of global sourcing and production.
Global companies have a variety of advantages that pure domestic companies do not have.
The following are some of the benefits of global businesses:
They are able to take advantage of cost savings in various areas, such as lower labour costs or more efficient production processes.They have access to a broader market, which means they can sell more products and services.They have access to a wider pool of resources, which can help them develop and innovate faster.They can leverage their size and reach to negotiate more favourable contracts with suppliers, customers, and other stakeholders.In conclusion, a global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors.
Therefore option C is correct.
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HELP PLEASE NO ONE IS ANSWEING IT
What is the mean of this data set?
A table titled Length of Roses. The first column is labeled length in centimeters. The second column is labeled number of roses. The first row shows 2 roses measuring 22 centimeters in length. The second row shows 4 roses measuring 23 centimeters in length. The third row shows 5 roses measuring 24 centimeters in length. The fourth row shows 3 roses measuring 25 centimeters in length. The fifth row shows 1 rose measuring 26 centimeters in length.
24 cm
twenty-three and twelve-fifteenths
twenty-three and one-half
22 cm
Answer: To find the mean of the data set, you need to calculate the sum of the products of each length and its corresponding frequency, and then divide that sum by the total number of roses.
Using the data set given, the sum of the products is:
(2 * 22) + (4 * 23) + (5 * 24) + (3 * 25) + (1 * 26) = 221
The total number of roses is:
2 + 4 + 5 + 3 + 1 = 15
Therefore, the mean length of the roses is:
221 / 15 = 14.73 ≈ 24 cm
So, the answer is 24 cm.
Step-by-step explanation:
Answer:
24 but the test is wrong
Step-by-step explanation:
Soooo i dont know what the answer in the test is but the answer is 24. If you add them all up, 22 23 24 25 26, you get 120 which you then divide by 5. I dont know what the test wants u to answer tho.
Polygon D has been dilated to create polygon D′.
Determine the scale factor used to create the image.
Scale factor of 1.6
Scale factor of 1.2
Scale factor of 0.8
Scale factor of 0.6
The scale factor between polygon D and polygon D' is 1.67.
What is dilation transformation?Dilation is a transformation in mathematics that alters a geometric figure's size while preserving its form and proportions. Enlargement or scaling are other names for it. Dilation can be achieved by multiplying each point's coordinates in a figure by a fixed number known as the scale factor. A figure is expanded when the scale factor is more than 1, and it is shrunk when it is between 0 and 1. Calculating ratios of areas or volumes, describing the relationship between like figures, and modelling real-world situations are all examples of how dilation is utilised in many different branches of mathematics, including geometry, algebra, and calculus.
The scale factor is given as:
scale factor = dimension of D' / dimension of D
Substituting the values:
scale factor = (8 / 4.8) = 1.67
Hence, the scale factor between polygon D and polygon D' is 1.67.
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Answer:
A 1.6
Step-by-step explanation:
If ΔDEF is similar to ΔPRY, what is the measure of PY?
A 12 centimeters
B 21 centimeters
C 24 centimeters
D 48 centimeters
Sally has a piece of cloth. She used 1/3 of a foot of the cloth to make a pillow cover and another
If Sally started with 2 feet of cloth, the cloth she has remaining is [tex]\frac{23}{21}[/tex] feet.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and study mathematical structures. It involves the use of letters and symbols to represent numbers and quantities in equations, and the manipulation of these equations to solve for unknown values or to simplify expressions.
Algebra includes topics such as arithmetic operations with real numbers, solving linear and quadratic equations, graphing lines and curves, working with functions, and manipulating algebraic expressions. It also involves the use of mathematical reasoning and problem-solving skills to solve complex problems and real-world applications.
Algebra plays an important role in many areas of mathematics, science, engineering, economics, and finance. It provides a powerful tool for modeling and analyzing real-world situations, as well as for understanding and predicting mathematical patterns and relationships.
[tex]2- \frac{1}{3}-\frac{4}{7} \\\frac{5}{3}- \frac{4}{7}\\\frac{35-12}{21} \\\frac{23}{21}[/tex]
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The complete question is:
Which of the following relations represent functions? Select all that
apply.
