You will need 0.75 cups of milk when quadrupling the recipe.
When quadrupling the recipe, you would need 12 tablespoons of milk. To make the calculations easier, it is more efficient to convert the tablespoons to cups. So, the question is how many cups of milk will you need? We know that there are 16 tablespoons in a cup. Therefore, we can find how many cups of milk you will need as follows:
12 tablespoons = (12/16) cups
12 tablespoons = 0.75 cups
So, you would need 0.75 cups of milk when quadrupling the recipe.
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please help !! set up the function using tan
The value of x in the given triangle is 36.87°.
What is Trigonometric function?One of the six functions in mathematics is the trigonometric function (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) In trigοnοmetry, sin cοs and tan values are the primary functiοns we cοnsider while sοlving trigοnοmetric prοblems. These trigοnοmetry values are used tο measure the angles and sides οf a right-angle triangle. Apart frοm sine, cοsine and tangent values, the οther three majοr values are cοtangent, secant and cοsecant.
According to Trigonometric function,
Tan θ = Opposite side/Adjacent side
Therefore,
Tan θ = 6/8
θ = arctan(6/8)
θ ≈ 36.87°
This is simplest way to calculate, there is no other way to calculate.
Thus, the value of x in the given triangle is 36.87°.
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2. A group of workers are harvesting oranges at a constant rate. An equation that represents the number of oranges the workers picked over a period of time, in hours, is y = 9x + 15. Complete sentences. Handwritten. Show work.
(a) What is the slope and the y-intercept for the equation that represents the number of oranges the workers picked over a period of time?
(b) What is the rate of change (slope) and the initial amount (y-intercept)? Explain the meaning of the rate of change and the initial amount for the situation. Answer in complete sentences
Step-by-step explanation:
(a) The slope of the equation y = 9x + 15 is 9, and the y-intercept is 15.
(b) The rate of change or slope of the equation y = 9x + 15 is 9, which represents the constant rate at which the workers are picking oranges. For every hour of work, they pick 9 more oranges. The initial amount or y-intercept of 15 represents the number of oranges they would have picked if they had started working from the beginning of time. However, since this is not possible, it can be interpreted as the number of oranges they picked before starting to work for the period of time that is being measured.
The equation for the number of baskets is an illustration of a linear function.
The slope is 9, and the y-intercept is 15The rate of change is 9, and the initial amount is 15The function is given as:
[tex]\bold{y=9x+15}[/tex]
(a) The slope and the y-intercept
A linear function is represented as:
[tex]\bold{y=mx+b}[/tex]
Where:
m represents the slope, and b represents the y-intercept
By comparison, the slope is 9, and the y-intercept is 15
(b) The rate of change and the initial amount
The rate of change is the slope, and the initial amount is the y-intercept
By comparison, the rate of change is 9, and the is 15
you may need to use the appropriate appendix table or technology to answer this question. after deducting grants based on need, the average cost to attend the university of southern california (usc) is $27,175. assume the population standard deviation is $7,400. suppose that a random sample of 57 usc students will be taken from this population. (a) what is the value of the standard error of the mean? (round your answer to the nearest whole number.) $ (b) what is the probability that the sample mean will be more than $27,175? (c) what is the probability that the sample mean will be within $1,000 of the population mean? (round your answer to four decimal places.) (d) what is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (round your answer to four decimal places.)
(a) The standard error of the mean is 129. (b) The probability that the sample mean will be more than $27,175 is 0.50 (c) The probability that the sample mean will be within $1,000 of the population mean is 0.955. (d) The probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100 is 0.999.
(a) The standard error of the mean is the square root of the population standard deviation divided by the sample size, which in this case is 7,400/57 = 129.12. The value of the standard error of the mean is therefore 129 (rounded to the nearest whole number).
(b) To find the probability that the sample mean will be more than $27,175, you can use the Z-score formula. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175)/129 = 0. The probability that the sample mean will be more than $27,175 is 50%, since the probability of any Z-score of 0 is 0.50.
(c) To find the probability that the sample mean will be within $1,000 of the population mean, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/129 = ±7.8. The probability that the sample mean will be within $1,000 of the population mean is 95.5%, since the probability of any Z-score of ±7.8 is 0.955.
