The required average velocity both conditions are -2 mm/s and -1/2 mm/s.
What is velocity?The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
According to question:To find the average velocity over the interval 1 < t < 3 for the position function s(t) = 12t - t^2, we need to find the derivative of the position function and then evaluate it at the limits of the interval. The derivative of the position function s(t) = 12t - t^2 is given by:
s'(t) = 12 - 2t
The average velocity over the interval 1 < t < 3 is given by:
v_avg = (s'(3) - s'(1)) / (3 - 1) = (12 - 23 - (12 - 21)) / (3 - 1) = -2
Therefore, the average velocity over the interval 1 < t < 3 for the position function s(t) = 12t - t^2 is -2 mm/s.
For the position function s(t) = ln(t), the derivative of the position function is given by:
s'(t) = 1/t
The average velocity over the interval 1 < t < 3 is given by:
v_avg = (s'(3) - s'(1)) / (3 - 1) = (1/3 - 1) / (3 - 1) = -1/2
Therefore, the average velocity over the interval 1 < t < 3 for the position function s(t) = ln(t) is -1/2 mm/s.
To know more about Function of time visit:
brainly.com/question/12174888
#SPJ4
The distribution of ph levels for all community swimming pools in a large county is approximately normal with mean 7. 5 and standard deviation 0. 2. According to swimming pool studies, the safest ph levels for water in swimming pools are between 7. 2 and 7. 8. (a) one community swimming pool in the county will be selected at random. What is the probability that the selected pool has a ph level that is not considered safe?.
The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.
1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5
2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5
3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668
4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332
5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
a vector has initial point 1=(−3,1) and terminal point 2=(,7). find all numbers so that has length 10
The terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).
The length of a vector can be calculated using the Pythagorean Theorem. The formula for calculating the length of a vector can be expressed as:
Length (vector) = √((x2 - x1)² + (y2 - y1)²).
In this case, the initial point is (x1, y1) = (-3, 1) and the terminal point is (x2, y2) = (x, y) = (x, 7). Substituting these values into the formula, we get:
Length = √((x - (-3))² + (7 - 1)²)
As we need the length of the vector to be 10, we can solve for x.
10 = √((x + 3)² + 6²)
100 = (x + 3)² + 36
164 = (x + 3)²
12.8 = x + 3
x = -15.8
Therefore, the terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).
Learn more about terminal point here:
https://brainly.com/question/29279682
#SPJ4
10 ≤ 2x ≤ x+9
I need an explanation in how to solve this step by step?
The solution to the given inequality, 10 ≤ 2x ≤ x+9, is 5 ≤ x ≤ 9
Solving Linear inequalitiesFrom the question, we are to solve the given inequality
The given inequality is
10 ≤ 2x ≤ x+9
Then,
We can write that
10 ≤ 2x and 2x ≤ x+9
First, solve the inequality 10 ≤ 2x
10 ≤ 2x
Divide both sides by 2
5 ≤ x
Now, solve
2x ≤ x + 9
2x - x ≤ 9
x ≤ 9
Thus,
5 ≤ x and x ≤ 9
5 ≤ x ≤ 9
Hence, the solution is 5 ≤ x ≤ 9
Learn more on Solving linear inequality here: https://brainly.com/question/24372553
#SPJ1
The population of winbug beetles in 1990 was 35,000. The population each year after 1990 is shown by the equation below.
P(t) = 6,000 + 29,000(1 + 0.031)^t
Which of the following best describes what will happen to the population of winbug beetles in the years after 1990?
A) As t approaches positive infinity, P(t) approaches zero
B) As t approaches positive infinity, P(t) approaches positive infinity.
C) As t approaches positive infinity, P(t) approaches negative infinity.
D) As t approaches positive infinity, P(t) remains constant.
B) P(t) increases as t increases toward positive infinity.
An exponent is what?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The population of winbug beetles after t years from 1990 is represented by the expression P(t) = 6,000 + 29,000(1 + 0.031)t.
We can see that when t grows, the exponential growth factor (1 + 0.031)t will eventually reach positive infinity. This implies that as t approaches positive infinity, the population of winbug beetles will similarly increase.
