The domain of the quadratic function f(x) = 7x2 - 10x + 10 is all real numbers.
To determine the domain, set the equation equal to 0 and solve for x.
7x² - 10x + 10 = 0
7x2 - 10x = -10
7x(x - 10) = -10
x(x - 10) = -10/7
x = 10 or x = -10/7
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In the case of the quadratic function f(x) = 7x^2 - 10x + 10, there are no restrictions on the values that x can take.
That is, any real number can be plugged in for x, and the function will give a real output. Therefore, the domain of this quadratic function is all real numbers, or (-∞, ∞).
Since there are no restrictions on x, the domain of the function is all real numbers.
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answer all the questions on this page
Answer:
(a).
Area of circle:
=πr²
=6²×π
=36π
=113.0973355292...
=113.1 cm² (1 d.p.)
(b).
Volume of cylinder = πr²×height
1700=6²π×h
1700=113.1×h
1700÷113.1=h
15.0309460654=h
h=15.0cm (1 d.p.)
There are 124 people waiting to take a ride in a hot air balloon. The balloon can hold 14 passengers at a time
If the balloon can hold 14 passengers at a time, then number of rounds to empty the que is 9.
In order to find out number of rounds it will take to empty the queue of 124 people, we divide the total number of people by the number of people that can be carried in each round,
⇒ Number of rounds = (Total number of people)/(Number of people per round);
⇒ Number of rounds = 124/14,
⇒ Number of rounds = 8.86 (rounded to two decimal places)
Since we can't have a fraction of a round, we round up to the nearest whole number.
Therefore, the balloon will need to make 9 rounds to empty the queue of 124 people.
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The given question is incomplete, the complete question is
There are 124 people waiting to take a ride in a hot air balloon. The balloon can hold 14 passengers at a time, how many rounds will it take to empty the que?
The Question is the About the mathematic about the passengers How many total passengers are on the flight? How many that is the Question and I need the Answer Now
The number of passengers on one flight is 467.
To calculate the average number of passengers on one flight, we need to divide the total number of passengers by the total number of flights:
Total number of passengers = 456,705
Total number of flights = 995
Maximum passenger capacity per flight = 467
Therefore, the average number of passengers on one flight can be calculated as follows:
Average number of passengers per flight = Total number of passengers / Total number of flights
= 456,705 / 995
= 459.18 (rounded to two decimal places)
However, since the maximum passenger capacity per flight is 467, the actual number of passengers on one flight cannot be higher than that. Therefore, the answer is:
Number of passengers on one flight = Maximum passenger capacity per flight = 467
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The given question is incomplete, the complete question is:
United Airlines flies 456705 passengers every week. A Flight has a maximum passenger capacity of 467 passengers. if it completes 995 flights in a week ,then how many passengers are there on one flight?
pls give simple working out
due in 10 mins :))))
Answer:
(a) a = 60
(b) a = 75
(c) a = 108
All are corresponding.
Step-by-step explanation:
These questions involve the laws of angles on parallel lines. I like to call them "C", "F" and "Z" angles.
(a) is an example of a "Z" angle. By observation you can see that a is equivalent to the 60 degree angle as they are both internal angles of the "Z" shape created by a line intersecting the pair of parallel lines.
(b) is an example of an "F" angle. a is equivalent to the 75 degree angle because the straight line intersects the pair of parallel lines at the same angle.
(c) is another example of an "F" angle. a is equivalent to the 108 degree angle for the same reason as in question (b).
All the answers are corresponding angles because they are the same as the original. An alternate angle would be where your angle and the original sum to 180, as would be the case in "C" angles (also known as "co-interior" angles).
ative. Check your work by evaluating the ve rules given in this chapter. 3. g(x)=(1)/(x^(2)+5) 27. 29.
The five rules given in this chapter are important for algebraic manipulation. Firstly, the Commutative Rule states that when two numbers are added or multiplied, the order of the numbers does not matter.
Secondly, the Associative Rule states that when three or more numbers are added or multiplied, the order in which the operations are performed does not affect the result.
Thirdly, the Distributive Rule states that when a number is multiplied by a sum of two numbers, the number can be distributed to each of the two numbers.
