It would take about 18 days for a pair of chickens to lay three dozen of eggs.
The unitary method is a method for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of just one unit is the key to answering such questions.
Given that 1.5 chickens can lay 1.5 eggs in a day.
The number of eggs 1 chicken can lay in a day = (1.5/1.5) eggs = 1 egg.
Then, two chickens can lay about 2 eggs in a day.
The number of days it takes for two chickens to lay 3 dozen (3×12=36) eggs is given by
[tex]\frac{\text{total number of eggs}}{\text{number of chicken}}=\frac{36}{2}=18\;\text{days}[/tex]
The answer is 18 days.
To know more about the unitary method:
https://brainly.com/question/22056199
#SPJ4
What equation represents this sentence. 5 less than a number is 12.
0 5-n=12
0 5 n-12
0 5 12-n
O n-5=12
Jack bought a coin for $200, which he sold later for $175. Find the percent of change. Did Jack make a good investment?
Need help Asap for 25 points
What is the solution to this inequality?
14x−5<−6
Responses
x<4
x less than 4
x<−4
x less than negative 4
x>4
x greater than 4
x>−4
Answer:
Your answer is B
Step-by-step explanation:
[tex]\frac{1}{4}x-5 < -6\\\\\frac{1}{4}x < -1 \\\\[/tex]
Multiply 4 to both sides leaving x by itself.
x < -4
Remember when you divide or multiply a negative to solve for x you switch the signs of greater than to less than or vice versa.
Please Help this is due soon!
based off of this information, what conclusions can be made about the mean value theorem? this contradicts the mean value theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 4) such that f '(c)
The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.
Explain the term Mean Value Theorem?The Mean Value Theorem says that there occurs a point c in the interval (a,b) so that f'(c) equals the function's average rate of change throughout [a,b] if a function f is continuous just on closed interval [a,b] as well as differentiable just on open interval (a,b).The function being used is;
f(x) = (x - 3)⁻²
If we separate this function according to x, we obtain;
f'(x) = -2/(x - 3)³
Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.
This suggests that;
0.06 - 0.25 = -2/(c - 3)³ x 6
-0.19 = -12/(c - 3)³
(c - 3)³ = 63.157
c = 6.98
If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).
But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.
To know more about the Mean Value Theorem, here
https://brainly.com/question/19052862
#SPJ4
The complete question is-
Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This does not contradict the Mean Value Theorem since f is not continuous at x = 3. This does not contradict the Mean Value Theorem since f is continuous on (1, 7), and there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 , but f is not continuous at x = 3. Nothing can be concluded.25. (06.04 MC)
The function f(x)=2x²+3 represents the rate of a boat traveling with the current in miles per hour. The function g(x)=x+ 2 represents the time the boat traveled in hours. Solve (f- g)(2), and interpret the answer. (1 point)
O(-a)(2)-15, the distance in miles the boat traveled
O(t-g)(2)-15, the number of boats
O(-a)(2)-44, the distance in miles the boat traveled
O (f-g)(2)-44, the number of boats
The value of the function given as (f . g)(2) is D. (f.g)(2) = 44, the number of boats
How to explain the function?It's important to note that functions are the expressions that are separated by an equal sign. It should be noted that that they've dependent as well as independent variables.
In this case, the function f(x)=2x²+3 represents the rate of a boat traveling with the current in miles per hour and the function g(x)=x+ 2 represents the time the boat traveled in hours. This will be illustrated as:
f(x) = 2x² + 3.
g(x) = x + 2
Therefore, we will evaluate the product
(f . g)(x) = (2x² + 3(x + 2)
(f . g)(x) = (2 × 2² + 3)(2 + 2)
(f . g)(2) = 44
The correct option is D.
Learn more about functions on:
brainly.com/question/25638609
#SPJ1
the teachers are planning an ice cream party. each student gets 1 cup of ice cream. how many quarts should they buy for 60 students?
15 quarts are required to plan ice cream party for 60 students which is
[tex]\frac{1}{4}[/tex] th fraction of quart.
1 quarts = 4 cups
so 1 cup = [tex]\frac{1}{4}[/tex] th fraction of quart
so in order to plan party for 60 students we need 60 cups as it is mentioned that each student gets 1 cup of ice cream.
and 1 quarts = 4 cups
so let we need x quarts for the planning of ice cream party
so total cups = 4 *x
so 4*x =60 , x= 60/4 , x=15
so 15 quarts are required for the ice cream party of 60 students .
