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
What is true about open-end credit? OA It is not typically used for a single purchase but for many purchases over a period of time. B. This type of credit is sometimes referred to as a consumer loan. OC. This type of credit is commonly used for big ticket things like mortgages or car loans. Payments typically stay the same amount from month to month.
Answers
Answer:
Option B
Step-by-step explanation:
Open end credit 's biggest example is our credit card
You use credit card and take the money borrow from bank as per your requirement.If you pay in time your credit score increases else decreases.Option B is correct
Evaluate the determinant
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4. (1) Solve forx: 13 11 3x+16 65
Answers
Step-by-step explanation:
13113x+1665
_____________________________
Rewrite 13113 as 9 . 1457
Rewrite 1665 as 9 . 185
= 9 . 1457x + 9 . 185
=9(1457x + 185)
50 POINTS PLEASE HELP What is the volume of this prism???
Answers
Answer:
128
Step-by-step explanation:
multiply length, width, and hight.
[Not including the "triangle roof"] 128 in²
V = L * W * H
V = 8 in * 4 in * 4 in
V = 128 in²
[Including the "triangle roof"] 176in²
V = [tex]\frac{ L * W * H}{2}[/tex]
V = [tex]\frac{8\text{ in }*\,4\text{ in }*\,3\text{ in }}{2}[/tex]
V = [tex]\frac{96\;in^2}{2}[/tex]
V = 48 in²
-
48 in² + 128 in² = 176in²
Select the statement that describes this expression: fraction 1 over 2 x (734 − 246).
Half the sum of 734 and 246
fraction 1 over 2 the difference between 734 and 246
fraction 1 over 2 the quotient of 734 and 246
2 times the difference between 734 and 246
Answers
Mrs Rohit gave a total of $64.90 to her three sons. The eldest son receive $4.30 more than the youngest son. The second son received $7.80 less than the youngest son. How much did the eldest son received?
NO ALGEBRA PLEASE! I HAVENT LEARN IT YET!
Answers
Answer: $25.90
Step-by-step explanation:
We will have x as the youngest son's share, (the youngests son's share is the basis)
(x + 4.30) as the eldest son's share, (the eldest received 4.30 more than the youngest)
(x - 7.80) as the second son's share, (the second received 7.80 less than the youngest)
and 64.90 as their share altogether.
To find the youngest son's share:
(x) + (x + 4.30) + (x - 7.80) = 64.90
x + x + 4.30 + x - 7.80 = 64.90
x + x + x = 64.90 - 4.30 + 7.80 (group all of the like terms together. variables with variables, numbers with numbers. 4.30 became negative since it was moved to the other side, the same happened with 7.80 since it was a negative, it became a positive when it moved to another side)
Solve...
x + x + x = 64.90 - 4.30 + 7.80
3x = 68.40 (divide both sides by 3)
[tex]\frac{3x}{3} = \frac{68.40}{3}[/tex]
x = 22.80
(The youngest son's share is $22.80)
To get the eldest son's share:
x + 4.30 (substitute x since it has already been solved)
22.80 + 4.30 = 27.10
The eldest son's share is $27.10
Help urgent need this help please
Answers
Answer:
First option is the correct answer
[tex] A(\triangle ABC) =572\: yd^2[/tex]
Step-by-step explanation:
Given scale is: 3 cm = 6 yd [tex] \implies[/tex] 1 cm = 2 ydBased upon the above scale, we find:Base of the triangle (AC) = 13 cm = 26 ydHeight of the triangle (h) = 22 cm = 44 yd[tex] A(\triangle ABC) = \frac{1}{2} * AC*h[/tex][tex] \implies A(\triangle ABC) = \frac{1}{2} (26)(44)[/tex][tex] \implies A(\triangle ABC) =572\: yd^2[/tex]This is had can you help me
Answers
Answer:
#9 is 6 #10 is 1 #11 is 7 #12 is 6
Step-by-step explanation:
PLEASE HELP!
Use the Euclidean algorithm to find integers $x$ and $y$ such that $164x + 37y = 1,$ with the smallest possible positive value of $x$. State your answer as a list with $x$ first and $y$ second, separated by a comma.
Answers
Using the Euclidean algorithm integer integers $x$ and $y$ is: [ (-30 + 37k ), (133 - 164k) ].
Euclidean AlgorithmGiven:
$164x + 37y = 1
First step
Sequence of quotients
4(37) + 16=164
2(16) + 5=37
3(5) + 1=16
4(1) + 1=5
1(1) + 0=1
4 2 3 4 1
1 0 1 2 7 30 37
0 1 4 9 31 133 164
Determinant
(164×30) - (37×133)
=4,920-4,921
= -1
164(-30) + 37(133)
=-4,920+4,921
= 1
Second step
Integer
[(x + bk), (y - ak) ]
Where:
x = -30
y = 133
k=integer
Hence:
[ (-30 + 37k ), (133 - 164k) ]
Therefore using the Euclidean algorithm the integer is: [ (-30 + 37k ), (133 - 164k) ].
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Look at the diagram. Which angle is supplementary to A. B. C. D.
