The function f(x) = 9x + 2x ^ - 1 * as one local minimum and one local maximum This function has a local maximum at x =
Answers
Explanation
To solve the question, we will make use of the graph of the function
\(f(x)=9x+2x^{-1}\)The graph of the function is shown below
From the graph
Looking at a graph, the local maxima and minima are the points where the graph flattens out and changes from increasing to decreasing or vice versa. When the graph is flat, that means the slope is zero.
\(\mathrm{Extreme\:Points\:of}\:9x+2\cdot \frac{1}{x}:\quad \mathrm{Maximum}\left(-\frac{\sqrt{2}}{3},\:-6\sqrt{2}\right),\:\mathrm{Minimum}\left(\frac{\sqrt{2}}{3},\:6\sqrt{2}\right)\)Therefore, the function has a local maximum at
\(x=\frac{-\sqrt{2}}{3}\)with a value of
\(-6\sqrt{2}\)For the local minimum
The function has a local minimum at
\(x=\frac{\sqrt{2}}{3}\)with a value of
\(6\sqrt{2}\)
Related Questions
Mother plans to buy 1/2 kilogram of chicken and 2/5 kilogram of beef How many kilograms of meat does she plan to buy?
Answers
Answer:
Step-by-step explanation:
Gladstone Community Center charges a one-time membership fee of $45 plus a monthly fee of $25. YMCA charges $39 a month. Write an inequality that shows the number of months it would take for Gladstone to be less expensive than the YMCA.
Answers
Answer:
31
Step-by-step explanation:
70 - 39 = 31
L. The Fluidfreeride Mantis electric scooter can go at a
speed of 16 miles in 20 minutes. At this rate, how many
minutes would it take it to travel 4 miles?
Answers
Answer:
It would take 5 min
Step-by-step explanation:
It would take him 5 min because he only need to travel a quarter of the distance so it's only a quarter of the time
Intelligence Iq scores are often reported to be normally distributed with u=100.0 and o=15.0. A random sample of 47 people is taken. What is the probability of a random person on the street having an IQ score of less than 96?
Answers
Given that the mean (μ) of IQ scores is 100 and the standard deviation (σ) is 15, we can convert the individual IQ scores into z-scores, which represent the number of standard deviations a particular IQ score is away from the mean.
The z-score can be calculated using the formula:
z = (x - μ) / σ
where x is the IQ score, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability of a random person having an IQ score less than 96. We need to find the z-score for an IQ score of 96 and then calculate the probability associated with that z-score using the standard normal distribution table.
First, calculate the z-score:
z = (96 - 100) / 15
z = -0.27
Next, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score. The probability of a random person having an IQ score less than 96 is the area under the standard normal curve to the left of the z-score -0.27.
Using a standard normal distribution table or a calculator, the probability associated with a z-score of -0.27 is approximately 0.3944.
Therefore, the probability of a random person on the street having an IQ score of less than 96 is approximately 0.3944 or 39.44%.
I hope this helps! :)
Can someone help me please
here is the picture
Answers
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
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3.) The line which is the graph of y = 2x -4 is transformed by the rule (x,y) (-x, -y). What is the
slope of the image?
Answers
The slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of the original line y = 2x - 4 is 2.
To find the slope of the image after the transformation, we can apply the transformation rule to two points on the original line, and then find the slope of the line passing through the images of those two points.
Let's choose two points on the original line:
Point 1: (0, -4)
Point 2: (1, -2)
Now we apply the transformation rule to each of these points:
Point 1 image: (-0, -(-4)) = (0, 4)
Point 2 image: (-1, -(-2)) = (1, 2)
The images of these two points lie on the line y = -2x + 4. The slope of this line is -2.
Therefore, the slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.
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which expression is equivalent to(x²y)³?
Answers
Answer:
x^6 y^3
Step-by-step explanation:
(x²y)³
We know that (ab) ^c = a^c * b^c
(x²y)³ = x^2 ^3 * y^3
We know that a^b^c = a^(b*c)
(x²y)³ = x^2 ^3 * y^3 = x^( 2*3) y^3 = x^6 y^3
Solve for b
10, b, 150degrees, 12degrees
Answers
Hello!
We have all angles of the triangle:
We will use the law of cosines. This relation is valid for all sides of any t
We have:
angle A = 12°
côté a = 10
angle B = 150°
This is therefore the first case of application of the sine law.
So:
\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)
\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)
b = 25cm
Find the cube root of Z =1+i the power of 5
Answers
Answer:
Cube Root Calculator
Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.