To know more about fraction click on below link:
https://brainly.com/question/8482939#
#SPJ4
Josie is moving to a new apartment. The cost of her
rent is $850 per month, and her landlord charges a
deposit of $1000.
a) Write a linear function to represent the total cost, C,
or renting the apartment for m months.
b) What will be the total cost of renting the apartment for one year?
Answer:
b
Step-by-step explanation:
suppose that the chosen ahlete test postitive. what the probability that he or she actually used steroids?
The probability that he or she actually used steroids is 0.779.
The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn't taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have actually taken steroids. Let's choose an athlete at random and administer the drug test.
Based on prior knowledge of conditions that might be related to the event, Bayes' theorem, which is named after Thomas Bayes and is used in probability theory and statistics, describes the probability of an event.
Using Baye's theorem:
P(steroids | positive) = P(steroids)*P(positive|steroids) / P(positive) = (0.10*0.95)/0.122 = 0.779
If the selected athlete passes the test, the probability that they used steroids: 0.779
Know more about Baye's theorem here: https://brainly.com/question/28096770
#SPJ4
(complete question)
A company has developed a drug test to detect steroid use by athletes. The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn’t taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have taken steroids. Let’s choose an athlete at random and administer the drug test.
Suppose that the chosen athlete tests positive. What’s the probability that he or she used steroids?
Can anyone help me with this please???????
Answer:$785
Step-by-step explanation:
since she took money out already you have to add the to the pre existing total.
An airplane has stopped to re-fuel. Fuel is being added to the airplane's tanks at a constant rate. After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel. Write a function in f(t) form that describes the amount of fuel in the plane at time t.
The function in f(t) form that describes the amount of fuel in the plane at time t will be;
⇒ f (t) = 112.25t + 31.425.75
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Now,
Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (32882 - 34902.5) / ((31 - 13)
m = 2020.5 / 18
m = 112.25
Thus, The equation of line with slope 112.25 is,
⇒ y - 32885 = 112.25 (x - 13)
⇒ y - 32885 = 112.25x - 1459.25
⇒ y = 112.25x - 1459.25 + 32885
⇒ y = 112.25x + 31.425.75
Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be;
⇒ f (t) = 112.25t + 31.425.75
Learn more about the equation of line visit:
brainly.com/question/18831322
#SPJ1
The length of the longer leg of a right triangle i 6inche more than twice the length of the horter leg. The length of the hypotenue i 9inche more than twice the length of the horter leg. Find the ide length of the triangle
The length of shorter leg is 15 inches, length of longer leg is 36 inches and the length of hypotenuse is 39 inches.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.
Let,
x = Longer leg of triangle
y = Shorter leg of triangle
h = Hypotenuse of triangle
Given: The length of the longer leg of a right triangle is 6inches more than twice the length of the shorter leg.
The length of the hypotenuse is 9inches more than twice the length of the shorter leg.
⇒ x = 6 + 2y
h = 9 + 2y
The given triangle is a right angled triangle.
⇒ x^2 + y^2 = h^2
(6 + 2y)^2 + y^2 = (9 + 2y)^2
36 + 24y + 4y^2 + y^2 = 81 + 36y + 4y^2
36 + 24y + 5y^2 = 81 + 36y + 4y^2
36 - 81 + 24y - 36y + 5y^2 - 4y^2 = 0
-45 - 12y + y^2 = 0
y^2 - 12y - 45 = 0
y^2 - 15y + 3y - 45 = 0
y(y - 15) + 3(y - 15) = 0
(y - 15)(y + 3) = 0
y - 15 = 0, y + 3 = 0
y = 15, y = -3
Since the length is not negative.
So, y = 15
Hence,
Shorter leg = 15 inchs
Longer leg = 6 + 2y = 6 + 2(15) = 36 inches
Hypotenuse = 9 + 2y = 9 + 2(15) = 39 inches
To know more about right triangle, click on the link
https://brainly.com/question/29801705
#SPJ4
letters x, y, and z are angle measures. which equations would guarantee that lines p and q are parallel? check all that apply.
a. x = z
b. x + y = 180 degree
c. x + z = 180 degree
d. x + y
e. y + z = 180
Answer:
Please read the assumptions that lead to the proposed answer of options a, b, and e being correct. Options c and d are easily rejected. The question is ambiguous about the locations of the angles.