(d) To find the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/74 = ±13.5. The probability that the sample mean will be within $1,000 of the population mean is 99.9%, since the probability of any Z-score of ±13.5 is 0.999.
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Which equation is parallel to: y = 5/7x + 2
Answer:
Whichever equation has a slope of 5/7.
Step-by-step explanation:
Parallel lines will always share the same slope. The slope is found by denoting where the variable m is at. It is noteworthy of the placement of m in the given slope equation:
y = mx + b
Therefore, whichever choice(s) have 5/7 as a slope would be your answer.
~
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Super entrepreneur Freddie Fandango is peddling a new brand of high-tech tennis shoes that make different kinds of sounds each time the wearer's foot hits the ground.(so far, the two most popular sounds are "water puddle" and 'fingernails on chalkboard.") If Freddie brings in an $80 profit from every pair of shoes he sells and his expenses are $100,000, how many pairs must he sell if he wants to earn a profit of $69,840?
Using division, we can find that he must sell 2123 pairs to get a profit of $69840.
Define division?One of the four fundamental operations in mathematics is division, along with addition, subtraction, and multiplication. The splitting of a large group into smaller groups so that each group contains an equal number of items is a straightforward definition of division. It is a mathematical process used for equitable grouping and distribution.
Here,
Profit by selling one pair of shoes = $80.
Now, expenses = $100,000
Total profit he wants = $69,840.
So, total revenue to be generated = 100000 + 69840
= $169840.
Let x be the total pairs sold.
So, x = 169840/80
= 2123.
Therefore, he must sell 2123 pairs to get a profit of $69840.
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a car is traveling at a speed of 63 km per hour. what is the car speed in kilometers per minute? how many kilometers will the car travel in 5 minutes? do not round your answer
Answer:
1) car speed = 1.05km/minute
2) 5.25 km in 5 minutes
Step-by-step explanation:
1) [tex]\frac{63km}{60minutes}=1.05km/minute\\[/tex]
2) 1.05 km × 5 minutes = 5.25 km
Answer:
1.05 per/min5.25 per/5minStep-by-step explanation:
process =63/60=1.05m/min
lara and pei play the same game to compare their scores. lara scored thirty thousand sixty five points and pei scored thirty thousand four hundred eight points. write a sentence using >,< or = to compare lara and pei's point
The score obtained by Lara is less than the score obtained by Pei, which can be modeled by this inequality 30,065 < 30,408.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Based on the information provided about the scores (points) scored by Lara and Pei after playing the same game;
Lara = thirty thousand sixty five points = 30,065 points.
Pei = thirty thousand four hundred eight points = 30,408 points.
In conclusion, we can logically deduce that 30,408 points is greater than 30,065 points or 30,065 points is less than 30,408 points.
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Solve the following problems. You can use your calculator..
1. How many cubic inches of metal are
contained in the hollow rectangular bar
below?
T
5 in.
3 in.
K
-4 in.
6 in.
10 in.
2. The
man
2 ft
The volume of metal that we have in the hollow bar is 180 cubic inches.
How many cubic inches of metal are in the bar?For a prism of length L, width W, and height H, the volume is:
V = L*H*W
Here we need to take the volume of the larger prism, and subtract the volume of the hole, then the volume of metal that we have is:
Volume = 5in*6in*10in - 3in*4in*10in
Volume = 300in³ - 120in³
Volume = 180 in³
The bar has 180 cubic inches of metal.
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find the area and circumference of each circle, rounding to the nearest tenth. use 3.14 for π look at the formula for finding the area and circumference if you need help.
Step-by-step explanation:
1) area= 2.4^2×3.14=18.0864
rounded=18ft^2
circumference= 4.8×3.14=15.072
rounded= 15ft
2) area= 6^2×3.14=113.04
rounded= 110ft^2
circumference= 12×3.14=37.68
rounded= 38ft
3) area= 32^2×3.14=3215.36
rounded=3220ft^2
circumference= 64×3.14=200.96
rounded=200ft
The mean of 21 numbers is 30. A number is added and the mean becomes 32. Determine the value of the new number
The new number that was added to the set is 74 by using mean formula for some numbers.
