The velocity of the particle at times t = a, t = 1, t = 2, and t = 3 are:
a) 4/a^2 m/s, 4 m/s, 1 m/s, 4/9 m/s.
b) The instantaneous velocity of the particle when t=1 is 4 m/s.
To find the velocity, we need to take the derivative of the displacement function with respect to time. The derivative of s = 4/t^2 is ds/dt = -8/t^3. So, the velocity of the particle at time t is given by v = ds/dt = -8/t^3.
For t = a, the velocity is v = -8/a^3 m/s. For t = 1, the velocity is v = -8 m/s. For t = 2, the velocity is v = -2 m/s. For t = 3, the velocity is v = -8/27 m/s.
To find the average velocity during the time period [1, 2], we need to find the displacement at t = 2 and t = 1, then calculate the change in displacement divided by the time interval: (4/4 - 4/1)/1 = 0 cm/s. To find the average velocity during the time period [1, 1.1], we need to find the displacement at t = 1.1 and t = 1, then calculate the change in displacement divided by the time interval: (4/1.1^2 - 4/1)/0.1 = -19.60 cm/s.
To estimate the instantaneous velocity of the particle at t = 1, we can plug in t = 1 to the derivative we found earlier: v = -8/1^3 = -8 m/s. Therefore, the instantaneous velocity of the particle when t = 1 is 4 m/s.
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81 x 62
Not sure how to do this lol
Answer:
5,022
Step-by-step explanation:
3.1 calculate the sum of vectors a and c from part 2. show all formulas and calculations (insert your calculations in the lab report)
The matching parts of vectors a and c to find a + c. For instance, (1, -2, 4) + (2, 3, -1) = (3, 1, 3).
The equations and calculations to determine the vectors a and c's sum are as follows:
Assume that vector an is shown as (a1, a2, a3) and that vector c is shown as (c1, c2, c3).
Then, by adding each of their respective components, it is possible to determine the vectors a and c's sum, denoted as a + c:
A plus C equals (A+C1, A+C2, A+C3, etc.)
For instance, if a = (2, 3, -1) and c = (1, -2, 4), we can use the following formula to get their sum:
a + c = (2 + 1, 3 - 2, -1 + 4) = (3, 1, 3) (3, 1, 3)
As a result, the vectors a and c's sum is (3, 1, 3).
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If the possibility of winning is 1/5 what is the possibility of losing
Answer:
4/5
Step-by-step explanation:
Because 1/5 is winning chance.
and the rest percentage will be losing
what is 2/3 of 3/7 in math
Answer:
(2x3) / (3x7) = 6/21
We simplify to get 2/7
Answer: 5/21 ?
im not 100% sure this is correct but I think so. sorry if its wrong
Estimate 3 1/2 -1 1/3
The estimated difference of 3 1/2 and 1 1/3 is 2 1/6.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Are two fractions 3 1/2 and 1 1/3.
Now, The difference between 3 1/2 and 1 1/3 would be,
1/2 - 1/3 is 1/6 and 3 - 1 is 2,
So, The estimated 3 1/2 -1 1/3 is 2 1/6.
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Th second number is 3 less than twice the first
Answer:
Step-by-step explanation:
If we represent the first number as "x", then the second number can be represented as "2x-3".
For example, if the first number is 5, then the second number would be 2(5)-3 = 7.
Alternatively, if the first number is 10, then the second number would be 2(10)-3 = 17.
In general, we can say that the second number is equal to twice the first number minus 3.
Translate the sentence into an inequality.
Seven increased by the product of a number and 10 is at least 22.
Use the variable b for the unknown number.
The correct inequality is,
⇒ 7 + 10b ≥ 22
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Translate the sentence into an inequality,
''Seven increased by the product of a number and 10 is at least 22.''
Now,
Let an unknown variable = b
Hence, We can formulate;
⇒ 7 + b × 10 ≥ 22
⇒ 7 + 10b ≥ 22
Therefore, The correct inequality is,
⇒ 7 + 10b ≥ 22
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find the number of outcomes in the complement of the given event. out of 216 books in a bookcase, 155 are nonfictional.
The number of outcomes in the complement of the given event is 61.