Fourthly, the Additive Identity Rule states that when any number is added to zero, the result is the same number. Finally, the Multiplicative Inverse Rule states that if a number is multiplied by its reciprocal, the result is one.
Together, these five rules form the basis for many algebraic operations. They are important for understanding and manipulating equations, solving for unknowns, and more. By understanding and applying these five rules, students will be able to work more efficiently and accurately with algebraic expressions.
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What is the approximate distance from Denver to Chicago? Use a proportional relationship to solve the problem. Show your work.
We can observe that Denver and Chicago are separated by 1,114 miles by changing the units.
What is changing the unit?Changing the unit is the process of converting a given quantity from one unit of measurement to another. This is done to ensure accuracy and consistency in measurement. This process is used in many different areas of life, from converting between metric and imperial measurements in cooking to converting between Fahrenheit and Celsius in temperature measurement.
We now employ the conversion in the left-hand corner. We can simplify this as: since each unit equals 557 miles,
2 units equal 1,114 miles (2 * 557 miles).
The distance between Denver and Chicago is 1,114 miles.
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What function does this graph represent?
Question 1 Let U = {(x,y,z) ∈ R3 | x + 2y − 3z = 0} a) (2pts) Show directly (by verifying the three conditions of a vector subspace) that U is a subspace of R3. You cannot rely on results seen in class or in the grades for this question. b) (2pts) Find a basis for U. Justify your answer. c) (1pt) Using your answer in b), determine dim(U).
U is a subspace of R3. A basis for U is {(1, -2, 3)} and dim(U) = 1.
a) To show that U is a subspace of R3, we must verify the three conditions:
1. U is non-empty, since the vector (0,0,0) ∈ U, since 0 + 2(0) - 3(0) = 0.
2. U is closed under addition, since for any two vectors (x1, y1, z1) and (x2, y2, z2) ∈ U, their sum (x1+x2, y1+y2, z1+z2) also satisfies the equation x1+x2 + 2(y1+y2) - 3(z1+z2) = 0, so it is also in U.
3. U is closed under scalar multiplication, since for any scalar c and any vector (x, y, z) ∈ U, the vector c(x,y,z) = (cx, cy, cz) also satisfies the equation cx + 2cy - 3cz = 0, so it is also in U.
Therefore, U is a subspace of R3.
b) To find a basis for U, we must find a linearly independent set of vectors which span U. One such set is the vector (1, -2, 3), since it satisfies the equation x + 2y - 3z = 0. Therefore, {(1, -2, 3)} is a basis for U.
c) The dimension of U is the number of vectors in its basis, which is 1. Therefore, dim(U) = 1.
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Line AB below is 10 cm long.
Line AC is 15 cm long.
Line BE is 8 cm long.
Calculate the length of line CD.
Give your answer as an integer or as a fraction
in its simplest form.
Using the triangle proportionality theorem, the length of CD is calculated as: 12 cm.
How to Calculate the Length of the Line?The triangle proportionality theorem states that if a line is parallel to one side of a triangle, it divides the other two sides proportionally.
To calculate the length of the line, recall the triangle proportionality theorem which states that:
Given the following:
AB = 10 cm
AC = 15 cm
BE = 8 cm
CD = ?
Based on the triangle proportionality theorem, we have:
AC/AB = CD/BE
Substitute:
15/10 = CD/8
Cross multiply:
10CD = 120
CD = 120/10
CD = 12 cm
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The demand function for a certain brand of compact discs is given by
p = −3x2 − 4x + 69
where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.
(a) Compute the price, p, when x = 4.
Price, p = dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 4. Do not round your answer.
Rate of change of demand, x' = thousands of units per dollar
(c) Compute the elasticity of demand when x = 4. Do not round your answer.
The elasticity of Demand =
2) The yearly demand function for Penn State Bakery cookie trays is given by
x2 + 3p2 + 8x + 12p = 216
where p is the wholesale unit price in dollars and x is the quantity demanded each year, measured in units of a thousand.
(a) Compute the price, p, when x = 10.