Let's begin by determining the mean of a set of numbers using the following formula:
average = (sum of numbers) / (number of numbers)
We can write: since we know that the mean of 21 numbers is 30.
/ 21 = 30 = (sum of 21 numbers)
Multiply LHS and RHS by woth 10:
sum of 21 digits equals 630
The new mean will now be determined by adding a new number to the set. Let's call the new number x since we don't yet know its value. We can write: 32 = (sum of 21 numbers + x) / 22 since we also know the new mean is 32.
The result of adding the two sides together is: total of the 21 numbers plus x = 704
We may change the equation to read 630 + x = 704 as we already know the sum of the original 21 values is 630.
630 is subtracted from both sides, giving us:
x = 74
74 is the new number that was so added to the collection.
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A square has an area of 585.64m2. Work out the perimeter of the square.
Answer:
perimeter = 96.8 m
Step-by-step explanation:
the sides of a square are congruent , then perimeter (P) is calculated as
P = 4s ( s is the side length )
the area (A ) of a square is calculated as
A = s²
given A = 585.64 , then
s² = 585.64 ( take square root of both sides )
s = [tex]\sqrt{585.64}[/tex] = 24.2
Then
P = 4 × 24.2 = 96.8 m
Answer:
= 96.8 m
Step-by-step explanation:
Area of a square = side²
Perimter of a square = 4*side
Then:
585.64 = side²
√585,64 = √side²
it is a geometric figure, therefore, only the positive value will be obtained
24.2m = side
Perimeter = 4*side
Perimeter = 4*24.2
Perimeter = 96.8msylvia was playing a shooting game and she attempts. Find the number of attempts where she missed her target?
a figure has a height of 25 inches. it was photocopied at a scale of 40%. what is the new height of the new figure?
Answer:
10 inches
Step-by-step explanation:
If the original figure has a height of 25 inches and it was photocopied at a scale of 40%, we can find the new height of the figure by multiplying the original height by the scale factor:
new height = 25 inches x 0.4
new height = 10 inches
Therefore, the new height of the figure is 10 inches.
Answer:
Wassup
Step-by-step explanation:
By multiplying the initial height by the scale factor, which is 40% or 0.4 in decimal notation, the new height of the image can be calculated.
New height: 25 inches times 0.4 to equal 10 inches.
The figure's revised height is 10 inches as a result.
......................................
Answer:
.............
Step-by-step explanation:
.............
Match each of the equations with their corresponding graph.
a) y = x³ + 2x² - 1
A
b) y = 2x²-x-3
V
c) y = 1 + 1
d) y = 2-3x²-x³
â
A
B
D
4.4
X
O
y
C
b)
X
X
B
E
-X
X
The graph of each function from a to d are attached below
What is the graph of the functions?Graphs of nonlinear functions are graphs of functions that do not have a constant rate of change or a linear relationship between the input and output values. Nonlinear functions include quadratic, exponential, logarithmic, trigonometric, and many other types of functions.
The shape of the graph of a nonlinear function can vary greatly depending on the specific type of function. For example:
The graph of a quadratic function (y = ax^2 + bx + c) is a parabola, which is a symmetric U-shaped curve.
The graph of an exponential function (y = a^x) is a curve that increases or decreases rapidly, depending on whether the base a is greater than or less than 1.
The graph of a logarithmic function (y = log_a(x)) is a curve that approaches a vertical asymptote as x approaches zero.
The graph of a trigonometric function (y = sin(x) or y = cos(x)) is a periodic wave that oscillates between a maximum and minimum value.
Nonlinear functions can exhibit complex and interesting behaviors, such as multiple intercepts, asymptotes, and singularities. The graphs of these functions can be used to model a wide range of real-world phenomena, such as population growth, radioactive decay, and the motion of objects under the influence of gravity.
The graphs of the functions given are attached below
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Which would not be considered a long-term savings
goal?