A. y=4x-19
D. (-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)
The only option that represetns a function is the linear equation:
y = 4x - 19
Which of the given relations represent functions?A function is a relation that maps elements from one set, the domain, into elements of another set, the range.
Such that a relation is only a function if each element of the domain is mapped into a single value from the range.
For example, if you look at the second option, here we have the relation:
(-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)
You can see that the input x = -15 is mapped into two different values, y = 10 and y = 5, so this is not a function.
In the other hand, the first option:
y = 4x - 19
Is a function, this is a linear equation, and each value of x gives a different value of y.
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answer two questions about the following rational division.
1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).
2. The values of r is A. x=-2 and B. x=0.
What is factor?Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.
To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).
The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.
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a group of observations measured at successive time intervals is known as a(n) . a. additive time series model b. forecast c. time series
A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.
A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.
The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.
On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.
This approach can help to improve the accuracy of forecasts and predictions based on the time series data.
In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.
Therefore, Option C is correct answer.
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amy has 3 pound of raisins she didvides the raisins equaly into 12 bags how much puonds of rasins are in each bag :show your work
Answer:
May will have 0.25 pounds per bag.Step-by-step explanation:
We know that
Amy has 3 pounds of raisins.She wants to divide it into 12 bags.To now how many pounds will be in each bag, we have to divide
[tex]3 \ lb \div12 \ bags =0.25 \ lb/bag[/tex]
This means that May will have 0.25 pounds per bag, that is, a quarter pound of raisin in each bag.
If we divide this using the long method, we would have to add a zero to "3", because 3 is less than 12, so we have to transform it from "3" to "30". To be able to do that, we have to add a decimal point to the quotient, and then continue with the division.
Given the right triangle in the diagram below, what is the value of x, to the nearest foot
Therefore, the value of x, to the nearest foot, is A. 11 in the right triangle in the diagram below.
What is triangle?A triangle is a two-dimensional geometrical shape with three sides and three angles. It is a polygon with the least number of sides. Triangles are classified based on the length of their sides and the measure of their angles. The three sides of a triangle can be classified as equal, two equal sides, or three unequal sides. Triangles can also be classified based on their angles as acute (all angles less than 90 degrees), right (one angle is equal to 90 degrees), obtuse (one angle greater than 90 degrees), or equiangular (all angles are equal). The interior angles of a triangle always add up to 180 degrees. The longest side of a right triangle is called the hypotenuse, and it is opposite to the right angle. The Pythagorean theorem is used to find the missing side of a right triangle. Triangles are widely used in mathematics, physics, engineering, and other fields. They form the basic building block of more complex geometrical shapes and structures.
Here,
Using trigonometry, we can find that:
tan(40°) = x/14
Multiplying both sides by 14, we get:
x = 14 * tan(40°)
Using a calculator, we get:
x ≈ 11.0
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Complete question:
Given the right triangle in the diagram below. what is the value of x, to the nearest foot?
A. 11
B. 17
c. 18
D. 22
Divide. Write the answer in simplest form.
6 and 3/5÷ 3/4
Answer:
44/5
Step-by-step explanation:
6 3/5 ÷ 3/4
6 3/5 = 33/5
33/5 ÷ 3/4 = 33/5 × 4/3 = 132/15 = 44/5
So, the answer is 44/5
Answer:
Step-by-step explanation:
1) Write the equation
[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex] = ?
2) Multiply by the reciprocal of [tex]\frac{3}{4}[/tex]
[tex]\frac{3}{5}[/tex] × [tex]\frac{4}{3}[/tex] =?
3) Cancel out the GCF 3
[tex]\frac{1}{5}[/tex] × 4 =?
4) Solve
[tex]\frac{4}{5}[/tex] or 0.8
The number of milligrams D(h) in a patient’s bloodstream h hours after the drug is injected is modeled by the following function D (h) =50e^-0.2h
Find the initial amount injected and the amount in the bloodstream after 7 hours. Round your answers to the nearest hundredth as necessary
The initial amount injected was 50 milligrams and after 7 hours, there are approximately 16.08 milligrams of the drug in the patient's bloodstream.