Step-by-step explanation:
Parallel lines have slopes that are identical. Lines p and q have the same slopes.
It is difficult imagining what angles are represented by x, y, and z. There are only 2 lines, and they do not intersect. The locations of the angles are not identified. The lack of an intersecting point means it is free range as to where we assign the angles.
The attached graph illustrates some possibilities for x, y, and z. It uses two simple equations as examples, with the same slope to make them parallel. Assinment of any angles requires the use of an imaginary line that intersects the two parallel lines. Even then, there aren't many unique locations for the angles. To illustrate the analysis, lets assign the angles x, y, and z to thelocations shown on the graph.
Even with this huge step, there is limited information to be able to identify which of the answer options is correct. We can say that:
x = z
x+y=180
y+z=180
The answer options (below) appear to have similar relationships, so let's agree that the use of the imaginary line, plus the locations of x, y, and z are valid. Looking at the answer options, we can match choices a, b, and e to the conclusions above. d makes no sense because it is not an equation. c says that both lines must be perpendicular to the x axis, a limitation that is relatively immaterial to whether they are parallel. The condition of being parallel depends on those two angles being the same (e.g., 45 and 45, 22 and 22, etc.) and not require that they both be 90.
Answer Options Guarantee Parallel?
a. x = z Yes
b. x + y = 180 degree Yes
c. x + z = 180 degree No
d. x + y No
e. y + z = 180 Yes
if a lawyer charges 120 an hour(or any fraction of an hour) how much is a mill for 3 hours and 20 minutes?
If a lawyer charges 120 an hour then the bill for 3 hours and 20 minutes will be 400
Bill: A bill is the printed or written statement of the money owed for goods or services.In later Latin, bulla became billa, and in English billa became bill. The word can still refer to various official documents, such as a proposed law that is brought before parliament, although it is now most commonly used for documents that request payment of money.
One hour = 60 minutes
3 hours and 20 minutes = 3×60 +20
= 180+20=200
Here, one hour=60 minutes charges 120
1 minute charges = 120/60
= 2
200 minute charges = 2×200=400
Therefore If a lawyer charges 120 an hour then the bill for 3 hours and 20 minutes will be 400.
Learn more about bills:
https://brainly.com/question/28603756
#SPJ4
What are the first four terms of a sequence where he rule is 7(n+2)?
Answer:
Step-by-step explanation:
for n=1 it is 7(1+2)=21
for n=2 it is 7(2+2)=28
for n=3 it is 7(3+2)=35
on a line segment of length 1, chooses two points independently at random. what is the probability the distance between them is more than 1/3?
The probability that the distance between the two points is more than 1/3 is 0.
The length of the given line segment is 1, so the two points chosen independently at random cannot be more than 1 unit apart.
That is, the maximum distance between the two points is 1. However, the question states that we are looking for the probability that the distance between them is more than 1/3.
Since the maximum distance between the two points is 1, and 1/3 is less than 1, it is impossible for the distance between them to be more than 1/3. Therefore, the probability that the distance between the two points is more than 1/3 is 0.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
find the product of the monomial and the polynomial
4x ^ 3 * y ^ 3 * (3x ^ 3 - 7x * y ^ 2 + 2xy - y)
The product of the monomial and the polynomial given is 12x⁶y³-28x⁴y⁵+8x⁴y⁴-4x³y⁴
What is polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations.
Given that, a polynomial and a monomial 4x³y³ and (3x³-7xy²+2xy-y)
To find the product of the monomial and the polynomial, we will multiply them,
4x³y³×(3x³-7xy²+2xy-y)
= 12x⁶y³-28x⁴y⁵+8x⁴y⁴-4x³y⁴
Hence, The product of the monomial and the polynomial given is 12x⁶y³-28x⁴y⁵+8x⁴y⁴-4x³y⁴
For more references on polynomials, click;
https://brainly.com/question/11536910
#SPJ1
The difference between the meaure of two comlementary angle i 14. Find the meaure of both angle
The measure of the first angle is 70° and the measure of the second angle is 100°.