A. Saving to go to a concert
B. Saving to buy a new house
O C. Saving for college
D. Saving for retirement
A
Consider concert tickets as a long-term savings objective.Therefore, the answer is A.
What is Savings or saving?Savings refers to anything that existing at any given moment, a stock variable, whereas saving refers to an action occurring over period, a flow variable. Even seasoned economists and financial experts frequently refer to "saving" for "savings" due to the widespread misunderstanding of this distinction.\
Saving for a concert is not a long-term savings goal because it is a short-term financial goal. Long-term savings goals typically involve saving money for events or expenses that will occur several years or even decades in the future, such as college, a down payment on a house, or retirement. Saving for a concert is unlikely to take more than a few months or a year, so it is not a long-term goal.
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Express cos G as a fraction in simplest terms.
E
20
F
25
15
G
Cos G therefore equals 4/5 since we must use mathematics to express cos G as a fraction in the simplest words.
what is triangle ?A closed, two-dimensional triangle in geometry is a shape having three straight sides and three angles. Triangles can be categorized according to the size of their angles and the length of their sides. In three locations known as vertices, a triangle's three sides come together. An angle is the place where two triangle sides intersect, and the angle that faces a given side is known as the opposing angle. A triangle's three angles can never add up to more than 180 degrees.
given
We may use the cosine rule to find cos G:
(E2 + F2 - G2) / cos G (2EF)
Inputting the values provided yields:
[tex]cos G = (20^2 + 25^2 - 15^2) / (2 * 20 * 25)[/tex]
= (400 + 625 - 225) / 1000 = 800 / 1000 \s= 4 / 5
Cos G therefore equals 4/5 since we must use mathematics to express cos G as a fraction in the simplest words.
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42 a random experiment consists of tossing a fair 6-sided die repeatedly. how many tosses are required to be certain that the probability that at leas
In order to be certain that the probability of at least one occurrence of each of the six faces of the die is greater than 0.99, you would need to toss the die a minimum of[tex]6 x 5 x 4 x 3 x 2 = 720[/tex] times.
For example, if you tossed the die 6 times, the probability of at least one occurrence of each of the six faces is 0.54. This probability increases with each additional toss, reaching 0.99 after 720 tosses.
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HELP ME A square pyramid is shown:
A square pyramid is shown. The sides of the square base are labeled 0.6 foot. The height of one of the triangular sides is labeled 7 feet.
What is the surface area of the pyramid? (1 point)
a
2.46 square feet
b
8.76 square feet
c
5.16 square feet
d
1.56 square feet
Answer:
B. 8.76 square feet------------------------
Each triangle face has height of 7 ft and base of 0.6 ft and the base of the pyramid is the square with side of 0.6 ft.
Total surface area includes a square base and four triangular faces and the measure of it is:
S = 0.6² + 4*(1/2)*0.6*7 = 0.36 + 8.4 = 8.76 ft²The matching choice is B.
Mindy works at a movie theater. One Friday, she collects a random sample of the type of tickets sold in the afternoon and the evening. She estimates that when 400 tickets are sold on a Friday evening, about 100 of them will be senior tickets. Is Mindy's estimate reasonable? Explain.
Answer: Yes
Step-by-step explanation:
To determine if Mindy's estimate is reasonable, we need to consider the context of the movie theater and the audience it serves. Generally, movie theaters offer tickets to various categories of customers, such as adults, children, and seniors. Seniors usually receive discounted tickets to encourage their attendance.
Mindy estimates that out of 400 tickets sold on a Friday evening, about 100 of them will be senior tickets. This means that she is estimating that 25% of the tickets sold are senior tickets (100 senior tickets / 400 total tickets = 0.25 or 25%).
While it's difficult to know the exact proportions of ticket categories sold without more information, a 25% estimate for senior tickets may be reasonable if the movie theater attracts a diverse audience and offers films or events that appeal to seniors. The actual proportion of senior tickets might vary depending on the location of the theater, the movies being shown, and the demographics of the surrounding community.
It would be helpful to gather more data on the actual distribution of ticket sales across different categories or to compare Mindy's estimate with industry averages to determine if her estimate is reasonable.