Consequently, the following is the best prediction of what will occur to the winbug beetle population in the years after 1990.
Learn more about Exponents here:
brainly.com/question/5497425
#SPJ1
does this interval give convincing evidence of a difference between the population proportions? justify your answer. no. because the interval does not contain 0, there is not convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. yes. because the interval does not contain 0, there is convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. no. because the interval does not contain negative numbers, there is not convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. yes. because the interval does not contain negative numbers, there is convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. no. because the conditions were not met, we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify egypt on the map is different from the true proportion of women that can identify egypt on a map.
The answer to the question is no, there is not convincing evidence of a difference between the population proportions.
Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.
In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.
Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.
To learn more about Confidence intervals,
Visit; brainly.com/question/24131141
#SPJ4
The answer to the question is no, there is not convincing evidence of a difference between the population proportions.
Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.
In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.
Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.
To learn more about Confidence intervals,
brainly.com/question/24131141
#SPJ4
COMPOUND INTEREST You depoit $100 i n an account that pay 6% annual
interet. How long will it take for the balance to reach $1000 for each given
frequency o f compounding?
The time it takes for the balance to reach $1000 depends on the frequency of compounding:
If compounding is done annually (once per year), it will take approximately 12.68 years for the balance to reach $1000.If compounding is done semi-annually (twice per year), it will take approximately 12.44 years for the balance to reach $1000.If compounding is done quarterly (four times per year), it will take approximately 12.33 years for the balance to reach $1000.If compounding is done monthly (twelve times per year), it will take approximately 12.25 years for the balance to reach $1000.This is calculated using the formula for compound interest: A = P * (1 + r/n)^(nt), where P is the initial deposit, r is the annual interest rate, n is the number of times compounded in a year, and t is the number of years.
Compound Interest CalculationI calculated the time it takes for the balance to reach $1000 using the formula for compound interest:
A = P * (1 + r/n)^(nt),
where A is the final balance, P is the initial deposit ($100), r is the annual interest rate (6%), n is the number of times compounded in a year (annually, semi-annually, quarterly, or monthly), and t is the number of years.
I solved for t, keeping all other variables constant, by taking the natural logarithm of both sides of the equation and rearranging the terms:
t = (ln(A/P)) / (ln(1 + r/n) * n)
I used a mathematical software or calculator to perform the calculations and obtain the values for t for each given frequency of compounding.
Learn more Compound Interest Calculation here:
https://brainly.com/question/25857212
#SPJ4
There are 2 red, 5 green, 3 blue and 4 white point on a circle. Find the number of line egment which have endpoint of different color at the given point
The number of those line segments which have endpoints of different colors is 40.5.
What is permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to organise the components of set A, as you can see.Given data :
There are 2 red, 5 green, and 3 blue points on a circle.
There are different colored endpoints on each line segment that starts at a red point and travels to either a green point or a blue point.
There are 2 red points and 7 segments from each of them, making a total of 14 segments.
There are different colored endpoints on each line segment that leaves at a green point and travels to either a red or blue point.
There are 5 green points and 8 segments from each, for a total of 40 segments.
There are different colored endpoints on each line segment that leaves at a blue point and travels to either a green point or a red point.
Each blue point has 9 segments, and there are a total of 3 blue points.
Add all the ways = 14 + 40 + 27
= 81 segments.
Number of segment = 81/2 = 40.5 Segments
Thus, the number of those line segments which have endpoints of different colors is 40.5.
Learn more about permutation refer to :
https://brainly.com/question/1216161
#SPJ4
Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
How many bags of popcorn will Team A need to sell to reach their goal?
Answer:
255
Step-by-step explanation:
Let's call the number of bags of popcorn sold by Team A as "x".
The total cost for the popcorn machine rental and supplies is $15 + 0.05x.
The revenue from selling the popcorn is 0.5x.
To reach their goal of $100, they need to satisfy the equation:
$100 = 0.5x - ($15 + 0.05x)
Expanding and solving for x:
$100 = 0.5x - $15 - 0.05x
$115 = 0.45x
x = $115 / 0.45 = 255 bags of popcorn
So, Team A needs to sell 255 bags of popcorn to reach their goal of $100.
