Answers
Answer:
Find the first and second derivatives:
[tex]\begin{aligned}f(x) & =-x-\dfrac{9}{x}\\& =-x-9x^{-1}\\\\\implies f'(x) & =-1-(-1)9x^{(-1-1)}\\ & =-1+9x^{-2}\\ & = -1+\dfrac{9}{x^2}\\\\\implies f''(x) & = 0+(-2)9x^{(-2-1)}\\& = -18x^{-3}\\& = -\dfrac{18}{x^3}\end{aligned}[/tex]
To find the stationary points (local minimum and maximum) set the first derivative to zero and solve for x:
[tex]\begin{aligned}f'(x) & = 0 \\\\\implies -1+\dfrac{9}{x^2} & = 0 \\\\\dfrac{9}{x^2} & = 1 \\\\9 & =x^2\\\\\implies x & = \pm 3\end{aligned}[/tex]
To determine the type of stationary points, input the found values of x into the second derivative.
[tex]f''(3)=-\dfrac{18}{3^3}=-\dfrac{2}{3} < 0 \implies \textsf{maximum}[/tex]
[tex]f''(-3)=-\dfrac{18}{(-3)^3}=\dfrac{2}{3} > 0 \implies \textsf{minimum}[/tex]
Finally, to find the y-values of the stationary points, input the found values of x into the original function:
[tex]f(3)=-3-\dfrac{9}{3}=-6 \implies (3,-6)[/tex]
[tex]f(-3)=-(-3)-\dfrac{9}{-3}=6 \implies (-3,6)[/tex]
Therefore:
[tex]\large \begin{array}{ r | r | c | c }\textsf{At} \: x= & \textsf{and} \: y= & \textsf{sign of} \: f''(x) & \textsf{conclusion}\\ \cline{1-4} -3 & 6 & + & \textsf{minimum} \\ \cline{1-4} 3 & -6 & - & \textsf{maximum}\end{array}[/tex]
Related Questions
Please help need to get it done in 10 minutes.Thank you
There are 12 inches in a foot.
Complete the table.
Inches: 12, ___, 60, 108
Feet: 1, 3, ___, ___
Answers
Answer:
Inches: 12, 36, 60, 108
Feet: 1, 3, 5, 9
Step-by-step explanation:
Inches: 12, 36, 60, 108
Feet: 1, 3, 5, 9
3*12 = 36
60/12 = 5
108/12 = 9
The ratio of side lengths for two similar cubes is 2/5.
Determine the ratios for each of the following.
the perimeter of one face of the smaller cube compared to the perimeter of one face of the larger cube
the total surface area of the smaller cube compared to the total surface area of the larger cube
the volume of the smaller cube compared to the volume of the larger cube
Answers
Explanation:
ratio of two cubes: 2 : 5
Perimeter of one face of cube: 4 × side
For small cube: 4 × 2 = 8
For big cube: 4 × 5 = 20
Ratio of perimeter of one face: 8 : 20 = 2 : 5
Total surface area of cube: 6a²
For small cube: 6(2)² = 24
For big cube: 6(5)² = 150
Ratio of total surface area: 24 : 150 = 4 : 25
Volume of cube: a³
For small cube: (2)³ = 8
For big cube: (5)³ = 125
Ratio of volume: 8 : 125
#1
Perimeter=4a
Find ratio
4(2)/4(5)8/202/52:5Samd
#2
TSA=6a²
6(2)²/6(5)²4/254:25#3
Volume=a³
2³/5³8/125Hi!
I am not quite sure the formula I am supposed to use for this or where each piece of information belongs. How would I solve this question?
Jeff Krause purchased 1,000 shares of a speculative stock in January for $1.89 per share. Six months later, he sold them for $9.26 per share. He uses an online broker that charges him $10.00 per trade. What was Jeff's annualized HPR on this investment?
Thanks!
Answers
Based on the price he purchased the stock and the amount he sold them for, Jeff's annualized HPR on the investment is 2,395%.
How much is Jeff's annualized HPR?First find the net profit:
= (1,000 x 9.26) - (1,000 x 1.89) - 10
= $7,360
The HPR is:
= 7,360 / (1,000 x 1.89)
= 389.4%
The annualized HPR is:
= (1 + 389.4%)² - 1
= 2,395%
Note: Taken to the power of 2 because there are two six-month periods in a year.
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Slide the green dot Use the number line to plot the numbers. Then arrange
them in order from smallest 1 to largest 4
Answers
I don't see any green dot, sorry.