RIGHT ANSWER GETS 30 POINTS AND BRAINLIEST IF YOU DONT KNOW DONT ANSWER. WRONG ANSWER WILL BE REPORTED
The solution to the given inequality expression is: x ≥ -8 and it is shown on the number line attached
How to find the solution to the Inequality?To represent inequalities on a number line we show the range of numbers by drawing a straight line and indicating the end points with either an open circle or a closed circle. An open circle shows it does not include the value. A closed circle shows it does include the value.
We are given the inequality expression as:
8x - 4 ≥ -68
Add 4 to both sides to get:
8x ≥ -64
Divide both sides by 8 to get:
x ≥ -8
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The perimeter of a square is 52cm.
Calculate the area
What is the spread of the data set {4, 2, 6, 10, 8, 0}? What does the spread of data even mean?
The data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.
What is mean?The mean is a measure of central tendency that represents the average value of a set of numbers. There are different types of means, including the arithmetic mean , the geometric mean , and the harmonic mean.
What is spread of a data?The spread of data refers to the variability or dispersion of a set of values. It provides information about how spread out or clustered the data is. A set of data can have a high or low spread, depending on the range of values and how they are distributed.
In the given question,
The spread of a data set refers to how much the individual data points in the set vary from each other. There are several measures of spread that are commonly used, including the range, variance, and standard deviation.
To find the spread of the data set {4, 2, 6, 10, 8, 0}, we can calculate the range, which is the difference between the maximum and minimum values in the set. The maximum value in the set is 10, and the minimum value is 0, so the range is:
Range = maximum value - minimum value = 10 - 0 = 10
Therefore, the spread of the data set is 10.
In other words, the data points in this set vary from 0 to 10. The spread of the data set gives us an idea of how much the individual data points differ from each other, and can help us understand the variability and distribution of the data.
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Answer:
Its 6
Step-by-step explanation:
Did the test
Hi, can you please help me with this question?
(With working out pls)
The answer is , (a) the length of AD is approximately 7.62 meters. (b) the size of angle DCB is approximately 59.04° degrees. 3. the angle of depression of the pedestrian from the man is approximately 38° degrees.
What is Pythagorean theorem?The Pythagorean theorem is a fundamental concept in mathematics that states that in a right triangle (a triangle with one angle measuring 90 degrees), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
2. (a) To calculate the length of AD, we can use the Pythagorean theorem,
In triangle ABD, we have:
AB² + BD² = AD²
Substituting the given values, we get:
7² + 3² = AD²
49 + 9 = AD²
58 = AD²
Taking the square root of both sides, we get:
AD ≈ 7.62 m
Therefore, the length of AD is approximately 7.62 meters.
(b) To calculate the size of angle DCB, we can use the trigonometric function tangent, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In triangle DBC, we have:
tan(DCB) = opposite/adjacent = BC/BD = 5/3
Using a calculator, we can find the inverse tangent of 5/3, which gives us:
DCB ≈ 59.04°
Therefore, the size of angle DCB is approximately 59.04° degrees.
3. Let's call the height of the building "h" and the angle of depression "θ".
From the man's point of view, we can draw a right triangle with the hypotenuse being the line of sight from the man to the pedestrian, and the opposite side being the height of the building "h". The adjacent side is the distance from the man to the pedestrian, which is 48 meters.
Similarly, we can draw another right triangle from the pedestrian's point of view, with the hypotenuse being the line of sight from the pedestrian to the top of the building, and the opposite side being the distance from the pedestrian to the foot of the building, which is 34.5 meters.
Now, we can use trigonometry to solve for the angle of depression "θ". We have:
tan(θ) = opposite/adjacent = h/48
tan(θ) = adjacent/opposite = 34.5/h
Solving for "h" in the second equation, we get:
h = 34.5/tan(θ)
Substituting this value of "h" in the first equation, we get:
tan(θ) = h/48 = 34.5/(48*tan(θ))
Simplifying this equation, we get:
tan²(θ) = 34.5/48
Taking the square root of both sides, we get:
tan(θ) = √(34.5/48) = 0.7975
Now, we can find the angle of depression "θ" by taking the inverse tangent (arctan) of this value:
θ = arctan(0.7975) = 38.3 degrees (rounded to the nearest degree)
Therefore, the angle of depression of the pedestrian from the man is approximately 38 degrees.