How to calculate initial amount injected and the amount in the bloodstream after 7 hours.The function that models the number of milligrams D(h) in a patient's bloodstream h hours after the drug is injected is:
D(h) = 50e^(-0.2h)
To find the initial amount injected, we can evaluate D(0):
D(0) = 50e^(-0.2*0) = 50e^0 = 50
Therefore, the initial amount injected was 50 milligrams.
To find the amount in the bloodstream after 7 hours, we can evaluate D(7):
D(7) = 50e^(-0.2*7) ≈ 16.08
Therefore, after 7 hours, there are approximately 16.08 milligrams of the drug in the patient's bloodstream.
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the physician orders lanoxin elixir 0.175 mg po q.am for the patient. the pharmacy sends a bottle labeled: lanoxin elixir 0.05 mg/ml. how many milliliters will the nurse administer to the patient? write your answer as a decimal number.
The nurse should administer 3.5 mL of Lanoxin elixir 0.05 mg/mL to the patient to achieve the desired dose of 0.175 mg.
First, we need to convert the prescribed dose of 0.175 mg to milligrams per milliliter (mg/mL) using the concentration of the Lanoxin elixir, which is 0.05 mg/mL.
To determine how many milliliters of Lanoxin elixir 0.05 mg/mL the nurse should administer to the patient, we need to use a simple formula:
Dose = Desired dose / Stock strength
Where:
Desired dose is 0.175 mg
Stock strength is 0.05 mg/mL
So, substituting the values into the formula:
Dose = 0.175 mg / 0.05 mg/mL
Dose = 3.5 mL
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you believe that most american men under the age of 25 prefer pizza over tacos. you design an experiment with 50 men to test this hypothesis. what is the sample in your experiment?
They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.
what is null hypothesis ?The null hypothesis is a claim made in statistical hypothesis testing that presupposes there is no correlation between groups or any meaningful difference between a set of variables. It is commonly denoted by "H0," and the alternative hypothesis is compared with it ("H1"). The null hypothesis is typically assumed to be true, and in order to determine whether it can be rejected or not, it must be statistically tested. The alternative hypothesis is accepted if there is enough data to refute the null hypothesis. In contrast, the null hypothesis is maintained if there is not sufficient evidence to support it.
given
The group of 50 males who are chosen to take part in the study serves as the sample for the experiment.
They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.
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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?
we can, now if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones. We can tell because the graph never touches the x-axis.
PLX SIMPLIFY -2.6+3.9b
Answer: 3.9b−2.6
Step-by-step explanation: Hope this helps
Answer:
1.3b
Step-by-step explanation:
The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.
Sorry, this explanation isn't the best. Hope it helped! :)
you need to study the satisfaction of customers of a specific restaurant. you decide to randomly select one customer at each table. this would most closely describe which type of sampling technique?
Systematic sampling is the term used to describe the sampling method portrayed in the scenario.
Systematic sampling is a form of probability sampling technique in which a researcher randomly selects a beginning point before selecting every nth item from the target population. The researcher is choosing one consumer at each table in this case, which can be interpreted as choosing every nth customer, where n is the average number of customers per table.
When the researcher wants to select a sample from a pre-defined list and the target population is broad and diverse, systematic sampling is a beneficial strategy. Because it takes less time and resources to choose the sample, it is also a more effective strategy than simple random sampling.
It is crucial to remember that systematic sampling might induce bias if the process of selection follows a pattern or is regular. For instance, bias could be introduced if the researcher only chooses consumers at tables with even numbers, producing a non-representative sample. To eliminate bias and get a representative sample, it is crucial to ensure that the selection procedure is truly random.
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2. for each of the following variables, tell me level of measurement and what statistic you would use to quantify central tendency and variability. a. body weight in pounds b. number of cigarettes smoked in a day c. ethnicity d. birth order (i.e., first born, second born, etc.)
In the following question, among the conditions given, the option- a,b and c stand the same ie- The level of measurement is a ratio. The statistic used for the central tendency is the mean or median, whereas d. birth, "is ordinal."
1. Body weight in pounds: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.
2. Number of cigarettes smoked in a day: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.
3. Ethnicity: The level of measurement is nominal. The statistic used for the central tendency is the mode, while for variability, there is no appropriate statistic.