To know more about Basic maths Calculations refer:
https://brainly.com/question/18221902
In isosceles ABC, AC is the base, Points D. Band
Fare the midpoints of AB. A and BC
respectively. The length of BD is 13 inches and
ZBFD 65. Find each measure
a. A
b. DE
G. AD
d. M EDF
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
The measure of each of the following are as follows :
the measure of A = 115 degree.
the measure of DE = √338/4.
the measure of AD = √338/2.
the measure of DEF = 57.5 degrees.
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
To know more about the triangles on brainly : brainly.com/question/9265928
#SPJ4
If F and f are differentiable function such that F(x) = integral^x_0 f(t) dt and if F(a) = -2 and F(b) = -2 where a < b which must be true? a. f(x) = 0 for some x such that a < X < b b. f(x) < 0 for all X such that a < X < b c. f(x) = 0 for some X such that a < X < b d. f(x) > 0 for all X such that a < X < b e. f(x) less than or equal to 0 for all X such that a < X < b
By differentiable polynomial f(x) = 0 for some x such that a < X < b , A is correct
What is an example of a differentiable function?
If a function's derivative is present at every location inside its domain, the function is said to be differentiable. If a function f(x) is differentiable at x = a, in particular, then f′(a) exists in the domain.
Let's examine a few instances of differentiable polynomial and transcendental functions, such as f(x) = x4 - 3x + 5.
A is correct
F receives two equal values in different places .
consider the line between them .
it cannot be in a coustant ascent nor descent, since it must return to the minimal value .
therefore, A, either coutant or has an surprising and descending area ,
thus from Fermat's rule the derivate must be equal to zero .
Learn more about differentiable function
brainly.com/question/30079101
#SPJ4
What is the domain function?
The domain of a function is the set of possible values that can be plugged into it.
What is meant by domain function?Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.
The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values. The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The entire range of possible values for the independent variable make up the domain of a function. In layman's terms, this definition states that the domain is the collection of all x-values that could possibly cause the function to "work" and produce actual y-values.
To learn more about domain function refer to:
https://brainly.com/question/29208286
#SPJ4
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Below are two dot plots containing sample means from the same population
How many samples are represented in each plot?
There are __ samples in both plot A and plot B. Each dot represents one sample.
The number of samples for each dot plot is given as follows:
32.
What is shown by the dot plot?The dot plot shows the number of times that each measure appears in the data-set.
Hence the dot plot in this problem shows the number of samples that had means of 10, 20, 30, 40, 50, 60, 70, 80 and 90.
Hence, the total number of samples is obtained by the number of dots in each of the dot plots, which is of 32, hence the sentence is completed as follows:
There are 32 samples in both plot A and plot B. Each dot represents one sample.
More can be learned about dot plot at brainly.com/question/24309209
#SPJ1
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer: 12
Step-by-step explanation:
Answer:
[tex] \sf \: x = 12[/tex]
Step-by-step explanation:
Given equation,
→ x - 9 = 3
Now the value of x will be,
→ x - 9 = 3
→ x = 3 + 9
→ [ x = 12 ]
Hence, the value of x is 12.
f the current population size is x individuals, what fraction of the resources are they using collectively?
The fraction of resources used collectively by X individuals can be represented as X/R, where R represents the total resources available. The fraction of resources not being used is represented as (R-X)/R. The per-capita growth rate can be represented as dX/dt = kX, where k is the proportionality constant. The differential equation for the population's size is dX/dt = kX.
A detailed explanation:
a) If the current population size is X individuals, then the fraction of resources they are using collectively can be calculated as X/R, where R represents the total resources available. This calculation gives us the proportion of resources used by X individuals relative to the total resources available.
b) To calculate the fraction of resources not being used, we subtract the fraction of resources used by X individuals from 1. So, the fraction of resources not being used is (R-X)/R.
c) The per-capita rate of change of X can be represented as dX/dt = kX, where k is the proportionality constant. This equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k.
d) To convert the equation into a differential equation for the population's size, we simply make X' stand alone on the left-hand side of the equation. So, the differential equation for the population's size becomes dX/dt = kX.
e) This differential equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k. This equation can be used to model the growth of a population over time and to understand the relationship between the population size and the rate of change of the population.
