First-principle differentiation of sec x results in ten times sec x.
Explain about the derivative of Secx?Regarding the variable x, y = f(x). Wherever the limit occurs is defined to be the derivative of f at x if this limit exists and is finite. The first principle of derivative is another name for this definition.
Sec x tan x is, as far as we are aware, the derivative of sec x. Determining that sec x equals the integral of sec x tan x. Specifically, sec x tan x dx = sec x + C
On a graph, the first derivative shows the slope of the function at a particular position, while the second derivative shows how the slope changes as the independent variable is changed. The second derivative accounts for the curve in the above graph for a function with a variable slope.
To learn more about derivative of Secx refer to:
https://brainly.com/question/22094158
#SPJ4
2. Use the difference of two perfect squares method to multiply the following problems.
a. (a − 3)(a + 3) = ?
b. (x+y)(x - y) = ?
c. (n + 5)(n-5) = ?
d. (z-2)(z + 2) = ?
Answer:
a . a²-9
b.x²-y²
c.n²-25
d.z²-4
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
Example
Mia babysits some children after school. For each child, she
charges x + 2 dollars per hour. One day she cared for 2
children for 3 hours each. She paid 54 per child for materials
for activities. Two students wrote expressions for the amount
of money Mia earned. Are their expressions equivalent?
Paolo wrote the expression 3(x + 2) + 3(x + 2) - 8.
Carla wrote the expression (3x + 6) - 4+ (3x + 6) - 4.
Simplify the expressions to see whether they are equivalent.
Paolo's Expression Carla's Expression
3(x + 2) + 3x + 2) - 8 (3x + 6) - 4+ (3x + 6) - 4
- 3x + 6 + 3x + 6-8 3x + 3x + 6 + 6 - 4 - 4
6x + 4
= 6x + 4
The expressions are equivalent.
Why did Paolo add 3(x + 2) to itself and subtract 8?
Mia earned a total of 6x + 4 from the two children. Both Paolo and Carla wrote equivalent expressions to calculate the amount Mia earned.
Paolo added 3(x + 2) to itself and subtracted 8 to calculate the total amount of money Mia earned from both children. Since she cared for two children for three hours each, she earned 3(x + 2) for each child for a total of 6(x + 2). He then subtracted the 8 dollars that Mia spent on materials for the activities.
Mia earned a total of 6x + 4 from the two children. Both Paolo and Carla wrote equivalent expressions to calculate the amount Mia earned. By simplifying the expressions, it was determined that they were indeed equivalent.
Learn more about expression here
https://brainly.com/question/14083225
#SPJ4
100 POINTS He also has an oak board that is 5. 5 inches wide, 1. 5 inches thick and 3 feet long. The board weighs approximately 8. 05 pounds.
What is the density of the oak board? Show your work
The board weighs approximately 8.05 pounds. Hence, its density is 46.80 lb/ ft³
The density of something is a measure of how heavy it is in relation to its size. When a thing is more dense than water, it sinks; when an object is less dense than water, it floats. Density is a feature of a substance that is independent of the amount of substance.
The formula for density is given by:
ρ = m/V
Where:
ρ = density
m = mass
V = volume
In this case, the dimension of the oak board is:
wide = 5.5 inches = 0.458 feet
thick = 1.5 inches = 0.125 feet
length = 3 feet
Hence, the volume of the board is:
V = 0.458 x 0.125 x 3 = 0.172 ft³
The weight is 8.05 pounds, therefore, the density:
ρ = 8.05/0.172 lb/ ft³
ρ = 46.80 lb/ ft³
Learn more about density here:
https://brainly.com/question/28348989
#SPJ4
evaluate the expression for x = 3 3/4 8x +8
The required solution of the expression y = 8x + 8 at x = 3 3/4 is given as after simplification is 38.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
y = 8x + 8
We are given that to determine the solution of the given expression at x = 3 3/4, Since x = 3 3 /4 = 15 / 4
Now, put x = 15/4 in the given expression,
y = 8 (15/4) + 8
y = 30 + 8
y = 38
Thus, the required solution of the given expression is y = 38.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
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
HELP ASAP
find 1/9 of 15. (simplest form)
HELP 50 POINTS!!!!
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.
What is the area of the parallelogram?
four hundred twenty-three and one-half ft2
four hundred twenty-seven and one-half ft2
four hundred thirty-three and one-eighth ft2
four hundred fifty-five and one-eighth ft2
The area of the parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet is,
⇒ four hundred thirty-three and one-eighth ft²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.
Now, We know that;
Area of a parallelogram = Base × Height
Substitute the given values, we get;
⇒ Area of a parallelogram = Base × Height
⇒ Area of a parallelogram = 22 1/2 × 19 1/4
⇒ Area of a parallelogram = 45/2 × 77/4
⇒ Area of a parallelogram = 3465/8
⇒ Area of a parallelogram = 433 1/8 ft²
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#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
2. Identify the multiplication problem that matches the model.
The multiplication problem that matches the model is, 3/5 x 3/10. So Option D is correct
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
Given that,
Two models
One having,
3 blue color filled sections and 2 blank sections
Another one having,
3 blue color filled semi-sections and 7 blank sections
we have to make analogy between multiplication of ratio of filled to total sections and multiplications of numbers,
Total sections in model 1 = 5
Total semi-sections in model 2 = 10
Ratio in 1 = filled/total = 3/5
Ratio in 2 = filled/total = 3/10
Now multiplying both the ratio,
⇒ 3/5 × 3/10
Hence, the analogy is 3/5 × 3/10
To know more about multiplication check:
brainly.com/question/5992872
#SPJ1
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
PLS HELP!!!! ITS DUE TMR!!! (u dont hv to do Assessment practice) ILL GIVE U ALL MY POINTS AND MARK U BRANLIEST!!