The measure of complementary angles is the sum of their angles equal to 180°. Thus, if one angle has a measure of 70°, then the other angle must have a measure of 180° - 70° = 110°. Since the difference between the two angles is 14°, the first angle must have a measure of 70°, and the second angle must have a measure of 100°. This is because if the first angle has a measure of 70°, then the second angle must have a measure of 110°. Since the difference between the two angles is 14°, the second angle must have a measure of 100° in order to meet this difference. Therefore, the measure of the first angle is 70° and the measure of the second angle is 100°.
Learn more about angle here
https://brainly.com/question/28451077
#SPJ4
I'm tuck on thi quetion
A 2-gallon container of diinfectant cot $23. 76. What i the price per quart?
The price per quart of disinfectant is = $2.97
According to the information given in the question,
Quantity of the container of the disinfectants = 2 gallon
The price of a 2-gallon container of disinfectants = is $23.76
The concept used in this question is Ratio and Proportion,
The ratio is defined as the representation of two numbers in a fraction but in the case of ratio and proportion two numbers are separated by using a sign = ":"
Let us assume two numbers a and b,
If we have to present these two numbers in fractions = [tex]\frac{a}{b}[/tex].
If we have to present these two numbers in ratios = a : b.
According to the given question,
A 2-gallon container of disinfectants costs = $23.76
1 gallon = 4 quarts
So if 2 gallons = $23.762
= 2 gallons = 2 x 4
= 8 quarts
So, 8 quarts = $23.76
Now we will be dividing both sides by 8,
⇒ 1 quart = [tex]\frac{23.76}{8}[/tex]
⇒ 1 quart = $2.97
Therefore, the price per quart of disinfectant is = $2.97
To know more about Ratios and Proportions,
https://brainly.com/question/2914376
#SPJ4
Aha wa not feeling well. She went to the doctor. The doctor aid her body temperature i 3 degree
more than the normal body temperature. He gave medicine which bought her body temperature
6 degree le than the current body temperature and 3 degree le than the normal body temperature. Find her current temperature:
Using logical reasoning, we know that Aha's current body temperature after taking the medicine is 34°C.
What is logical reasoning?Deductive reasoning, often known as logical reasoning, is the process of drawing conclusions from a body of facts or evidence.
It involves putting specific premises in front of conclusions.
Induction and abduction are two additional categories of logical reasoning that are typically distinguished in addition to the formal deduction.
If one has a premise or precondition, a conclusion or logical consequence, and a rule or material conditional that signals the conclusion given the premise, one can explain the following.
So, we know that:
The normal body temperature of the body is 37°C.
Aha current body temperature is 3 more than normal body temperature, then it is: 37 + 3 = 40°C (Current body temperature)
After taking medicine,
Temperature is 6° less than current body temperature, that is:
40 - 6 = 34°C
Temperature is 3° less than the normal body temperature, that is:
37 - 3 = 34°C
Then, the current temperature after taking medicine: 34°C
Therefore, using logical reasoning, we know that Aha's current body temperature after taking the medicine is 34°C.
Know more about logical reasoning here:
https://brainly.com/question/29516872
#SPJ4
find the measures of the numbered angles.
Look below for images I will give brainliest whoever gets its right! There are 5 trigonometry problems.
The measures of the angles and the values of the trigonometric functions are as follows;
33 (e) The angle is (450 - π)°
34 (f) The reference angle is 75°
40 (e) cos(θ) = -8/9
43 (e) sin(θ) = √3/2
What are trigonometric functions?The trigonometric functions provides the relationships between an angle and the three sides of a right triangle.
33 (e) The measure of the angle from the curve of the angle mark is found as follows;
The angle turned = 360 + (90 - θ)
Where; θ = π
Angle = 360° + (90 - π)° = (450 - π)°
34 (f) The reference angle is smallest (acute) angle made by the terminal side and the x-axis.