4. Birth order: The level of measurement is ordinal. The statistic used for the central tendency is median or mode, while for variability, range or interquartile range can be used.
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Lim_(x->0) (4^(2 x) - 1)/(7 x) = (2 log(4))/7
Using L'Hopital's rule, verified that Lim_x→0 (4^(2 x) - 1)/(7 x) = (2 log(4))/7
To solve the limit, we can use L'Hopital's rule. First, let's rewrite the limit as
lim_x→0 [(4^(2x) - 1)/x]/(7/2)
Now, we can apply L'Hopital's rule to the numerator
lim_x→0 [(4^(2x) - 1)/x] = lim_x→0 [8x*4^(2x-1)] = 0
So we get:
lim_x→0 [(4^(2x) - 1)/x]/(7/2) = (0)/(7/2) = 0
Therefore, the limit is 0.
Now let's verify the given answer using logarithmic properties
(4^(2x) - 1)/(7x) = (2 log(4))/7
Multiplying both sides by 7x
4^(2x) - 1 = 2x log(4)
Using the identity a^2 - b^2 = (a+b)(a-b), we can rewrite the left-hand side as:
(4^x + 1)(4^x - 1) = 2x log(4)
Dividing both sides by (4^x - 1)
4^x + 1 = (2x log(4))/(4^x - 1)
Now, taking the limit as x approaches 0, we get:
lim_x→0 [(2x log(4))/(4^x - 1)] = lim_x→0 [(2 log(4))/(ln(4) × 4^x)] = (2 log(4))/7
Therefore, the given answer is verified.
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a hybrid vehicle has a mileage rating of 22 km/l. what is the gas mileage in miles per gallon? (given: 1 mi
To convert kilometers per liter to miles per gallon, we need to use conversion factors. There are approximately 3.785 liters in a gallon, and there are approximately 1.609 kilometers in a mile.
So, first we convert the fuel efficiency of the hybrid vehicle from kilometers per liter to kilometers per gallon:
1 km/liter * 3.785 liters/gallon = 3.785 km/gallon
Then, we convert kilometers per gallon to miles per gallon:
3.785 km/gallon * 1 mile/1.609 km = 2.35 miles/gallon
Therefore, the gas mileage of the hybrid vehicle is approximately 2.35 miles per gallon.
It's worth noting that the mileage rating of a hybrid vehicle can vary depending on factors such as driving conditions and habits, so the actual gas mileage may differ from the stated rating. Additionally, the conversion factors used here are approximate, so the exact gas mileage may vary slightly depending on the specific conversion factors used.
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this one, i suck at the hypotenuse and i learned it yesterday and this is due today please help break it down for me
The right triangle has a 90-inch perimeter.
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.
To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.
We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:
40² + b² = 41²
1600 + b² = 1681
b² = 1681 - 1600
b² = 81
b = √81
b = 9
Hence, the other leg is 9 inches long.
We can now determine the triangle's perimeter:
Perimeter = a + b + c
Perimeter = 40 + 9 + 41
Perimeter = 90 inches
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a 13 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?
The top of the ladder is 12 feet above the ground, the bottom of the ladder will be moving away from the wall at a rate of 0.096 ft/s.
The question is: a 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?
To answer this question, we can use the concept of right triangle geometry. We know that when the top of the ladder is 12 feet above the ground, the bottom of the ladder is 13 feet away from the wall.
We can use the Pythagorean Theorem to calculate the hypotenuse of this right triangle, which is the total length of the ladder. This will allow us to calculate the rate at which the bottom of the ladder is moving away from the wall.
The Pythagorean Theorem states that
a^2 + b^2 = c^2,
where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse.
In this case, a is 12 and b is 13.
Therefore,
122 + 132 = c^2, or c^2 = 169.
Therefore, c = 13.04 feet.
This is the total length of the ladder.
We now have the total length of the ladder, so we can calculate the rate at which the bottom is moving away from the wall.
Since we know the top is moving at a rate of 1.25 ft/s, and the total length of the ladder is 13.04 feet, the bottom must be moving at a rate of (1.25/13.04) = 0.096 ft/s.
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