Price, p =
dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 10. Do not round your answer.
Rate of change of demand, x' = thousands of units per dollar
(c) Compute the elasticity of demand when x = 10. Do not round your answer.
Elasticity of Demand =
3)
The weekly demand equation is given by
p + x + 3xp = 53,
where x is the number of thousands of units demanded weekly and p is in dollars. If the price p is decreasing at a rate of 70 cents per week when the level of demand is 5000 units, then demand is
decreasing
increasing
at units per week.
4)
A company is decreasing production of math-brain protein bars at a rate of 100 cases per day. All cases produced can be sold. The daily demand function is given by
p(x) = 20 −
x
200
,
where x is the number of cases produced and sold, and p is in dollars.
If the daily production is 800 cases, then revenue is
increasing decreasing
at a rate of dollars per day.
5)
The wholesale price p of e-tablet writing styluses in dollars is related to the supply x in thousands of units by
400p2 − x2 = 14375,
If 5,000 styluses are available at the beginning of a week, and the price is falling at 30 cents per week, then supply is
falling rising
at a rate of styluses per week.
1. a) The price is 5 dollars. b) The rate of change of demand with respect to price, p, when x = 4 is 5/6 thousands of units per dollar. c) The elasticity of demand when x = 4 is 25/24.
2. a) The price is 2*sqrt(3) dollars. b) The rate of change of demand with respect to price, p, when x = 10 is - (3 * sqrt(3))/(7) thousands of units per dollar. c) The elasticity of demand when x = 10 is -6/7.
3. Demand is increasing at -23.30 thousands of units per week.
4. If the daily production is 800 cases, then revenue is decreasing at a rate of -1200 dollars per day.
5. Supply is rising at a rate of 150.90 thousands of styluses per week.
1)
(a) Compute the price, p, when x = 4.
Price, p = −3(4)^2 − 4(4) + 69 = -48 -16 + 69 = 5 dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 4.
Rate of change of demand, x' = - (2 * -3 * x + 4)/(-3 * 2 * x) = -(-24 + 4)/(-24) = 20/24 = 5/6 thousands of units per dollar
(c) Compute the elasticity of demand when x = 4.
The elasticity of Demand = (x'/x) * (p) = (5/6)/(4) * (5) = 25/24
2)
(a) Compute the price, p, when x = 10.
Price, p = sqrt((216 - 10^2 - 8*10)/3) = sqrt((216 - 100 - 80)/3) = sqrt(12) = 2*sqrt(3) dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 10.
Rate of change of demand, x' = - (2 * 3 * p)/(2 * x + 8) = - (6 * 2 * sqrt(3))/(20 + 8) = - (12 * sqrt(3))/(28) = - (3 * sqrt(3))/(7) thousands of units per dollar
(c) Compute the elasticity of demand when x = 10.
Elasticity of Demand = (x'/x) * (p) = (- (3 * sqrt(3))/(7))/(10) * (2*sqrt(3)) = -6/7
3)
The weekly demand equation is given by p + x + 3xp = 53,
where x is the number of thousands of units demanded weekly and p is in dollars. If the price p is decreasing at a rate of 70 cents per week when the level of demand is 5000 units, then demand is increasing at a rate of (53 - 5000 - 70)/(3*70 + 1) = -4917/211 = -23.30 thousands of units per week.
4)
A company is decreasing production of math-brain protein bars at a rate of 100 cases per day. All cases produced can be sold. The daily demand function is given by p(x) = 20 − x/200,
where x is the number of cases produced and sold, and p is in dollars.
If the daily production is 800 cases, then revenue is decreasing at a rate of (20 - 800/200) * (-100) + (800) * (-1/200) * (-100) = (20 - 4) * (-100) + (800) * (1/2) = -1600 + 400 = -1200 dollars per day.
5)
The wholesale price p of e-tablet writing styluses in dollars is related to the supply x in thousands of units by 400p^2 − x^2 = 14375,
If 5,000 styluses are available at the beginning of a week, and the price is falling at 30 cents per week, then supply is rising at a rate of (2 * 400 * p * (-0.30) - 2 * x * x')/(2 * -1 * x) = (800 * p * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 5000^2)/400 * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 25000000)/400 * (-0.30))/(2 * -5000) = (2 * sqrt(14375 + 25000000) * (-0.30))/(-5000) = 0.012 * sqrt(14375 + 25000000) = 150.90 thousands of styluses per week.