To learn more about fraction, visit:
https://brainly.com/question/10354322#
#SPJ11
Complete questin:
If the current population size is X individuals, what fraction of the resources are they using collectively? c) In the same situation, what fraction of the resources are not being used? d) The per-capita rate of change of X can be written as 7%. The key assumption mentioned above says that this quantity is pro- portional to the expression you wrote down in part (c). Call the proportionality constant 1', and write an equation for the per-capita growth rate. e) Convert this equation into a differential equation (change equa- tion) for the population's size. (Just make X' stand alone on the left-hand side of the equation.)
What is the area of the trapezoid?
43.4 m²
33.4 m²
86.8 m²
20.2 m²
Answer:
43.4 m²
Step-by-step explanation:
side 1= 4+7 m=11m
side 2=3m
height = 6.2 m
we have
the area of the trapezoid = [tex]\frac{1}{2} height*(side1+side2)[/tex]
=[tex]\frac{1}{2} *6.2*(11+3)[/tex]
=[tex]\frac{1}{2} *6.2*14[/tex]
=43.4 m²
Work out:
2 x 2.2 x 10^12 × 1.5 × 10^12/
2.2 x 10^12 - 1.5 x 1012
Give your answer in standard form correct to 3 significant figures.
The index forms is expressed as 9. 40 × 10¹²
What are index forms?Index forms are simply described as representation of a number in the form of an exponential expression or a single number that is raised to a number or variable.
Other names for index forms are standard form and scientific notation.
It also explains how many times a number contains itself.
From the information given, we have that;
2 x 2.2 x 10^12 × 1.5 × 10^12/2.2 x 10^12 - 1.5 x 1012
Represented as;
2(2.2) × 10¹² × 1.5 × 10¹²/ 2.2 × 10¹² - 1. 5 × 10¹²
We can add or subtract the index forms because they have the same exponential value, we have;
4.4(1.5)× 10²⁴/0.7 × 10¹²
Find the quotient
9. 4 × 10¹²
Hence, the value is 9. 4 × 10¹²
Learn about index forms on:
https://brainly.com/question/15361818
#SPJ1
Find the diameter of the circular garden whose circumference is 124.03 cm.
39.5cm the diameter of the circular garden whose circumference is 124.03 cm.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Perimeter refers to the total outside length of an object.
here, we have,
circumference is 124.03 cm.
i.e. pi*d= 124.03 cm.
we know,
pi = 3.14
i.e. d= 124.03/3.14
=39.5cm
Hence, 39.5cm the diameter of the circular garden whose circumference is 124.03 cm.
Learn more about perimeter here:
brainly.com/question/397857
#SPJ1
If f(x) = 4x2 - 3x + 2, evaluate f(-1) and If f(x) = 4x + 3, evaluate f(x+h)
The value of f(-1) is 9
The value of f(x+h) is 4x + 4h + 3
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
f(x) = 4x² - 3x + 2 Now replace x with -1.
f(-1) = 4(-1)² -3(-1) + 2
f(-1) = 4 + 3 + 2
f(-1) = 9
f(x) = 4x + 3 Now replace x with x + h.
f(x+h) = 4(x+h) + 3
Distribute and simplify
= 4x + 4h + 3
To learn more about the equation from the given link
https://brainly.com/question/28218072
#SPJ4
An elevator went up 20 floors, down 13 floors, up 10 floors, and down 19 floors. Find its location.
Note: 1st floor (1) - Ground floor
Zero (0) - Parking Lot
Negative one (-1) - Underground
Negative two (-2) - Basement
Answer: -2 (basement)
Step-by-step explanation:
20-13=7
7+10=17
17-19= -2
Answer:
the basement
20-13=7+10=17-19=-2
when commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. the history of a particular fleet indicates that 69% of the planes inspected have no wing cracks, 21% have detectable wing cracks, and 10% have critical wing cracks. five planes are randomly selected. (round your answers to three decimal places.) (a) find the probability that one has a critical crack, two have detectable cracks, and two have no cracks. 0.063 correct: your answer is correct. (b) find the probability that at least one plane has critical cracks.
The probability of two planes having no cracks is 0.063 and The probability of no plane having critical cracks is 0.405.