Sheila has $51 to buy graphing pads for her math class. Each pad costs $7.
How many pads can she buy?
Answers
Answer:
She can buy 7 pads because 7 x 7 = 49.
Answer:
7
Step-by-step explanation:
7×7=49 and you cant by a portion of a graphing pad sooo the answer is 7
find all solutions
36x²+12x=0
Answers
Answer:
x = -1/3 or 0
Step-by-step explanation:
Given equation:
[tex]36x^{2} + 12x = 0[/tex]We can factor 12x on the L.H.S since 12x is divisible by 36x² and 12x.
[tex]\implies 36x^{2} + 12x = 0[/tex]
[tex]\implies 12x(3x + 1) = 0[/tex]
This can lead to two solutions. I have listed them below!
Solution 1:Divide 12x on both sides to open the parentheses.
[tex]\implies 12x(3x + 1) = 0[/tex]
[tex]\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}[/tex]
Note: zero divided by any non-zero number is 0.
[tex]\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}[/tex]
[tex]\implies 3x + 1 = 0[/tex]
Isolate 3x on one side of the equation.
[tex]\implies 3x + 1 = 0[/tex]
[tex]\implies 3x = 0 - 1[/tex]
[tex]\implies 3x = -1[/tex]
Divide 3 both sides to determine the value of x.
[tex]\implies 3x = -1[/tex]
[tex]\implies \dfrac{3x}{3} = \dfrac{-1}{3}[/tex]
[tex]\implies \boxed{x = \dfrac{-1}{3}}[/tex]
Solution 2:Divide (3x + 1) on both sides to isolate 12x.
[tex]\implies 12x(3x + 1) = 0[/tex]
[tex]\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}[/tex]
Note: zero divided by any non-zero number is 0.
[tex]\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}[/tex]
[tex]\implies 12x = 0[/tex]
Divide 12 both sides to determine the value of x.
[tex]\implies 12x = 0[/tex]
[tex]\implies \dfrac{12x}{12} = \dfrac{0}{12}[/tex]
[tex]\implies \boxed{x = 0}[/tex]
Therefore, the solutions for x are -1/3 or 0.
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Answer:
x = 0 or x = -1/3
Step-by-step explanation:
In the equation 36x²+12x=0 we have :
36x² = 6x × (6x)
12x = 2 × (6x)
This means that 6x is a common factor,so let’s factor :
36x²+12x=0
⇔ 6x × (6x) + 2 × (6x) = 0
⇔ 6x × (6x + 2) = 0
⇔ 6x = 0 or 6x + 2 = 0
⇔ x = 0 or x = -2/6
A rectangular park has a perimeter of 374 feet and a length of 65 feet.
What is the width of the park?
Answers
Answer:
122 feet
Step-by-step explanation:
We know that the length of the park is 65 feet long and the park is rectangular. Therefore we add 65+65 to find the total of both length sides.
65+65=130
Next we subtract 130 from the total amount of 374 to find the total of both width sides.
374-130=244
Now we divide what is left by 2 to find the width of an individual side.
244÷2=122
The width is 122.
Check your answer by inserting the numbers into the equation for perimeter.
P=2W+2L
374=(2×65)+(2×122)
374=130+244
374=374
9. 144^14/144^2
A. 144^16
B. 144^12
C. 144^28
D. 144^14/2
Answers
The correct result of this expression is 144¹²
This question is related to the division of potentiation of equal basesPotentiation is a multiplication of equal factors. When dividing bases or equal numerator and denominator - just keep the bases and subtract the exponents.
= 144¹⁴ / 144²
= 144¹⁴‐²
= 144¹²
So, the correct answer will be 144¹²
which relation is a function
Answers
Top Right
the V shape
6 minus the diffrence x and 3
Answers
Answer: It's 3
The sum of 6 and 3 divided by the difference of 6 minus 3
Step-by-step explanation:
The sum of 6 and 3: 6+3The difference of 6 minus 3: 6-3The sum of 6 and 3 divided by the difference of 6 minus 3:
I hope this helps :) [tex]\frac{6}{3} \frac{6}{3} =\frac{9}{3} =3[/tex]
Part A: Which polynomial below is a fourth-degree polynomial in standard form? Explain how you know it is a fourth-degree polynomial and how do you know it’s in standard form.
(Image Below)
Part B: Explain the closure property as it relates to polynomials and give an example.