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The angles supplementary. to ∠DOC are ∠DOA and ∠COB.
What is supplementary angle?Two angles are called supplementary when their measures add up to 180 degrees.
1. Take, ∠COB:
So, ∠DOC+ ∠COB = ∠DOB = 180°. (Linear pair)
Hence, ∠DOC and ∠COB are supplementary.
2. Now, take angle DOA:
∠DOC + ∠DOA = ∠COA = 180°. (Linear pair)
Thus, ∠DOC and ∠DOA are supplementary.
Hence, the angles supplementary. to ∠DOC are ∠DOA and ∠COB.
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Given that circumference of a circle is 44m. Calculate it's area
Answers
Answer:
Area=154.062 [tex]m^{2}[/tex]
Step-by-step explanation:
As Circumference of a circle is given by;
[tex]C=2\times \pi\times r[/tex]
As the circumference is 44m so we can calculate the value of r by using the above formula.
[tex]44=2\times \pi \times r\\\\\frac{44}{2\pi} =r\\\\\implies r=\frac{22}{\pi} =7.003 m[/tex]
Now to Calculate the Area of a Circle.
As the area of a circle is,
[tex]Area =\pi \times r^{2}\\ Area=\pi \times (7.003)^{2} \\Area=\pi \times 49.039\\Area=154.062m^{2}[/tex]
find x ...............
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In the first circle, x is the radius and also the hypotenuse of a right triangle with legs measuring 9 and 12. So by the Pythagorean theorem,
x² = 9² + 12² = 225 = 15² ⇒ x = 15
In the second circle, the chords AB and CD have the same length, and each of AP, BP, CP, and DP are radii of the circle and also have the same length. This means ∆ABP and ∆CDP are congruent, so the two labeled angles are also congruent, so x = 54.
Find the area of the figure.
Answers
Answer:
Area = 38 ft^2
Step-by-step explanation:
Divide two parts of a rectangle.
Big Rect: A = 10 ft * 3 ft = 30 ft^2
Small Rect: A = 2 ft * 4 ft =8 ft^2
Total Area = 30 + 8 = 38 ft^2
what is :
2 tons + 10 pounds
And
4 tons + 10 pounds
and then explain it properly
Answers
2 tons + 10 pounds = 4,010 pounds
4 tons + 10 pounds = 8,010 pounds
Step-by-step explanation:
2,000 POUNDS EQUALS 1 TON.
a.) 2 tons = 2,000 X 2 = 4,000 pounds
4,000 pounds + 10 pounds = 4,010 pounds
2 tons + 10 pounds = 4,010 pounds
b.) 4 tons = 2,000 X 4 = 8,000 pounds
8,000 pounds + 10 pounds = 8,010 pounds
4 tons + 10 pounds = 8,010
Aaron is designing a party game in which he needs exactly 24 possible outcomes. Which sets of actions can he use to have a statistically fair game?
Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.
Select a card from a set of cards with the letters A through D, then spin this once.
Randomly select a number from 1 to 16, then roll an 8-sided number cube with the digits 1 to 8.
Spin this and roll an 8-sided number cube with the digits 1 to 8.
Randomly select an odd digit {1, 3, 5, 7, 9}, then flip a coin twice.
Select a card from a set of cards with the letters A through N, then spin this once.
Answers
The set of actions that should be used is: toss a coin twice, then roll a 6-sided number cube
Which sets of actions can he use to have a statistically fair game?
We know tath the game has 24 possible outcomes. Then we need to find a set of actions that gives 24 different outcomes all with the same probability.
Of the given options, the only one that has a sample space of 24 elements is the first one.
Toss a coin twice and then roll a D6.
For each coin toss, the outcomes are 2 (tails and heads).
For the D6 there are 6 outcomes (1, 2, 3, 4, 5, 6)
Then the total number of outcomes for two tosses and rolling the number cube is given by the product between the numbers of outcomes for each individual part:
C = 2*2*6 = 4*6 = 24.
From this, we conclude that this is the correct option.
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Answer:
the correct ones are
2, Select a card from a set of cards with the letters A through D, then spin this once.
5,Toss a coin twice, then roll a 6-sided number cube with the digits 1 to 6.
6, spin this and roll an 8-sided number cube with the digits 1 to 8.
Step-by-step explanation:
so basically both the colored wheel answers and the one with the coin and cube
plato 2022
Use the substitution method to determine the solution to the system of equations below. y-2x+2=1 6x - 3y = 3
Answers
Answer:
y = 2x - 1
Step-by-step explanation:
y - 2x + 2 = 1
6x - 3y = 3
[tex]y - 2x + 2 = 1 \\ +2x - 2 +2x - 2\\y = 2x - 1[/tex]
Plug in for y:
6x - 3(2x - 1) = 3
6x - 6x + 3 = 3
Simplified, 3 = 3
Answer: this solution has infinite solutions
Step-by-step explanation:
original system:
y-2x+2 = 1
6x-3y = 3
Move 2 to right side of equation
y -2x = -1
-3y+6x = 3
solve for y in first equation
⇒ y = 2x - 1
insert y into second equation
⇒ -3(2x-1) + 6x = 3
simplify
⇒ -6x+3+6x = 3
simplify once more
⇒ 3 = 3
this solution has infinite solutions
That’s the Answer in the right order
Answers
Answer:
3rd one
Step-by-step explanation:
i hope have a great day
One number is ten more than twice another. Their sum is one. Find the numbers.