(a) The probability of one plane having a critical crack is 10% or 0.10. The probability of two planes having detectable cracks is (0.21)^2 = 0.0441. The probability of two planes having no cracks is (0.69)^2 = 0.4761. So, the desired probability is 0.10 * 0.0441 * 0.4761 = 0.063.
(b) To find the probability that at least one plane has critical cracks, we can use the complementary probability approach, i.e., finding the probability that no plane has critical cracks and then subtracting it from 1. The probability of no plane having critical cracks is (0.90)^5 = 0.595. So, the desired probability is 1 - 0.595 = 0.405.
Learn more about Probability here:
https://brainly.com/question/25839839
#SPJ4
The mean is the measure of central tendency most likely to be affected by an outlier.true or false
The mean is the measure of the central tendency most likely to be affected by an outlier.
The following statement is correct.
The term "mean" is another synonym for "average." When there is an outlier in the data set, the mean suffers the most. The only measure of central tendency on which an outlier will always have an effect is the mean.
The mean is the only measure of central tendency that is affected by all values since it is calculated by dividing the total of the values by the number of observations.
The arithmetic mean is the average quantity in a given set of data. It is defined as the sum of all observations in the data divided by the total number of observations in the data. As a result, because it comprises all of the data in a series, the mean is influenced by the extreme values.
For more questions on Mean
https://brainly.com/question/26941429
#SPJ4
find the local minimum of and local maximum of values for the function: f ( x ) = { − x , x < − 1 2 − x 2 , x ≥ − 1
The local minimum of the of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.
The local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = -1. This is because when x = -1, the value of the function is f(-1) = -1. This is the lowest the function can get since the function is decreasing for x < -1 and increasing for x > -1.
The local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = 0. This is because when x = 0, the value of the function is f(0) = 0. This is the highest the function can get since the function is increasing for x < 0 and decreasing for x > 0.
Therefore, the local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.
Learn more about function here:
https://brainly.com/question/12431044
#SPJ4
evaluate the following. give your answers as exact fractions. 2 x2−4 dx −2 = 2 x2−4 dx −2 =
After evaluating the given equation ∫(x²-4)dx, we get -32/3.
Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function. If a function is integrable and if its integral over the domain is finite, with the limits specified, then it is the definite integration. If F(x) is a particular anti-derivative of f(x) on an interval I, then every anti-derivative of f(x) on I is given by ∫ f(x) dx = F(x) + C.
Here, ∫ f(x) dx represents the whole class of integral.
C is the arbitrary constant, and all the antiderivatives of f(x) on I can be obtained by assigning a particular value to C.
Here f(x) is the integrand,
The variable x in dx is called the integrator and the whole process of finding the integral is called the integration. The ∫ sign stands for the sum.
The given equation is:
∫(x²-4)dx for interval (-2,2).
Integrate the above equation, we get
∫(x²-4)dx = x³/3 -4x +c
Now, solving this for the interval (-2,2), we get
= (2³/3 - 4×2) - ((-2)³/3 - 4×-2)
= (8/3)-8 + 8/3 - 8 = -32/3
Thus, after evaluating the given equation ∫(x²-4)dx, we get -32/3.
To learn more about integration, visit brainly.com/question/18125359
#SPJ4
You have a total of 200 Coins, Consisting of nickels and dimes. The total value of the 200 Coins is $16.85. How many of each do you have?
Answer:
Below
Step-by-step explanation:
n = # nickels value = 5n
(200-n) = # dimes value = 10(200-n)
summed, these equal 1685
5n + 10(200-n) = 1685
5n + 2000 -10 n = 1685
-5n = -315
n = 63 then dimes = 137
find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) 2 x5 dx
The indefinite integral is [tex]\frac{x^6}{3} +c[/tex].
What is indefinite integral?
An integral is considered to be indefinite if it has no upper or lower bounds.
The most generic anti-derivative of f(x) is known as an indefinite integral and denoted, in mathematics, by F(x), which is any anti-derivative of f(x).