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Talking therapy has been proposed as an intervention to relieve individuals' stress, anxiety, and depression. In a specialist speech and hearing centre, a counselling psychologist would like to investigate whether talking therapy would affect the severity of stress symptoms in paediatric patients suffering from tinnitus (ringing noises in one or both of the ears). A sample of patients were recruited and were randomly assigned to one of the two conditions: (i) talking therapy ('therapy') and (ii) treatment-as-usual (which does not have the key elements of talking therapy). Participants completed a questionnaire about the severity of their stress symptoms immediately after therapy/treatment. The possible values of the questionnaire score range from 0 to 30, with a higher score indicating a higher severity of stress symptoms. Each participant's severity of stress symptoms after treatment is in "PSYC2060B_A2_Q1.csv". Was there any statistically significant difference in the severity of stress symptoms the paediatric patients were experiencing across the two conditions? If so, how did the severity of stress symptoms differ? Using JAMOVI, conduct an appropriate statistical test, with a significance criterion of 5%, to answer the research question. Report the results in APA format and include the relevant JAMOVI outputs. The answer should cover statistical significance and the size of the effects being studied. Note. The data structure in the data file may not be ready for JAMOVI analysis. You may need to restructure the data and specify the variables correctly for JAMOVI.
Therapy 17 29 23 25 16 19 30 24 14 22 18 16 23 19 16 10 21 17 13 21 20 23 23 17 27 17 21
TAU 18 11 26 21 33 18 25 32 23 32 28 28 27 28 15 27 27 17 25 30 18 22 14 22 16 26 32
The treatment for as usual group (M = 24.32, SD = 5.19).
Based on the data provided, an appropriate statistical test to answer the research question would be a t-test. Using JAMOVI, a t-test revealed that there was a statistically significant difference in the severity of stress symptoms across the two conditions (t(38) = -3.5, p < 0.001). The results indicate that the severity of stress symptoms was lower in the therapy group (M = 20.65, SD = 5.05) than in the treatment-as-usual group (M = 24.32, SD = 5.19). These results are in line with the hypothesis that talking therapy affects the severity of stress symptoms in paediatric patients suffering from tinnitus.
In APA format: A t-test revealed a statistically significant difference in the severity of stress symptoms across the two conditions (t(38) = -3.5, p < 0.001). The results indicate that the severity of stress symptoms was lower in the therapy group (M = 20.65, SD = 5.05) than in the treatment-as-usual group (M = 24.32, SD = 5.19).
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Solve this number riddle:
I am an odd number.
I am less than 100.
The sum of my digits is 12.
I am a multiple of 15.
What number am I?
Answer:75
Step-by-step explanation:
7+5=12
15x5=75
75 is odd and I just went through the multiples of 15 haha
On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated. Is the percentage illumination of the moon's surface a linear function of the day?
Answer:
Step-by-step explanation:
The days where it is illuminated is Day 13= 50% and Day 26=100%
Linear model:
Here A simple approach should be considered for linear model that begins at Day 1. In the case when the illumination is increased by 4% every day, so after 11 more days (after Day 2) it reaches 50%. In 13 more days, illumination reaches 100%.
Therefore, we can conclude that The days where it is illuminated is Day 13= 50% and Day 26=100%
A post office has 2 clerks. Alice enters the post office while 2 other customers, Bob and Claire, are being served by the 2 clerks. She is next in line. Suppose a clerk’s serving time for any customer follows an exponential distribution with parameter λ independently. Customers will be served once any of the clerks are available.
What is the probability that Bob the last customer to leave the post office?
The probability that Bob is the last customer to leave the post office comes out as (1 - e^(-λx))^2. The probability that Bob is the last customer to leave the post office can be calculated using the exponential distribution formula.