It will help you alot.
Step-by-step explanation:
It took Jesse 195 minutes to write an essay for school.
How many hours did it take Jesse to write the essay for
school?
Answers
Answer: 3 hours and 15 minutes
Step-by-step explanation:
Answer:
Time taken by Rahm to write the essay and finish the science project = 12.5 hours
Step-by-step explanation:
Now, we need to find the total time spent by Rahm to finish the both writing the essay and the science project.
Hence, Time taken by Rahm to write the essay and finish the science project = 12.5 hours
S= hp + 2B.
h = height
p = perimeter of base
b = area of base
Solve for h and b
Answers
The equation solved for the variable are;
h = S- 2B/p
b = S - hp/2
How to determine the equationsTo determine the equation, we need to know that the subject of formula for an equation is described as the variable that is made to stand on one end of the equality sign.
It is the variable that is being worked out.
From the information given, we have that;
S= hp + 2B.
To make the height with the variable 'h' the subject, we have;
collect the terms
hp = S - 2B
Divide by the coefficient
h = S- 2B/p
For b, we have;
S - hp = 2b
divide by the coefficient
b = S - hp/2
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Why are there two solutions for the equation |6 + y| = 2?
Answers
Answer:
it can be negative or positive. You can change the number after the equal to a negative, or a positive depending on what the number is.
Choose the number sentence that illustrates the distributive property of multiplication over addition.
3 × (7 + 2) = (3 + 7) × (3 + 2)
3 × (7 + 2) = (3 × 7) + 2
3 × (7 + 2) = (3 × 7) + (3 × 2)
Answers
Answer:
3*(7 + 2) = 3*7 + 3*2
Option 3
Step-by-step explanation:
Distributive property of multiplication over addition:
a*(b+ c) = (a*b ) + (a * c)
Answer:
Answer b
Step-by-step explanation:
because it is dp
During practice, the players on a softball team warm up by running the bases. This graph shows the relationship between the number of hours, x, of practice the players attend and the number of minutes, y, the players spend running the bases.
How many minutes do the players spend running the bases during each hour of practice?
Answers
The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
In the context of this problem, the variables x and y are given as follows:
Variable x: number of hours.Variable y: time spent running the bases.The equation for the constant is given as follows:
k = y/x.
Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.
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A local dry-cleaning company bought new equipment and its estimated useful life is 4 years. Using the straight-line depreciation method, what is the rate of depreciation each year?
Answers
Answer:
$2,500 or 25%
Step-by-step explanation:
Let's use the same example:
Cost of Equipment = $10,000
Useful Life = 4 years
Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100
Annual Depreciation = Cost of Equipment / Useful Life
Annual Depreciation = $10,000 / 4 years
Annual Depreciation = $2,500
Depreciation Rate = ($2,500 / $10,000) * 100
Depreciation Rate = 0.25 * 100
Depreciation Rate = 25%
What is the slope of the line shown below?
(9, 1) and (-3, -7
Answers
Answer:
The slope is 4
Step-by-step explanation:
I think it's right
What is 1 2/3 - (-5 2/3)?
• 6 1/3
• 6 2/3
• 7 1/3
• 7 2/3
Answers
Step-by-step explanation:
What we'll be using:
The integer rule.
Rule: When a positive number is being subtracted by a negative number, the negative number changes to a positive.
Implying the rule:
\(1 \frac{2}{3} + 5 \frac{2}{3}\)
Add:
\(1 \frac{2}{3} + 5 \frac{2}{3} = 7 \frac{1}{3} \)
Third option is correct.
Which is the inverse of the function f(x) = 4x^2?
y = 4x^2
y=√x/2
y=√x/4
y=2√x
Answers
Answer:
the answer is y= √x/4
Step-by-step explanation:
f(x)= 4x^2
y= 4x^2
x= 4y^2
4 4
x/4= y^2
√x/4 = √y^2
y= √x/4
you are sent to the local tea shop to pick up 9 drinks. You purchase 3 sweet teas and 6 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
Answers
The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21
The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:
Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84
Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14
Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28
Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21
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half of number q is 4
Answers
1/2 (1q) = 4
insert extra text here
Part (a) and part (b).
Answers
The time spent exercising for a student who spends 6 hours texting is 6 hours.
The scatter plot is given in the question,
As per the given scatter plot, we take the two points (9, 1) and (3,7).