From the diagram, the reference angle is 360° - 285° = 75°
40 (e) The angle is in the Quadrant III
cos(θ) in Quadrant III is -cos(φ), where;
φ = θ - 180
From the diagram, cos(φ) = 8/√((-8)² + 17)
cos(θ) = -8/(√((-8)² + 17)) = -8/9
40 (f) The angle is in Quadrant II
sin(θ) = sin(φ), where; φ = 180 - θ
Therefore;
sin(φ) = 5/√((-3)² + 5²) = 5/√(34)
sin(θ) = sin(φ) = 5/√(34)
43 (e) sin(120°) = sin(180° - 120°) = sin(60°) = √3/2
Learn more about trigonometric functions here:
https://brainly.com/question/6904750
#SPJ1
the lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 15 days. in what range would you expect to find the middle 50% of most pregnancies? between and .
The range is ( 290, 230).
In statistics, the standard deviation is a measure of the amount of variation. The low standard deviation indicates that the values tend to be close to the expected value of the set, while a high standard deviation indicates that the values are spread out over a wide range.
According to the question,
The middle 50% of the pregnancies are within two standard deviations of the mean: 260 ± 2*15
= ( 260 + 2*15 , 260 - 2*15)
= ( 260 + 30, 260-30)
= ( 290, 230)
Hence the range is ( 290, 230).
Read more about standard deviation :
https://brainly.com/question/24298037
#SPJ4
PLS answer il give brainliest
The length, b, of the longest side of the triangle is 13.17 cm
Calculating the length of a side of a triangleFrom the question, we are to determine the length, b, of the longest side of the triangle
From the given information,
Area of the triangle = 22.4 cm²
Then, we can write that
22.4 = 1/2 × a × 3.7 sin97
44.8 = a × 3.7 sin97
44.8 = a × 3.6724
a = 44.8/3.6724
a = 12.199
a = 12.2
Given that the sides of the triangle are a, b, and c,
Then,
From the law of cosines, we can write that
b² = c² + a² - 2ac cosB
b² = 3.7² + a² - 2×a×3.7 cos97°
b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°
b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°
b² = 173.53
b = √173.53
b = 13.17 cm
The length of b is 13.17 cm
Learn more on Calculating the length of a side of a triangle here: https://brainly.com/question/23282500
#SPJ1
where would you have to be on this date to experience 12 hours of daylight and 12 hours of darkness? june 21
Answer:
Step-by-step explanation:
home
what is the first word in the alternative statistical hypothesis for any experiment with three levels of a single iv?
Answer: The first word in the alternative statistical hypothesis for an experiment with three levels of a single independent variable (IV) is "differences." This is because the alternative hypothesis typically involves the existence of differences between the levels of the IV.
Step-by-step explanation:
Here is how to formulate the alternative hypothesis for an experiment with three levels of a single IV:
Identify the independent variable (IV) and the levels of the IV. In this case, there is a single IV with three levels.
Determine the relationship between the IV and the dependent variable (DV). In other words, consider how the levels of the IV may affect the DV.
Write the alternative hypothesis in terms of the relationship between the IV and the DV. The alternative hypothesis should state that there are differences between the levels of the IV in their effect on the DV.
For example, if the IV is "type of exercise" and the levels are "running," "cycling," and "swimming," and the DV is "improvement in cardiovascular fitness," the alternative hypothesis might be "There are differences in the improvement in cardiovascular fitness between the three types of exercise."
What is the null hypothesis in an experiment?
The null hypothesis in an experiment is a statement that there is no relationship between the IV and the DV, or that there are no differences between the levels of the IV in their effect on the DV. The null hypothesis is typically denoted as H0. In the example given above, the null hypothesis might be "There is no difference in the improvement in cardiovascular fitness between the three types of exercise."
This means that the hypothesis is testing whether there are significant differences between the means of the three levels of the IV. Therefore, the first word in the alternative statistical hypothesis for any experiment with three levels of a single IV is "differences."
To learn more about alternative statistical hypothesis from the given link https://brainly.com/question/15980493
#SPJ1
The first word in the alternative statistical hypothesis for any experiment with three levels of a single IV is "difference," which refers to the difference between the means of the three levels of the IV.
What is hypothesis?
Hypothesis is an educated guess or prediction made in response to a question or problem. It is based on prior knowledge and experience, as well as available evidence. The purpose of a hypothesis is to suggest a possible explanation for an observed phenomenon and then to test the validity of the hypothesis through further research or experimentation. If the hypothesis is proven correct, it can become a theory. Hypotheses can also be disproven or modified through further testing.