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Constant percent rate of change in the equation f(x)=2(3)^x
The constant percent rate of change in the exponential function [tex]f(x) = 2(3)^x[/tex] is 200%, indicating a doubling of the output value for each unit increase in the input value.
The equation [tex]f(x) = 2(3)^x[/tex] represents an exponential function. Exponential functions have a constant percent rate of change, which means that the percent change between any two points on the graph of the function is the same.
In this case, we can find the percent rate of change by calculating the ratio of the output values for any two input values that differ by 1. For example, if we compare the output value when x=1 to the output value when x=0, we get:
[tex]f(1) = 2(3)^1 = 6[/tex]
[tex]f(0) = 2(3)^0 = 2[/tex]
The percent change from x=0 to x=1 is:
percent change = (f(1) - f(0)) / f(0) x 100%
= (6 - 2) / 2 x 100%
= 200%
This means that the output value increased by 200% when the input value increased by 1. We can also express this as a constant percent rate of change by dividing the percent change by the change in input value:
constant percent rate of change = percent change / change in input value
= 200% / 1
= 200%
Therefore, the equation [tex]f(x) = 2(3)^x[/tex] has a constant percent rate of change of 200%.
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of a triangle, having three sides of all different lengths. is called?
Answer: scalene triangle
Step-by-step explanation:
can be defined as a triangle whose all three sides have different lengths, and all three angles are of different measures. The angles of a scalene triangle follow the angle sum property and always add up to 180.
Answer:
scalene triangle is the triangle
A pre-image has coordinates Y(9,2),Z(3,-2) and W(6,4). The image has coordinates Y'(-9,2), Z'(-3,-2) and W'(-6,4). What type of reflection accoured? Explain how you know your answer is correct
need help (if its correct ill give brainliest)
Answer:
a. vertical angles
b. supplementary angles
c. complementary angles
Use the table to describe the intervals over which f(x) = 15x² is increasing and decreasing.
f(x)=15x²
(x,y)
(-2,60)
60
15
(-1,15)
0
15
60
X
-2
-1
0
1
2
(0,0)
(1,15)
(2,60)
The function f(x) is increasing over the interval x>0¹.
(Simplify your answer. Type an inequality.)
The function f(x) is decreasing over the interval
(Simplify your answer. Type an inequality.)
Answer:
Step-by-step explanation:
The function f(x) = 15x² is increasing over the interval x > 0.
To see why, we can look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. When x is zero, f(x) reaches its minimum value of zero. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is increasing over the interval x > 0.
The function f(x) is decreasing over the interval x < 0.
To see why, we can again look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. But as x approaches zero from the left, f(x) begins to decrease, reaching its minimum value of zero at x = 0. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is decreasing over the interval x < 0.
For the following exercises, find the derivative
of y = sec−1 ⎛
⎝
1
x
⎞
the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²). To find the derivative of y = sec⁻¹(1/x), we will use the chain rule of differentiation. Let's start by using the definition of the inverse secant function:
sec⁻¹(θ) = cos⁻¹(1/θ)
Then we can rewrite the given function as:
y = cos⁻¹(x)
Using the chain rule, the derivative of y with respect to x is:
dy/dx = d/dx [cos⁻¹(x)]
= -1/√(1 - x²) * d/dx [x]
= -1/√(1 - x²)
Therefore, the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).
We can check this result by taking the derivative of y using the definition of the inverse secant function:
y = sec⁻¹(1/x)
sec(y) = 1/x
cos(y) = x
-sin(y) dy/dx = 1
dy/dx = -1/sin(y)
Using the Pythagorean identity sin²(y) + cos²(y) = 1, we can solve for sin(y) as:
sin(y) = √(1 - cos²(y)) = √(1 - x²)
Substituting this expression into the derivative, we get:
dy/dx = -1/√(1 - x²)
which is the same result we obtained using the chain rule. Therefore, we have confirmed that the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).
To know more about inverse secant function: click here:
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