The equation of the line of best fit:
Let the approximate equation would be as:
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 9, y₁ = 1
x₂ =3, y₂ = 7
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
y - 1 = (7 - 1)/(3 - 9)](x - 9)
y - 1 = (- 6/6)(x - 9)
y - 1 = -1(x - 9)
y = -x + 9+ 1
y = -x + 10 ...(i)
The time spent exercising by a student who spends 4 hours texting
This means that x = 4.
Substitute the value x =4 in the equation (i), and solve for y
y = -4 + 10
y = 6
Hence, the time spent exercising for a student who spends 6 hours texting is 6 hours.
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Write an explicit formula for an, the nth
term of the sequence 75, -15, 3, ....
Answers
Step-by-step explanation:
The sequence is geometric as the ratio between consecutive terms is common:
3/-15 = - 1/5-15/75 = - 1/5The first term is:
t₁ = 75r = - 1/5The explicit formula is:
tₙ = t₁rⁿ⁻¹Substitute values of the first term and common ratio to get:
tₙ = 75*(- 1/5)ⁿ⁻¹Write the name for the decimal value of point M on the number line.
A number line has endpoints 5.6 and 5.7 with 9 tick marks between them. Point M is on the fourth tick mark after 5.6.
Answers
The decimal value of point M on the number line is 5.644.
What is a number line?Number line is a straight line divided with numbers placed at equal intervals or segments along its length.
From the question:
Point M = 5.6 + (4/9) * (5.7 - 5.6) = 5.644
The decimal value of point M on the number line is 5.644.
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are 6, 2, and 3 factors
Answers
2 and 3 are factors of 6
What is the domain of the equation?
Answers
The domain of the equation include the following: D. all real numbers.
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-∞, ∞] or all real numbers.
Range = [-4, ∞}
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(q2) A civil engineer wants to find out the length of a rod which stretches for 1 meter and can be given by the function x=2y^((3)/(2)) Find the length of the rod.
Answers
The Length of the rod is 3/5 meters.
The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).
To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,
we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,
we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.
Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,
we have:x = 2/5 y^(5/2) + 3/5
The length of the rod is given by the value of x when y = 1. Substituting y = 1,
we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5
The length of the rod is 3/5 meters.
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Critique each of the following proposed research plans. Your critique should explain any problems with the proposed research and describe how the research plan might be improved. Include a discussion of any additional data that need to be collected and the appropriate statistical techniques for analyzing the data.
(a) A researcher is interested in determining whether a large firm is guilty of gender bias in setting wages. To determine potential bias, the researcher collects salary and gender information for all of the firm’s employees. The researcher then plans to conduct a "difference in means" test to determine whether the average salary for women is significantly different from the average salary for men.
(b) A researcher is interested in determining whether time spent in prison has a permanent effect on a person’s wage rate. He collects data on a random sample of people who have been out of prison for at least fifteen years. He collects similar data on a random sample of people who have never served time in prison. The data set includes information on each person’s current wage, education, age, ethnicity, gender, tenure (time in current job), and occupation, as well as whether the person was ever incarcerated. The researcher plans to estimate the effect of incarceration on wages by regressing wages on an indicator variable for incarceration, including in the regression the other potential determinants of wages (education, tenure, and so on).
Answers
The information provided indicates that the means test is too narrow because it excludes factors like the type of engineer, amount of education, and experience. The type of engineer or educational level may be a reflection of the gender with lower earnings.
Additional information on the factors, including gender, education, and the type of engineer, could enhance the research.
Then, it is advised to build a multiple regression where the wage is the dependent variable and the other four variables are independent variables. The "difference in means" test is not appropriate for identifying gender bias in salary setting due to the significance of the omitted variable.
The variables which are likely useful to add to the regression to control for important omitted variables are excessive drug or alcohol use and their gang activity.
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A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?
Answers
Answer:
t = 6.8 years
Step-by-step explanation:
The formula for compound interest is
\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.
We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal). We must solve for t and round to the nearest tenth:
\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)
PLEASE HELP IM BEING TIMED !! Find the perimeter of a quadrilateral with the given vertices: M(-1, 7), A(5, 2), T(-3, -3), H(0, 5)
Answers
Answer:
28.02
Step-by-step explanation:
How to make 28 tens and ones
Answers
Answer:
2 tens and 8 ones
Step-by-step explanation:
10 + 10 = 20
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
20 + 8 = 28
Answer:
Step-by-step explanation:
2 tens and 8 ones
20=10/2
10x2=20
8/1=8
8x1=8
20+8=28