The complement of the event "choosing a nonfictional book from the bookcase" is "choosing a fictional book from the bookcase. "Number of outcomes in complement = Total number of books - Number of nonfictional books
The number of outcomes in the complement is equal to the total number of books in the bookcase minus the number of nonfictional books in the bookcase:
Number of results in complement = Number of nonfiction books - Overall number of books = 216 - 155 = 61
Therefore, there are 61 outcomes in the complement of the given event.
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A plane leaves an airport and flies due north. Two minutes later, a
second plane leaves the same airport flying due east. The flight
plan shows the coordinates of the two planes 10 minutes later. The
distances in the graph are measured in miles. Use the Pythagorean
Theorem to find the distance shown between the two planes.
(Example 2)
The distance between the two planes after 10 minutes is 10 miles.
Step by step explanationWe can use the Pythagorean Theorem to find the distance between the two planes. According to the theorem, the distance between two points in a plane is given by the equation:
d = √( (x2 - x1)^2 + (y2 - y1)^2 )
where (x1, y1) and (x2, y2) are the coordinates of the two points.
The first plane is flying due north, so its position after 10 minutes will be (0, 10). The second plane is flying due east, so its position after 10 minutes will be (10, 0).
We can plug these coordinates into the equation to find the distance between the two planes:
d = √( (10 - 0)^2 + (10 - 0)^2 )
d = √( 100 )
d = 10
So the distance between the two planes after 10 minutes is 10 miles
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El agua de un recipiente varía su temperatura de 12 °C a 38°C, cuando se le transfieren 205 calorías. ¿Cuál es la masa de agua en el recipiente?
The mass of the water is 7880.1 grams.
What is specific heat capacity?Specific heat capacity is the amount of heat energy required to raise the temperature of a substance per unit of mass.
Mathematically -
Q = mcΔT
where -
{Q} = heat energy
{m} = mass
{c} = specific heat capacity
{ΔT} =change in temperature
Given is the water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it.
Specific heat capacity of water = 4.186 J/g°C
205 calories = 857720 Joules
We can write -
Q = mcΔT
857720 = m x 4.186 x (38 - 12)
857720 = 108.836 x m
m = 857720/108.836
m = 7880.1 grams
Therefore, the mass of the water is 7880.1 grams.
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{QUESTION IN ENGLISH -
The water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it. What is the mass of water in the container?}
Suppose a researcher Is Interested in the effects of a new treatment on extraversion. She randomly selects four participants (n=4), Implements the new treatment, and asks them to complete a personality test. The participants achieve the mean score of M- 115 on the test. The personality test has the population mean of μ- 100 and a-30. Is the sample mean an especially unlikely result based on the population parameters for the personality test? That is, can the researcher conclude that the new treatment has an effect on extraversion? Show your work.
A one-sample t-test can be used to determine whether the sample mean of M=115 is a particularly improbable outcome given the population parameters.
The test's null hypothesis is that the new treatment has no impact on extraversion, in which case the population mean remains at or above 100. The alternative theory is that the new treatment has an impact on extraversion, causing the population mean to deviate from the reference value of 100.
Using the following method, we can determine the test's t-statistic:
(M - ) / (s / sqrt(n)) t
Where M denotes the sample mean, denotes the population mean, s denotes the population standard deviation, and n denotes the sample number.
By entering the numbers we have:
t = (115 - 100) / (30 / sqrt(4)) = 3.33
The measure has n-1 = 3 degrees of freedom. We can use a calculator to determine the critical t-value, which is roughly 3.182, using a two-tailed t-test with alpha = 0.05 and 3 degrees of freedom.
The sample mean is a particularly improbable result based on the population parameters for the personality test because the calculated t-value of 3.33 is higher than the critical t-value of 3.182, and we can therefore reject the null hypothesis.
The evidence from the sample allows the researcher to draw the conclusion that the novel treatment has an impact on extraversion.
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Can someone help me please another graph
Step-by-step explanation:
the function
Kendal(x) = y = 90
is just a flat line (that's why people call it a flat rate). it does not matter how many hours it takes, it costs the same.
the function
Mona(x) = 10x + 70
as we know, $10 per hour, plus $70 for the material, which is the same cost no matter how many hours it takes.
the solution, when both cost the same, means again both functions are equal at that point :
90 = 10x + 70
20 = 10x
x = 20/10 = 2 hours
after 2 hours both cost the same : $90.
the graphic should look like the attached picture.
the flat line is at y = 90. that means it is a horizontal line that goes through the y gridline marker 90.
just draw the line along the y 90 gridline from left to right.