This is a reference to the null hypothesis, which states that there is no difference between the means of the different levels of the IV. The alternative hypothesis is that there is a difference between the means of the different levels of the IV.
To learn more about hypothesis
https://brainly.com/question/15980493
#SPJ1
Find the x and y intercepts
4x - 5y = 40
Answer:
x-intercept is (10,0)
y-intercept is (0, -8)
Step-by-step explanation:
Our equation is 4x - 5y = 40
Let's find x-intercepts first
X-intercepts is when the y = 0
So we put 0 in for the y, and we have the equation
4x =40
x =10
So our x-intercept located at (10,0)
Now find the y-intercepts
Y-intercepts is when the x = 10
So we put 0 in for the x, and we have the equation
-5y = 40
y= -8
So our y-intercept is located at (0,-8)
Answer:
Step-by-step explanation:
Y-int: (0, -8)
X-Int: (10, 0)
To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 4(0)-5y=40 you get this by plugging in the 0 for x and then you solve. 4 x 0 is 0 so you'd get -5y=40 divide -5 on both sides and get y=-8 meaning that is the y-intercept.
You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 4x-5(0)=40. -5 x 0 is 0. So you'd have 4x=40 divide both sides by 4 and you'd get x=10 meaning that is the x intercept.
Remember that when looking for the y- intercept there should always be a zero in front meaning the x-value, and when looking for the x-intercept there should always be a zero in the back meaning the y-value.
(Hopefully you were able to understand how I got the x and y intercepts for this equation)
why is h=root3*a/2
(equilateral triangle)
Answer:cause why not
Step-by-step explanation:
the figure above shows the graph of f the derivative of the function f the domain of f is the set
Since the function increases; stops; and decreases x= -2 has to be a maximum. Similarly, x=0 is a minimum and x=2 is an inflection point. (They are "relative" max/mins as opposed to absolute.
"Critical Points" (maximums, minimum and inflection points) occur when the first derivative of the function is zero. Here f(x) is neither increasing nor decreasing at that exact point. When f '(x) is positive, f(x) is increasing; when f '(x)is negative f(x) is decreasing. In this case, the critical points are x= -2, 0, 2. For x<-2 the derivative is positive so the function is increasing, for x>-2 the derivative is negative so the function is decreasing.
b) When f '(x) is positive, f(x) is increasing; when f '(x) is negative f(x) is decreasing. In this case, the critical points are x= -2, 0, 2. For x<-2 the derivative is positive so the function is increasing, for x>-2 the derivative is negative so the function is decreasing.
Concavity is determined by the second derivative, which is easy to sketch from the first. Where f '(x) is decreasing, f ''(x)is negative; where f '(x) is increasing f ''(x) is positive. Where f '(x) is zero, f ''(x) has critical points. Now from this graph, where f ''(x) is positive, f(x) is concave up, where f ''(x)is negative, f(x) is concave down. I get that f(x) is concave up on(-1,1) and (2,3).
c) Now it should be easy to graph f from the maxs mins and critical points. There is my attempt.
To learn more about derivatives
https://brainly.com/question/25324584
#SPJ4
Find a power series representation for the function.f(x) = x8 tan−1(x3)f(x) =[infinity] leftparen1.gifrightparen1.gifsum.gifn = 0
A power series representation for the function is:
x^8 tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^(6n + 11)/2n + 1)
In this question we need to find a power series representation for the function.
f(x) = x^8 tan^-1(x^3)
We know that the Maclaurin series:
1/(1 - x) = ∑[n = 0 to ∞] x^n
Replacing x with -x^2 we get,
1/(1 + x^2) = ∑[n = 0 to ∞] (-x^2)^n
= ∑[n = 0 to ∞] (-1)^n x^2n
Integrating above equation we get,
tan^-1(x) = ∑[n = 0 to ∞] (-1)^n (x^(2n + 1)/2n + 1) + c
For x = 0 we get c = 0
so, tan^-1(x) = ∑[n = 0 to ∞] (-1)^n (x^(2n + 1)/2n + 1)
Now we replace x by x^3, we get,
tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^3(2n + 1)/2n + 1)
Therefore, the required power series would be,
x^8 tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^(6n + 11)/2n + 1)
Learn more about the power series here:
https://brainly.com/question/29896893
#SPJ4