[tex]\int[/tex]f(x) = F(x) + C
Here the given integral is [tex]\int{2x^5} dx[/tex]
=> [tex]\int{2x^5} dx[/tex]
=> [tex]2\int x^5 dx[/tex]
We know that [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex] where c is constant then,
=> [tex]2[\frac{x^{5+1}}{5+1} ]+c[/tex]
=> [tex]2\frac{x^6}{6} +c[/tex]
=> [tex]\frac{x^6}{3} +c[/tex]
Now take [tex]\frac{x^6}{3}[/tex] and differentiate to check the results then,
=> [tex]\frac{d}{dy}[\frac{x^6}{3} ][/tex]
=> [tex]\frac{1}{3} \frac{dx^6}{dy}[/tex]
We know that [tex]\frac{d}{dy} x^n = nx^{n-1}[/tex] then
=> [tex]\frac{1}{3}\times6x^{6-1}[/tex]
=> [tex]2x^5[/tex]
Hence the indefinite integral is [tex]\frac{x^6}{3} +c[/tex].
To learn more about indefinite integral refer the below link
https://brainly.com/question/30416236
#SPJ4
how to find area of a triangle
Answer:
To find the area of a triangle you got A=1\2×b×h
you are moving to a new home and have rented a truck to assist you with the move. trailside truck rentals charges $39.95 per day plus 64 cents per mile. you will need the truck for 5 days and will travel 460 miles. what will be your total cost (in dollars) for the truck rental?
The total cost for the truck rental will be $495.75
The cost of the truck rental can be calculated using the formula:
Cost = Daily rate + Per mile rate * Total miles
where:
Daily rate = $39.95 per day
Per mile rate = 64 cents per mile = $0.64 per mile
Total days = 5 days
Total miles = 460 miles
Substituting the values in the formula, we get:
Cost = $39.95 * 5 + $0.64 * 460
Cost = $199.75 + $296
Cost = $495.75
Therefore, the total cost for the truck rental will be $495.75.
To learn more about equations,
Visit; brainly.com/question/29657983
#SPJ4
The total cost for the truck rental will be $495.75
The cost of the truck rental can be calculated using the formula:
Cost = Daily rate + Per mile rate * Total miles
where:
Daily rate = $39.95 per day
Per mile rate = 64 cents per mile = $0.64 per mile
Total days = 5 days
Total miles = 460 miles
Substituting the values in the formula, we get:
Cost = $39.95 * 5 + $0.64 * 460
Cost = $199.75 + $296
Cost = $495.75
Therefore, the total cost for the truck rental will be $495.75.
To learn more about equations,
brainly.com/question/29657983
#SPJ4
Persevere in Problem Solving You roll two number cubes at the same time.
Each cube has sides numbered 1 through 6. What is the probability that the sum of
the numbers rolled is even or greater than 9? (Hint: Create and fill out a probability
chart.)
The probability that the sum of the numbers rolled is even or greater than 9 is 25/36.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, two number cubes at the same time. Each cube has sides numbered 1 through 6.
There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Probability of getting sum as even number:
Number of favourable out comes = 18
Total number of outcomes = 36
Now, probability = 18/36
Probability of getting sum as greater than 9:
Number of favourable out comes = 7
Total number of outcomes = 36
Now, probability = 7/36
So, the probability of event is 18/36 + 7/36
= 25/36
Therefore, the probability that the sum of the numbers rolled is even or greater than 9 is 25/36.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ1
. STATE YOUR ASSUMPTION Breelyn is making cookies using a cookie cutter in the shape of a parallelogram. What are the perimeter and area of each cookie? Explain any assumptions that you make. Round your answers to the nearest hundredth, if necessary. order of get
The perimeter and area of a parallelogram can be determined if the length and width are known.
How to explain the perimeterThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.
Learn more about perimeter on:
https://brainly.com/question/19819849
#SPJ1
Is or Is Not? what is the correct answer?
The ordered pair (-2, 1) is not a solution
How to determine if the ordered pair is a solution or notFrom the question, we have the following parameters that can be used in our computation:
6x + 5y = -7
2x - 4y = -8
The ordered pair is given as
(-2, 1)
Substitute the known values in the above equation, so, we have the following representation
6(2) + 5(-1) = -7 == false
The above equation is false
Hence, the ordered pair is not a solution
Read more about equation at
https://brainly.com/question/13729904
#SPJ1