Answers
answer:
x = 4
y = -3
steps :
x = 10 + 2y
x + y = 1
2y = x - 10 -> y = 1/2x - 5
x + y = 1 -> y = 1 - x
since theyre both equal to y they are equal to each other
1/2x - 5 = 1 - x
3/2x = 6
x = 4
plug 4 back where x is
y = 1 - 4
y = -3
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Which term best describes the shape of this distribution?
normal
skewed left
skewed right
uniform
Answers
The shape of the distribution described the Left skewed.
What is left- skewed histogram?A left skewed histogram is a histogram that attains a peak (which is the mode) towards the right side of the graph and has a “tail” towards the left side.
A histogram in which most of the data falls to the left of the graph's peak is known as a left-skewed histogram.
A left-skewed histogram is a type of histogram that is not symmetrical and in which the peak of the graph lies to the right of the middle value or the median.
Hence, considering the above definition the given histogram data falls on right side.
So, it is left skewed graph.
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In the given right triangle, write all trigonometric ratios ?
Answers
Answer:
see below
Step-by-step explanation:
You will need the hypotenuse 12 ^2 + 9^2 = h^2 h = 15
In a right triangle:
S O H C A H T O A
sin s = S A H = Opposite / Hypotenuse = 12/15
cos r = C A H = Adjacent / Hypotenuse = 12/ 15
Tan s = T O A = 12 / 9
cos (theta) = cos s = 9 / 15
Tan r = 9/12
arc cos(theta) = theta = arccos(9/15) = 53.13 degrees
The measure of an angle is 60 greater than the measure of its complement find the measure of each angle
Answers
Answer:
[tex] \\ \\ 90-60=30degree \\ \\ [/tex]
Answer:
15° and 75°
Step-by-step explanation:
The sum of the measures of complementary angles is 90.
Angle 1 measures x.
Angle 2 measures x + 60.
Their sum is 90.
x + x + 60 = 90
2x + 60 = 90
2x = 30
x = 15
x + 60 = 75
Answer: 15° and 75°
what are the zeros of this function? f(x) = 3x^2 + 2x - 8
Answers
Answer:
4/3, -2
Step-by-step explanation:
There are 24 pictures on a roll of film. Adelle had 84 pictures from her trip home. She said that 12 other pictures were spoiled. How many rolls of film did Adelle use?
Answers
Answer:
Total pictures = 84+12 = 96
roll of films = 96 / 24 = 4
she used 4 rolls
2.2 Determine the general solution of 2.2.1 3 sin x = cos x
2.2.2 2 cos²x + 5 sin x = 4
Answers
Step-by-step explanation:
try this solution, note, the answers are underlined with green colour.
Slope intercept form of an equation of a line
Answers
Answer:
Step-by-step explanation:
4a. yes: 5 = 3(2)-1 5 = 6 - 1 5 = 5
4b. No: 1 = 3(4) + 1
1 = 12 + 1
1 ≠ 13
4c. No; 1 = 3 - 3
1 ≠ 3
4d. yes; 7 = -3(5) + 22
7 = -15 + 22
7 = 7
4e. no; -8 = -2(-4)
-8 ≠ 8
4f. no; 8 = -2 + 11
8 ≠ 9
In a certain family, the probability of having twins in 0.08 and the probability of having a single baby is 0.92.
What is the probability of a family having two sets of twins?
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Answer: SE = √. pA(1 - pA). nA. +. pB(1 - pB). nB. = √. 0.08(0.92). 200. +. 0.344(0.656). 200. = 0.039. (b) The sample sizes of 200 are large enough
Step-by-step explanation:
Sophia is 12 years old. Her Uncle Reynald tells her that if she adds 5 to her age, multiplies the sum by 3, and then subtracts 4 from the product, she will find his age. She tells him that his age equals the expression 12 + 5 × 3 − 4 . Is Sophia correct? Choose the correct answers from the drop-down menus. Sophia is Choose... . Her uncle's actual age is Choose... .
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Answer:
Yes, Sophia is correct
Step-by-step explanation:
The expression is correct and if you solve it, you get 23 which should be her uncle's age.
Ms. Wall will roll a dice. What is
the probability that she will roll an even number?
Answers
Answer:
50%
Step-by-step explanation:
half of the numbers on dice are even
PLEASE HELP 25 POINTS!!!
Answers
Sequence: 2 + 1 + 1/2 + 1/4 + 1/8 + ...
Explanation:
Here Given Sum to Infinity
[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]
Identify following
a1 = 2r = 1/2Solve:
[tex]\rightarrow \sf S \infty \ =2 \ x \ \dfrac{1}{1-\frac{1}{2} }[/tex]
[tex]\rightarrow \sf S \infty \ =4[/tex]
The sum of this infinity series is 4
what transformation of figure 1 results and figure 2?
reflection
dialation
translation