Answers
In the given question, all the equations are fourth degree polynomial because they all have the highest power of 4
What is degree of polynomial?A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
In the given question, all the equation are fourth degree polynomial
2x^3 -3x^2 + 1 + 5x^45x^4 + 2x^3 -3x^2 + 1-3x^2 + 1 + 5x^4 + 2x^31 - 3x^2 + 2x^3 + 5x^4What closure property relates here is that when we add two different polynomial, the result will definitely be a polynomial.
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James uses of a cup of sugar in his cookies, and Jade uses of a cup of sugar in her cookies. Noel takes the sum of the two amounts of sugar and divides it into two equal portions, planning to use only one portion of it in his cookies. How much sugar does Noel use in his cookies?
Answers
Answer:
5/8 of a cup
Step-by-step explanation:
. Bri replaced the window blinds on 42 of the 60 windows in the library. Which percent
is equivalent to
Answers
Answer:
70%
Step-by-step explanation:
42/60 x 100 = 70%
if A=-3+5i, B=4-2i and C=1+6i, where i is imaginary unit, then A-BC equals to what?
Answers
Multiplication is the process of multiplying. The value of A-BC is equal to -19-17i.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The value of BC is,
BC = (4-2i)×(1+6i)
BC = 4 + 24i - 2i -12i²
BC = 4 + 22i - 12(-1)
BC = 4 + 22i +12
BC = 16 + 22i
Now, the value of A-BC will be equal to,
A-BC = (-3+5i)-(16+22i)
= -3+5i-16-22i
= -19 - 17i
Hence, the value of A-BC is equal to -19-17i.
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Angie read 2 books in 5 days, and each book contained 330 pages. If Angie read the same number of pages each day, how many
pages did she read per day?
A. 73
В. 330
C. 132
D. 660
Answers
Answer:
C. 132
Step-by-step explanation:
330 x 2(books) = 660(total pages)
Multiply. 132(pages?) x 5(days)
= 660
A placebo is a medically ineffectual treatment that looks like a real treatment. Sometimes patients given a placebo treatment, unaware of the fact that it is indeed a placebo, will have a perceived or actual improvement in their condition. This phenomenon is commonly called the placebo effect.
A group of doctors was interested in comparing the effectiveness of placebo pills (made of sugar) and real pills in treating migraines. They randomly assigned a group of 300 patients suffering from migraines into two groups. One group was given a real pill and the other was given a placebo. Both groups were told which kind of pill they got.
Before taking the pills, and a day afterwards, the patients were asked to fill out questionnaires regarding their condition. Then, the doctors analyzed the overall changes in questionnaires for each group and compared them.
What type of statistical study did the doctors use?
A. Sample Study
B. Experiment
C. Observational Study
Is the study appropriate for the statistical questions it's supposed to answer?
A. Yes, because the patients filled the same questionnaire before and after taking the pills.
B. No, because telling patients about the pills introduces bias.
C. Yes, because the patients were randomized between the two groups.
D. No, because we don’t know how effective the real pills are.
Answers
Experimental studies were the type of statistical study used by doctors in research on comparing placebo pills with real pills.
The study carried out is not appropriate for the statistical questions that must be answered, because telling patients about the pills introduces bias.
What is an experimental study?It is a method of scientific research in which there is the introduction of an intervention by the researchers, in which the resulting effects will be objects of study.
Therefore, in an experimental study there will be randomization of participants, who will be randomly grouped into a group to carry out the controlled trial.
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Answer: Experiment
No, because telling patients about the pills introduces bias
Which of the following sets of whole numbers represents all the odd three-digit numbers that have a 4 in the hundreds place and a 7 in the tens place?
741; 743; 745; 747; 749
470; 472; 474; 476; 478
740; 742; 744; 746; 748
471; 473; 475; 477; 479
Answers
Answer:
D) 471, 473, 475, 477, 479
Step-by-step explanation:
Lets say the three-digit number is ABC.
4 in the hundreds place, thus A = 4
7 in the tens place, thus B = 7.
The number is odd, therefore C = {1, 3, 5, 7, 9}
There are five possible solutions for three-digit number ABC = {471, 473, 475, 477, 479}
establish the exact displacement expression and shape functions for the given tapered axial member. Formulate the relevant stiffness matrix
Answers
The displacement is represented from the starting position to the final position.
What is displacement?Your information is incomplete. Therefore, an overview of displacement will be given. It should be noted that displacement simply means a vector whose length is the shortest distance from the initial position to the final position.