Mona's graph goes through the solution point (2, 90) and the point for x = 0 : (0, 70) because y = 10×0 + 70 = 70.
for (0, 70) you go from 0 the y-axis straight up to the gridline marker 70 and mark the point there.
for (2, 90) you go on the x-axis from 0 to the right to the gridline marker 2. from there you go straight up to the y gridline 90. and you mark the point there.
and both lines intersect at (2, 90), which is the solution.
can you see and understand it now how that works ?
The cost is $90
What is graphing?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The function for Kendal(x) is:- y = 90
The function for Mona(x) :- 10x + 70
$10 per hour, plus $70 for the material
The solution, when both cost the same, means again both functions are equal at that point :
90 = 10x + 70
20 = 10x
x = 20/10 = 2 hours
after 2 hours both cost the same : $90.
Graph the lines both lines intersect at (2, 90), which is the solution.
Hence, the cost is $90
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The height of a 20-inch tall plant that grows 5 inches each month for x months.
I would assume its 4
7x-5y=
12z+2y to the 2nd power=
2xy+8z=
The values of the expressions are 7x - 5y = -1, 12z + 2y² = 6 and 2xy + 8z = 4
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
x = 2, y = 3 and z = -1
Substitute the known values in the given equations, so, we have the following representation
7x - 5y = 7 * 2 - 5 * 3
7x - 5y = -1
12z + 2y² = 12 * -1 + 2 * 3²
12z + 2y² = 6
2xy + 8z = 2 * 2 * 3 + 8 * -1
2xy + 8z = 4
Hence, the expressions have their values to be -1, 6 and 4
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Complete question
Consider the following expressions:
7x-5y=
12z+2y²=
2xy+8z=
Determine the values when x = 2, y = 3 and z = -1
prove or disprove the following proposition. for all nonnegative integer x, x can be expressed by the sum of at most two squares and a cube of nonnegative integers.
The proposition is false, and there exist nonnegative integers x that cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.
This proposition is false. A counterexample is x = 7.
Assume for the sake of contradiction that there exist nonnegative integers a, b, and c such that x = a² + b² + c³. Since a² and b² are always nonnegative, we must have c³ ≤ 7. The only possible values for c are 0, 1, and 2, since 3³ = 27 > 7.
For c = 0, we have x = a² + b², which is the sum of two squares, and is a well-known result.
For c = 1, we have x = a² + b² + 1. However, it is a known result that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 7 is of the form 4(8×0 + 7), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.
For c = 2, we have x = a² + b + 8. Similarly, it can be shown that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 8 is of the form 4(8×1 + 0), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.
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f(x)=x+6, g(x)=x-6
Verify that f and g are inverse functions
The functions f and g are inverse functions because f(g(x)) = g(f(x)) = x
How to verify that f and g are inverse functionsFrom the question, we have the following parameters that can be used in our computation:
f(x) = x + 6
g(x) = x - 6
To determine the inverse function, we calculate
f(g(x)) and g(f(x))
Using the above as a guide, we have the following:
f(g(x)) = x + 6 - 6 = x
g(f(x)) = x + 6 - 6 = x
So, we have
f(g(x)) = g(f(x)) = x
Hence, the functions are inverse functions
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How do you work this problem?
Answer:
Attached. Hope this helps
What is the image point of (-6, 1) after the transformation R180 0 D4?
O
The image point will be (0, -4).
How to transform 180 counterclockwise?When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.
Given:
Coordinate of a point → (0, 1)
Rule for the transformation has been given as,
[tex]R_{180[/tex] o D₄
First use [tex]R_{180[/tex] → Rotation of the point by 180° counterclockwise
Rule :
(x, y) → (-x, -y)
(0, 1) → (0, -1)
Now, D₄ → Dilation of the point by a scale factor of 4 about the origin
If a point (x, y) is dilated by a scale factor 'k' about the origin rule for the dilation is,
(x, y) → (kx, ky)
By applying this rule,
(0, -1) → (0, -4)
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Use the Venn diagram to determine the roster form of set (A-C)'
Using the Venn diagram to determine the roster form of set (A-C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }.