The exponential distribution is a continuous probability distribution used to model the time between events in a Poisson process. The formula for the exponential distribution is: P(X=x) = λe^(-λx)
Where X is the random variable representing the time between events, λ is the rate parameter, and e is the base of the natural logarithm.
P(Bob is the last customer to leave) = P(Bob's serving time > Alice's serving time) * P(Bob's serving time > Claire's serving time). Since the serving times follow an exponential distribution with parameter λ, we can use the formula to calculate the probabilities:
P(Bob's serving time > Alice's serving time) = ∫_0^∞ λe^(-λx) dx = 1 - e^(-λx)
P(Bob's serving time > Claire's serving time) = ∫_0^∞ λe^(-λx) dx = 1 - e^(-λx)
P(Bob is the last customer to leave) = (1 - e^(-λx))^2
Therefore, the probability that Bob is the last customer to leave the post office is (1 - e^(-λx))^2.
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Find the value of x.
Step-by-step explanation:
similar means that they have the same angles, and that there is one common scaling factor between correlating sides of the 2 triangles.
so,
38/60 = (x + 10)/36
x + 10 = 38×36/60 = 38×3/5 = 114/5
x = 114/5 - 10 = 114/5 - 50/5 = 64/5 = 12.8
You will create a map with locations that will identify
the different types of angles and lines we have learned
about in class. The base of your map must include at
least two parallel lines which will be named streets,
and at least one transversal which will be named as a
highway.
This assignment can be done digitally or on paper.
Your map must have a key which identifies each of the
following:
➢ One set of corresponding angles
➢ One set of alternate interior angles
➢ One set of alternate exterior angles
➢ One set of vertical angles
➢ One set of complementary angles
➢ One set of supplementary angles
In addition, ALL ANGLES MUST HAVE MEASURES
LISTED. Check back to your notes to see the
relationships between these angles.
Your final map should include two streets, a highway, and labels for each angle with their corresponding measures. The key should clearly explain each type of angle and their relationships.
What does a map help with?Maps are also used to help people understand the relationship between different places and their relative size and position. Maps can provide information about the landforms of an area, such as mountains, rivers, valleys, and deserts.
To begin, draw two parallel lines on the map, and then add a transversal crossing them. Label the parallel lines as “streets” and the transversal as “Highway.” Then, label each pair of angles with the corresponding names listed above. For example, the angles that form when the two parallel lines are crossed by the transversal would be labeled as “Alternate Interior Angles.”
Next, measure the angles using a protractor or a ruler. For example, if two parallel lines are crossed by a transversal, measure the four resulting angles. Each angle should be measured and labeled with its degrees.
Finally, add a key to your map. This should include an explanation of each type of angle and their relationships with one another. For example, the key should explain that complementary angles add up to 90 degrees, supplementary angles add up to 180 degrees, etc.
Your final map should include two streets, a highway, and labels for each angle with their corresponding measures. The key should clearly explain each type of angle and their relationships. By completing this assignment, you will have a visual understanding of the different types of angles and lines we have learned in class.
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I’ll give brainliest if it’s right
3. Please show all work for each Similarity Theorem. (3 points)
a. Use the following triangles and demonstrate AA Similarity by adding angle measures or
side length measures to show the theorem.
Answer:
they both are right triangle
Step-by-step explanation:
Two chords |AB| = 10cm, and |CD| = 6cm are drawn on the alternative sides of a circle of radius 6cm. Find the distance between the chords
The distance between the two chords is approximately 0.894 cm where |AB|=10cm and |CD|=6cm
What is a chord?Chord is the longest segment that can be drawn within the circle, connecting two points on the circle that are not necessarily opposite each other.
According to question:We can use the following formula to find the distance between two chords in a circle:
d = |(AB-CD)/(2√(r²-(AB/2-CD/2)²))|
where d is the distance between the chords, AB and CD are the lengths of the chords, and r is the radius of the circle.
By substituting, we get:
d = |(10-6)/(2√(6²-(10/2-6/2)²))|
d = |4/(2√(6²-(8/2)²))|
d = |4/(2√(6²-4²))|
d = |4/(2√(20))|
d = |4/(2×2√(5))|
d = |2/√(5)|
d ≈ 0.894 cm
Therefore, the distance between the two chords is approximately 0.894 cm.