In this case, the displacement will be:
= Final position - Initial position
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1 Square yard = what Square inches
Answers
Answer: 1296 square inches
Step-by-step explanation:
1 square yard is 36 times 36 square inches
36 times 36 is 1296 square inches
erica earned a total of $67,850 last year from her two jobs.the anount she earned from her job at the store was $1,450 more than three times the amount she earned from her job at the college.how much did she earn in dollars from ger job at the college?
Answers
Answer:
Step-by-step explanation:
PLEASE HELP IF I DONT DO THIS
TOMORROW I DONT GRADUATE
Next we will draw in each deviation from the mean.
Now, think about the average size (length) of all of those deviations, and use this as an estimate for the size of the
Standard Deviation. Don't worry about whether the deviation is to the left or right of the mean. Just consider all of
the lengths. Draw the length of the standard deviation below.
Answers
The standard deviation is a measure of a collection of values' variance or dispersion. The standard deviation of the below graph can be drawn as shown below.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
The standard deviation of the below graph can be drawn as shown below.
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What is the square root of A=121 ft2
Answers
The result of the square root of the equation A = 121 ft² is √A = 11 ft
What are square roots?Square roots are numbers multiplied by itself to give another number
How to determine the square root?The equation is given as:
A = 121 ft²
Take the square root of both sides
√A = √121 ft²
Evaluate the square root
√A = 11 ft
Hence, the square root of the equation A = 121 ft² is √A = 11 ft
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Find sin 2x if cos x=-2/3 and x is in quadrant 2
Answers
Answer:
-4√5/9.
Step-by-step explanation:
if cos x = -2/3 then sin x = √(1 - (-2/3)^2)
= √(5/9)
= √5/3.
(As x is in quadrant 2 sin x is positive).
So:
sin2x = 2 sin x cos x
= 2 * √5/3 * -2/3
= -4/3 * √5/3
= -4√5/9.
A design for a garden is composed of a triangle and 2 rectangles. Some side lengths of the garden design are shown.
What is the area of the garden in square feet?
Answers
Answer:
215.625square feet
Step-by-step explanation:
area rectangle = l x w = 7.5x12.5
area triangle = ½ x b x h = ½x 7.5 x 7.5
area of shape = 93.75+93.75+28.125= 215.625square feet
Whát are the quotient and remainder of (x^5-x^3 +1-5) / (x - 2)?
a. x + 2x2 + 9x + 13; 21
x + 2x2 + 3x + 6x + 13; -21
b. x + 2x + 3x2 + 6x + 13; 12
d. + 2x2 + 3x2 + 6x + 13:21
Answers
Answer:
x⁴+2x³ +3x²+6x +12r is the answer
Please Help! Brainliest is available to the best Answer!
Which of the following correlation coefficients best represent the given scatter plot
Answers
Answer:
C
Step-by-step explanation:
Evaluating the options :
a : 0.01
Not the likely option because it is very close to 0, indicating there is no correlrationBut from the graph we understand there is a positive correlationSo, it comes down to :
(b) 0.51 or (c) 0.98
If we try and plot a line of best fit, we will obtain a line that passes through the origin and seems similar to y = x.
Hence, the best option is C
Enter the correct answer in the box.
The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Replace the values of h and k in the equation.
Answers
The equation of function g(x) = 2(x -7)² - 1, and the values of h and k are 7 and -1, respectively.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable.
The standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The function is given as:
f(x) = 2x² - 1
When the function is translated with 7 units left, the transformation rule is:
(x,y) -> (x + 7, y)
So,
g(x) = 2(x -7)² - 1
A quadratic function is expressed as:
g(x) = a(x -h)² + k
By comparison, the values of h and k are 7 and -1, respectively.
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Give me the right answer this time pls ♥️.
Answers
Answer:
10 and please:
please see photo for detailed analysis
marking brainliest
please help!!!!
Answers
You have to find the height then use the height to find the x value
Which of the following integers is least?
A
-5 + (-2)
B
-5 ÷ (-2)
C
-5 × (-2)
D
-5
Answers
Answer:
A) -7 is the least
Step-by-step explanation:
A) (-5) + (-2) = (-7)
If two numbers have same sign, add and the result will have the common sign.
b) (-5) ÷ (-2) = 2.5
In division negative number divided by another negative number will give a positive number.
c) (-5)*(-2) = 10
In multiplication multiplication of two negative numbers will give a positive number.
d) = -5
In these (-7) is the least integer