What are the elements for (A - C )?The difference of the sets A and C in this order is the set of elements which belong to A but not to C.
A - C = elements in set A but not in set C
A - C = { 3, 4 , 8 }
The A minus C complements include the following;
(A - C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }
Thus, using the Venn diagram to determine the roster form of set (A-C)' depends on the number of elements in the universal set.
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For each value of y, determine whether it is a solution to 22 ≤-7y+1
A.-3 B. 4 C. 9 D. -9
The solution of the inequality is -3.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
22 ≤-7y+1
Solving the inequality
22 ≤-7y+1
22 - 1 ≤-7y
21 ≤-7y
21/7 ≤-y
3 ≤-y
y≤ -3.
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senior management of a consulting services firm is concerned about a growing decline in the firm's weekly number of billable hours. the firm expects each professional employee to spend at least 40 hours per week on work. in an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. rather than reviewing the records of all the firm's full-time employees, the management randomly selected a sample of size 51 from the available frame. the sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively. construct a 88% confidence interval for the mean of the number of hours this firm's employees spend on work-related activities in a typical week. place your lower limit, in hours, rounded to 1 decimal place, in the first blank. for example, 6.7 would be a legitimate entry. place your upper limit, in hours, rounded to 1 decimal place, in the second blank. for example, 12.3 would be a legitimate entry.
The population standard deviation representing the number of hours spend by the employees on work related activities in a typical week for 88% confidence interval is equal to [ 46.862 , 50.138 ].
Mean '[tex]\bar{x}[/tex]' = 48.5 hours
Standard deviation 'σ' = 7.5 hours
Confidence interval = 88%
Level of significance = 100 - 88%
= 12%
= 0.12
Z-score at 88% confidence interval = 1.56
sample size 'n' = 51
Population standard deviation
= [tex]\bar{x}[/tex] ± [tex]Z_{\alpha /2}[/tex] (σ / √n )
= 48.5 ± 1.56 ( 7.5 / √51 )
= 48.5 ± 1.56 ( 7.5 / 7.14)
= 48.5 ± 1.56 ( 1.05 )
= 48.5 ± 1.638
= [ 46.862 , 50.138 ]
Therefore, the number of hours spend on work related activities in a typical week given by population standard deviation is equal to [ 46.862 , 50.138 ].
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In an experiment, a 5-kg mass is suspended from a spring. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 75 cm. The mass is then displaced 36 cm upward from its spring-mass equilibrium and then given a sharp downward tap, imparting an instantaneous downward velocity of 0.45 m/s. Set up (but do not solve) the initial value problem that models this experiment. Assume no damping is present.
I have the following answer: 5y''=-65.3y+49 y(0)=-0.36 y'(0)=0.45
Can anyone confirm that this is correct, or show me where I went wrong?
The correct initial value problem is: y'' + (9.81/0.75) y = 0, y(0) = -0.36, y'(0) = -0.45.
Here's how you can set up the initial value problem
Let y(t) be the displacement of the mass from its spring-mass equilibrium position at time t. Then, the force acting on the mass is given by Hooke's Law:
F = -ky
where k is the spring constant.
Since the mass is at rest at its equilibrium position, the force acting on it is balanced by the force of gravity.
mg = ky_eq
where y_eq is the equilibrium position of the spring-mass system.
Substituting F = -ky into the equation and solving for k, we get:
k = mg/y_eq
Substituting k and the values given, we get:
y'' + (9.81/0.75) y = 0
where y'' is the second derivative of y with respect to time.
When the mass is displaced 36 cm upward from its spring-mass equilibrium and then given a sharp downward tap, the initial conditions are:
y(0) = -0.36 m
y'(0) = -0.45 m/s (note that the velocity is downward, so it's negative)
Therefore, the initial value problem that models this experiment is:
y'' + (9.81/0.75) y = 0
y(0) = -0.36
y'(0) = -0.45
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given the following data, find the weight that represents the 45th percentile. weights of newborn babies 7.8 5.5 7.6 8.3 7.1 7.3 8.6 7.4 8.5 7.7 6.5 9.4 8.4 8.1 6.5
The 45th Percentile from the data is 7.65
Percentiles are a method for dividing data into 100 equal parts. So, there are 99 percentile values.
single data percentile formula is
Px = [tex]\frac{x (y+1)}{100}[/tex]
Px = Percentile x
y = lots of data
How to find the 45th percentile weight of newborn babies?
first, we must be sorted from the smallest to the largest.