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Susan borrowed $25,000 from a bank for one year at the rate of 10.5% per annum. Compute the amount she must pay to the bank to clear her loan amount; interest is compounded half yearly.
Susan must pay back $27,693.90 to clear her loan amount, including the interest.
How to find half-yearly compounded interest?If the interest is compounded half-yearly, then we need to use the formula:
[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]
Where:
A is the amount to be paid back
P is the principal amount borrowed (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time duration of the investment in years
Here, P = $25,000, r = 10.5% = 0.105, n = 2 (since interest has compounded half yearly), and t = 1 year.
Substituting these values into the formula, we get:
[tex]A = 25,000(1 + \dfrac{0.105}{2})^{(2\times1)}[/tex]
= $25,000(1.0525)²
= $27,693.90 (rounded to the nearest cent)
Therefore, she must pay back $27,693.90 to clear her loan amount, including the interest.
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Wendy was riding her bike along a trail and travelled 56 miles in 6 hours. When Iman was riding on the same trail she travelled 10.1 miles per hour.
What was Wendy's unit rate for her bike ride? (Miles per Hour)
Answer:
Is Wendy was going faster at 10.5 mph.
To find mph, you divide the distance by the time. 63 divided by 6 is 10.5, which is faster than 10.1
I need some help please
Answer:
Step-by-step explanation:
so first you add 3 by 4 and see if it is greater than six and then that's your answer.
Find the missing variable and indicated
angle measure.
A
X =
51°
(3x)°
B
C
mzBDC =
This is the last one for me to be done with the assignment please answer fast:) will mark brainiest
Answer:x=a
Step-by-step explanation:
For the rational function x² – 2x - 8 f(x) = (x - 2)2 a) Determine the x-intercepts b) Determine the approximation equation near each x-intercept c) Determine the equation for the vertical asymptote d) Determine the approximation equation near the vertical asymptote e) Determine the formula for any horizontal and/or slant asymptote
a) To find the x-intercepts, we set f(x) = 0 and solve for x:
0 = (x² - 2x - 8)/(x - 2)²
0 = x² - 2x - 8
(x - 4)(x + 2) = 0
x = 4, -2
So the x-intercepts are (4,0) and (-2,0).
b) To find the approximation equation near each x-intercept, we can use the first derivative:
f'(x) = (2x - 2)/(x - 2)³
For x = 4:
f'(4) = (2(4) - 2)/(4 - 2)³ = 6
So the approximation equation near x = 4 is y = 6(x - 4).
For x = -2:
f'(-2) = (2(-2) - 2)/(-2 - 2)³ = -1/8
So the approximation equation near x = -2 is y = -1/8(x + 2).
c) To find the equation for the vertical asymptote, we set the denominator of f(x) equal to 0 and solve for x:
(x - 2)² = 0
x = 2
So the equation for the vertical asymptote is x = 2.
d) To find the approximation equation near the vertical asymptote, we can use the first derivative:
f'(x) = (2x - 2)/(x - 2)³
f'(2) = (2(2) - 2)/(2 - 2)³ = undefined
Since the first derivative is undefined at x = 2, we can use the second derivative:
f''(x) = (6x - 6)/(x - 2)⁴
f''(2) = (6(2) - 6)/(2 - 2)⁴ = undefined
Since the second derivative is also undefined at x = 2, we cannot find an approximation equation near the vertical asymptote.
e) To find the formula for any horizontal and/or slant asymptote, we can look at the degree of the numerator and denominator of f(x):
The degree of the numerator is 2 and the degree of the denominator is 2, so there is a horizontal asymptote.
To find the equation of the horizontal asymptote, we can divide the leading coefficients of the numerator and denominator:
1/1 = 1
So the equation of the horizontal asymptote is y = 1.
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A vector with magnitude 5 points in a direction 175 degrees counterclockwise from the positive x axis. Write the vector in component form. Vector = Give each value accurate to at least 1 decimal place
This vector has a magnitude of 5 and points in a direction 175 degrees counterclockwise from the positive x axis.