Answer:
I finished
Step-by-step explanation:
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
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
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.
x and y are plotted on the number line below order the experesions from least to greatest use the number line if it helps your thinking
The change in demand is $15 per barrel.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the price of oil increases from 20 to 5 per barrel.
A change in quantity demanded refers to a change in the specific quantity of a product that buyers are willing and able to buy. This change in quantity demanded is caused by a change in the price.So we can write the change in demand as -
$20 per barrel - $5 per barrel
$15 per barrel
Therefore, the change in demand is $15 per barrel.
To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ1
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
The largest
volcanic eruption in the last 10000 years was at Thera in 1520 BC. It brought about the
end of the Minoan civilisation in Greece.
The volume erupted by Thera equals that of a 400000 km column that reaches from the
Earth to the Moon. If this column has a square cross-section, find its width.
If this column has a square cross-section, the width of the square cross-section is 1 km.
How did we find the width?Let's call the width of the square cross-section "w".
The volume of the column can be calculated as the area of the cross-section multiplied by its height.
w * w * 400,000 km = 400,000 km^3
Solving for w:
w^2 * 400,000 km = 400,000 km^3
w^2 = 400,000 km^3 / 400,000 km = 1 km^2
w = √(1 km^2) = 1 km
So, the width of the square cross-section is 1 km.
learn more about square cross-section: https://brainly.com/question/29189824
#SPJ1
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
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
Rav provide foofd for a event
lat year 550 people attenedde an event
Thi year there will be 748 people attending the event
The skill of inspecting produce properly requires much training and expertise.
What is to blame?Mashgichim must be knowledgeable with the halakhas of slaughtering meat, preparing meat and fish[13], and separating meat and dairy, depending on the task. She or he must be familiar with the operation of boilers and shipping boats, as high temperatures and extended storage durations might jeopardize the kosher status of meals.
However, one of the most important tasks of mashgichim is the checking in and verification of shipments. Before using a food product, Mashgihcim must confirm that it has a dependable hekhsher (certification). When a product is out of stock, suppliers frequently substitute non-kosher goods. These alternatives would normally be tolerated by non-kosher institutions.
To learn more about meat and fish to refer;
https://brainly.com/question/8323801
#SPJ4
which step is the same when constructing an inscribed square and an inscribed regular hexagon? (1 point)
The same process is used to build an inscribed square and an inscribed regular hexagon: creating the circle.
A square that fits inside a specific shape and has sides that are perpendicular to it is said to be inscribed. The sides of the square that is inscribed are as long as they can be while still fitting entirely inside the provided shape and being perpendicular to it.
A regular hexagon that fits inside another shape so that its vertices contact it is called an inscribed regular hexagon. The sides of the inscribed hexagon are as long as they can be while still fitting entirely inside the predetermined shape and being perpendicular to it.
To learn more about Inscribed square
https://brainly.com/question/30100652
#SPJ4
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
What is an advantage of using a stem-and-leaf instead of a histogram?
Answer: Stem and leaf plots have one advantage over histograms-- they display the original data, while histograms merely summarize them.
Step-by-step explanation:
Stem-and-leaf plots contain original data values while histograms do not.
What is Stem-and-leaf plotting?In order to categorise discrete or continuous variables, a stem and leaf plot, also known as a stem plot, is used. Data collection and organisation are done using a stem and leaf plot.
A bar graph is a good analogy for a stem and leaf plot. Because every number in the data is divided into a stem and a leaf, the name stem and leaf was chosen. The number's entirety - all but the final digit—is contained in the stem. There will always be one digit in the number's leaf. A stem and leaf plot's main benefit is the grouping of the data and the display of all the original data.
Learn more about Stem-and-leaf plots
https://brainly.com/question/12857419
#SPJ4
A farmer sells 7.8 kilograms of pears and apples at the farmer's market.
1
4
of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Let's call the weight of pears sold x.
So the weight of apples sold would be 7.8 - x.
And we know that x = 7.8 * 1/4 = 1.95 kilograms.
Therefore, the weight of apples sold is 7.8 - 1.95 = 5.85 kilograms.
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
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
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
Use the pigeonhole principle to determine how many people are needed in a group to say that five were born in the same month. In this case, what is the number of pigeons and what is the number of holes?
By using the unitary method, we can determine that 5 people are needed in the group, with 12 holes and 5 pigeons.
The Pigeonhole Principle is a mathematical theorem that states that if you have more objects than containers and all objects are placed in containers, then at least one container must have more than one object.
In the context of determining the minimum number of people needed in a group for five people to have been born in the same month, we can use the unitary method. The unitary method involves dividing the total number of possibilities by the number of objects we want to place in each container.
So, if we have 12 months in a year and we want to place 5 people in containers take one person per container, we need at least
=> 5/12 = 5/1 = 5 people in the group.
In this case, there are 12 holes and 5 pigeons. So, we need 5 people in the group to ensure that 5 of them were born in the same month.
To know more about Pigeonhole Principle here.
https://brainly.com/question/30322724
#SPJ4
how to find area of a triangle
Answer:
To find the area of a triangle you got A=1\2×b×h