5.5 6.5 6.5 7.1 7.3 7.4 7.6 7.7 7.8 8.1 8.3 8.4 8.5 8.6 9.4
After sorting the data, we can plug it into a single data percentile formula
Px = P45
x = 45
y = 15
P45 = [tex]\frac{45 (15+1)}{100}[/tex]
P45 = [tex]\frac{36}{5}[/tex]
P45 = 7.2
The 45th percentile is in the order of the 7th & 8th digits
the order of the 7th & 8th numbers is 7.6 & 7.7
after that we average the 7th & 8th numbers to find out the 45th percentile value
[tex]\frac{7.6 + 7.7}{2}[/tex] = [tex]\frac{15.3}{2}[/tex] = 7.65
the 45th percentile of newborn weight data is 7.65
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Andre said he is thinking of a 2-digit number. He makes the number from tens and ones in 8 different ways. In one way, there is 1 more ten than there are ones. What is Andre's number? Show your thinking using drawings, numbers, or words.
Andre's number is 43.
What is Andre's number?Generally, Let's call the tens digit of Andre's number "t" and the ones digit "o".
We know that Andre can make the number in 8 different ways. This means that there are 8 different combinations of t and o that can make up the number.
One of these ways has 1 more ten than ones, which means that the number is 10 more than the sum of the digits. In other words:
t + o + 10 = 10t + o + 1
Simplifying this equation, we get:
9t = 9o + 9
Dividing both sides by 9, we get:
t = o + 1
This means that the tens digit is 1 more than the ones digit, which narrows down our possibilities.
Since the number is a 2-digit number, the tens digit must be between 1 and 9 (inclusive), and the ones digit must be between 0 and 9 (inclusive). We also know that the tens digit is 1 more than the ones digit.
Using these constraints, we can create a table of all the possible combinations of t and o that satisfy these conditions:( table attached below)
Out of these 8 numbers, only one of them can be made in a way where there is 1 more ten than ones. Looking at the table, we can see that the number is 43, since it is the only number where the tens digit is 1 more than the ones digit, and it can be made by combining the digits in a way where there is 1 more ten than ones (i.e., 3 tens and 4 ones).
Therefore, Andre's number is 43.
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Jesse wishes to draw a square of equal area to a given circle with diameter 1 inch.
What is the side length of the square that will give the closest approximation to the area of the circle described?
a. s = π/2 inches
b. s = 3/4 inches
c. s = 8/9 inches
d. s = 1/2 inches
e. s = π/4 inches
The side length of the square that will give the closest approximation to the area of the circle described is e. s = π/4 inches
What is the Area of a Circle?The region encircled by a circle with a radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.
The area of a circle with a diameter of 1 inch is given by the formula πr^2, where r is the radius of the circle. The radius of the given circle is 1/2 inch, so its area is approximately π * (1/2)^2 = π/4 square inches.
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12x + 51y = 156
- 8x - 34y = - 104
14. Look for Relationships Does this system have one solution, no solutions, or infinitely many solutions? Write another system of equations with the same number of solutions that uses the first equation only.
12x+51y=156
-8x-34y= -104
Anοther system οf linear equatiοns with the same number οf sοlutiοns is 12x + 51y = 156
24x + 102y = 312
What is linear equatiοn?A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal space. It is an equatiοn that has οnly οne independent variable and οne οr mοre cοefficients that represent the slοpe and intercept οf the line.
The general fοrm οf a linear equatiοn is: y = mx + b
Where: y is the dependent variable x is the independent variable
m is the slοpe οf the is the y-intercept
Accοrding tο the questiοn:
Tο determine whether this system οf equatiοns has οne sοlutiοn, nο sοlutiοns, οr infinitely many sοlutiοns, we can use variοus methοds such as substitutiοn οr eliminatiοn. Here, we'll use the eliminatiοn methοd:12x + 51y = 156-8x - 34y = -104
Tο eliminate οne οf the variables, we need tο find a cοmmοn multiple οf the cοefficients οf x οr y in bοth equatiοns. In this case, the cοmmοn multiple is 17, because 51 and -34 have 17 as a cοmmοn factοr:12x + 51y = 156 (multiply by 2)-16x - 68y = -208 (multiply by 2)
Nοw, we can add the twο equatiοns tο eliminate
y:12x + 51y = 156-16x - 68y = -208---------------4x - 17y = -52
We can sοlve fοr y in terms οf x:-4x - 17y = -5217y = -4x + 52y = (-4/17)x + 52/17This is the equatiοn οf a line in slοpe-intercept fοrm, with slοpe -4/17 and y-intercept 52/17.