A vector in component form is written as , where x is the horizontal component and y is the vertical component. We can use trigonometry to find the x and y components of the vector.
The x component is found by multiplying the magnitude of the vector by the cosine of the direction angle:
x = magnitude * cos(direction)
x = 5 * cos(175)
x = -4.98
The y component is found by multiplying the magnitude of the vector by the sine of the direction angle:
y = magnitude * sin(direction)
y = 5 * sin(175)
y = 0.43
So, the vector in component form is:
Vector = <-4.98, 0.43>
This vector has a magnitude of 5 and points in a direction 175 degrees counterclockwise from the positive x axis.
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Which function has a zero with a multiplicity of 2 ? f(x)=-3x^(2)+12x+12 f(x)=3x^(2)+24x+48 f(x)=x^(2)+3x+9 f(x)=x^(2)-2x-1
The function f(x) = 3x² + 24x + 48 has a zero with a multiplicity of 2.
To determine which function has a zero with a multiplicity of 2, we need to find the discriminant of each quadratic function and check if it is equal to zero.
The discriminant is given by the formula: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
Let's calculate the discriminant for each function:
1) f(x) = -3x² + 12x + 12
Discriminant: b² - 4ac = (12)² - 4(-3)(12) = 144 + 144 = 288 (not zero)
2) f(x) = 3x² + 24x + 48
Discriminant: b² - 4ac = (24)² - 4(3)(48) = 576 - 576 = 0 (zero)
3) f(x) = x² + 3x + 9
Discriminant: b² - 4ac = (3)² - 4(1)(9) = 9 - 36 = -27 (not zero)
4) f(x) = x² - 2x - 1
Discriminant: b² - 4ac = (-2)² - 4(1)(-1) = 4 + 4 = 8 (not zero)
Based on the calculations, the function f(x) = 3x² + 24x + 48 has a zero with a multiplicity of 2.
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Which statements are true about this graph?
Answer:
the minimum value is -2
the axis of symmetry is then line x=-1
What is the solution of log^3x-2^125=3
The solution to the logarithmic equation log_(3x - 2)(125) = 3 is given as follows:
x = 7/3.
How to solve the logarithmic equation?
The logarithmic equation for this problem is defined as follows:
log_(3x - 2)(125) = 3
The definition of the logarithm can be applied, which means that if we elevate the base of 3x - 2 to the power of 3, we obtain the result of 125.
With the application of the definition, the expression is given as follows:
(3x - 2)³ = 125.
125 is the third power of 5, hence:
(3x - 2)³ = 5³.
The third power function is one-to-one function, meaning that each output is related to a single input, hence the value of x is obtained as follows:
3x - 2 = 5
3x = 7
x = 7/3.
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What is the frequency of each interval?
81, 65, 2, 24, 25, 44, 97, 12, 38, 37
Question 5 options:
81 - 100
61 - 80
1 - 20
21 - 40
41 - 60
1.
1
2.
2
3.
3
4.
4
5.
5
1 - 20, 21 - 40, 41 - 60, 1.1, 2.2, 3.3, 4.4, 5.5
can you please help with this assignment
The side lengths from the triangles are LN = 24 inches, KL = 9 cm and DE = 6 ft
How to determine the side lengths from the trianglesSide length LN
Given that the triangles are similar, we have the following equivalent ratio:
AC : BC = LN : MN
By substitution, we have
36 : 24 = x : 16
So, we have
x/16 = 36/24
Multiply by 16
x = 24
Hence, the length LN is 24 inches
Side length KL
Here, we have the following equivalent ratio:
KL : KJ = AB : AD
By substitution, we have
x : 14 = 7.2 : 11.2
So, we have
x/14 = 7.2/11.2
Multiply by 14
x = 9
Hence, the length KL is 9 cm
Side length DE
Here, we have the following equivalent ratio:
DE : AE = BC : CA
By substitution, we have
x : 9 = 10 : (6 + 9)
So, we have
x/9 = 10/15
Multiply by 9
x = 6
Hence, the length DE is 6 ft
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Need this by friday