We can alsο write anοther system οf equatiοns with the same number οf sοlutiοns that uses the first equatiοn οnly by multiplying bοth sides οf the equatiοn by a cοnstant
12x + 51y = 156
24x + 102y = 312
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box with 2 red and 1 blue ball pick one randomly and replace with blue what is the expected number to get rid of all red balls
The expected number is 1, that means that if you randomly pick one ball and replace it with a blue ball, then you have a greater than 50/50 chance of eliminating all the red balls.
The expected number of blue balls needed to eliminate all red balls is calculated using the formula[tex]n = (x-1)/(y-1)[/tex]. In this scenario, x = 3 (the total number of balls in the box) and y = 2 (the number of red balls). Therefore, n = (3-1)/(2-1), which equals 1. So, the expected number of blue balls needed to eliminate all red balls is 1.
To illustrate this, imagine a box with 3 balls: 2 red and 1 blue. If you randomly pick one ball and replace it with a blue ball, then you have a 50/50 chance of eliminating all the red balls. If the ball you pick is red, then you need to pick another ball and replace it with a blue ball to get rid of the remaining red ball. This means that you need a total of 2 blue balls to get rid of all the red balls. However, since the expected number is 1, that means that if you randomly pick one ball and replace it with a blue ball, then you have a greater than 50/50 chance of eliminating all the red balls.
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complete question
What is the expected number of blue balls needed to eliminate all red balls from a box with 3 balls, 2 of which are red?
A store can print your soccer team's name on 12 T-shirts in 10 minutes you want to buy 30 T-shirts how long will it take the store to print 30 T-shirts if the T-shirts are always printed at the same rate
Answer:
Step-by-step explanation:
12 In 10 min
30 in 25mins
It will take the store 25 mins
12+12+6=30 t shirts
10+10+5=25mins
find the derivative of the following function using the definition. no credit will be given for using derivative rules. f(x)= 1/ (1+x^2). please solve and explain
Strictly using the limit definition of the derivative to find the derivative of the function:
The limit definition of the derivative looks like this:
[tex]\lim_{h \to \zero} \frac{f(x+h) - f(x) }{h}[/tex]
If we replace f(x) with −3x, we get:
[tex]\lim_{h \to \zero} \frac{-3(h+x) - 3x }{h}\\\\\lim_{h \to \zero} \frac{-3h-3x) - (-3x) }{h}\\[/tex]
Simplifying, we get:
[tex]\lim_{h \to \zero} \frac{-3h }{h}\\[/tex]
So, the derivative of −3x must be −3.
We know that the secondary means the rate of change of the function. Graphically, this means that the outgrowth is the pitch of the graph of that function.
Since −3x is a first degree polynomial, we know that it'll always have the same pitch, and therefor the same outgrowth. We can also corroborate this by looking at the graph, noticing that it's a straight line:
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SH . Given f(x)=x²-3x and g(x)=2x-5, find each value. a. f(-4) b. g(1)-f(-3) c. f(g(-4))
a. To find f(-4), we simply substitute -4 for x in the function f(x):
f(-4) = (-4)² - 3(-4) = 16 + 12 = 28
Therefore, f(-4) = 28.
b. To find g(1)-f(-3), we first need to find g(1) and f(-3) separately.
g(1) = 2(1) - 5 = -3
f(-3) = (-3)² - 3(-3) = 9 + 9 = 18
Then, we can substitute these values into the expression:
g(1)-f(-3) = -3 - 18 = -21
Therefore, g(1)-f(-3) = -21.
c. To find f(g(-4)), we first need to find g(-4) and then substitute this value into f(x).
g(-4) = 2(-4) - 5 = -8 - 5 = -13
Then, we can substitute -13 for x in the function f(x):
f(g(-4)) = (-13)² - 3(-13) = 169 + 39 = 208
Therefore, f(g(-4)) = 208.