Verify that the function f(x) = -4x2 + 123 – 4In x attains an absolute maximum and absolute [ì, 2] minimum on Find the absolute maximum and minimum values. Hint: In 2 ~0.7, In ~ -0.7.
Answers
Therefore, the absolute maximum value of the function on [ì, 2] is f(ì) = 115.48, and the absolute minimum value of the function on [ì, 2] is f(2) = 107.92.
To verify that the function f(x) = -4x^2 + 123 – 4In x attains an absolute maximum and absolute minimum on [ì, 2], we need to find the critical points of the function and then evaluate the function at those points as well as at the endpoints of the interval.
First, we need to find the derivative of the function:
f'(x) = -8x - (4/x)
Setting f'(x) = 0 to find the critical points:
-8x - (4/x) = 0
-8x^2 + 4 = 0
x^2 = 0.5
x = ± √(0.5)
However, √(0.5) is not in the interval [ì, 2], so we only have one critical point, which is x = -√(0.5).
Now we evaluate the function at the critical point and the endpoints of the interval:
f(-√(0.5)) = -4(-√(0.5))^2 + 123 – 4In (-√(0.5)) = 123.54
f(ì) = -4ì^2 + 123 – 4In ì = 115.48
f(2) = -4(2)^2 + 123 – 4In 2 = 107.92
Learn more about absolute maximum here:
https://brainly.com/question/29030328
#SPJ11
Related Questions
This graph represents the distance a train traveled over a 20-hour time period. Approximately
how far has the train traveled after 1 hour? After 4 hours?
1: After 1 hour 50 miles, after 4 hours 150 miles
2: After 1 hour 20 miles, after 4 hours 100 miles
3: After 1 hour 25 miles, after 4 hours 100 miles
4:After 1 hour 25 miles, after 4 hours 150 miles
Answers
Determine whether the ratios are equivalent.
28 : 32 and 7 : 8
Answers
Answer:
They are
Step-by-step explanation:
28:32 is equal to 7/8
true or false:
If ab>0 then a>0 and b>0.
Answers
Answer:
false
Step-by-step explanation:
because a<0 and b<0 then ab>0
Answer:
False
Step-by-step explanation:
You don't know what a or b is for example it could be a=-3 b=-4. In that case ab= 12 but a and b indavidually are less than zero making this statment false
Can somebody help me solve this inequality it’s kinda hard for me to solve
Answers
Answer:
54 chickens
Step-by-step explanation:
This problem requires you find the area of Thomas's field, then use that area to find the number of chickens he can keep. The irregularly-shaped field can be considered as composed of shapes that you know how to find the area of.
__
field areaThere are many ways the area can be divided. One of them is shown in the attachment. That shows the area to be the sum of the areas of a triangle and a trapezoid.
The triangle has a base of 20 m and a height of 7 m, so an area of ...
A = 1/2bh
A = 1/2(20 m)(7 m) = 70 m²
The trapezoid has bases of 11 m and 18 m, and a height of 14 m. Its area is ...
A = 1/2(b1 +b2)h
A = 1/2(11 m +18 m)(14 m) = 1/2(29 m)(14 m) = 203 m²
The area of the field is the sum of these areas:
field area = triangle area + trapezoid area
field area = 70 m² +203 m² = 273 m²
__
chickensEach chicken requires an area of 5 m², so the total area for n chickens is ...
area for n chickens = 5n . . . . square meters
This area cannot exceed the area of the field, so an inequality can be written:
area for n chickens ≤ field area
5n ≤ 273
n ≤ 54.6 . . . . . . divide by 5
Thomas can keep a maximum of 54 chickens in the field.
I have a math question could I send you a picture of that to solve that for me
Answers
2) In these problems, let's make use of the Law of Cosines since in each triangle we have their legs and just want to know the measure of one angle.
a) Let's begin with that, bearing in mind the following formula:
\(\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ r^2=s^2+t^2-2st\cdot cos(R) \end{gathered}\)Note that the leg "r" is opposite to the angle (R):
\(r^2=s^2+t^2-2st\cdot cos(R)\)But note that we have a right triangle and we don't know the side "t". So, let's use the Pythagorean Theorem to find the missing side "t":
\(\begin{gathered} a^2=b^2+c^2 \\ 10^2=8^2+c^2 \\ 100-64=c^2 \\ c=\sqrt[]{36} \\ c=6 \end{gathered}\)So now, let's get back to the Cosines Law:
\(\begin{gathered} r^2=s^2+t^2-2st\cdot cos(R) \\ 8^2=10^2+6^2-2(10)(6)\cdot\cos (R) \\ 64=100+36-120\cos (R) \\ 64=136-120\cos (R) \\ 120\cos (R)=136-64 \\ \frac{120\cos (R)}{120}=\frac{72}{120} \\ R=\cos ^{-1}(\frac{72}{100}) \\ R=43.94\approx44^{\circ} \end{gathered}\)b) In this one, we can see the angle 38º and the missing angle "A". We can use the Law of the Sines to find that angle.
\(\begin{gathered} \frac{c}{\sin(C)}=\frac{b}{\sin (B)} \\ \frac{55}{\sin(38)}=\frac{85}{\sin (B)} \\ 55\sin (B)=85\cdot\sin (38) \\ \frac{55\sin (B)}{55}=\frac{85\cdot\sin (38)}{55} \\ \sin (B)=0.95147 \\ B=\sin ^{-1}(0.95147) \\ B=72.5865\approx73^{\circ} \end{gathered}\)Now, that we know angle B, we can write out this equation since the sum of the interior angles is 180º
\(\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+73+38=180 \\ \angle A=180-(73+38) \\ \angle A=69^{\circ} \end{gathered}\)c) Finally, we can apply the Cosines Law for this triangle:
\(\begin{gathered} p^2=q^2+r^2-2qr\cdot\cos (P)_{} \\ 2.5^2=1.7^2+2.2^2-2(1.7)(2.2)\cos (P) \\ 6.25=2.89+4.84-7.48\cos (P) \\ 6.25=7.73-7.48\cos (P) \\ 6.25-7.73=-7.48\cos (P) \\ -1.48=-7.48\cos (P) \\ P=\cos ^{-1}(\frac{1.48}{7.48}) \\ P=78.58^{\circ}\approx79^{\circ} \end{gathered}\)2) Thus the answer is:
\(\angle R=44^{\circ},\angle A=69^{\circ},\angle P=79^{\circ}\)
4.620 in expanded form
Answers
Hope this helps
For the pair of similar triangles, find the value of x.
2x8
x+8
24
The value of x is a
(Simplify your answer. Use a comma to separate answers as needed.)
Answers
Answer: x = 22
Step-by-step explanation:
Compare the 2 triangles
\(\frac{2x-8}{24} = \frac{45}{x+8}\)
Cross multiply
(2x-8) (x+8) = 45 x 24
2x^2 + 16x - 8x - 64 = 1080
2x^2 + 8x - 64 - 1080 = 0
2x^2 + 8x - 1144 = 0 ---> divide by 2
x^2 + 4x - 572 = 0
(sum and product)
x^2 - 22x + 26x - 572 = 0
x(x - 22) + 26(x - 22) = 0
(x + 26) (x - 22) = 0
x + 26 = 0
x = -26
x - 22 = 0
x = 22
A baseball statistician finds that his team uses a left-handed pitcher 90% of the time against an opponent. Of the times that the team uses a left-handed pitcher, 20% result in that team winning the game. On the other hand, 70% of the time that teams use a right-handed pitcher results in winning the game. According to the data that informed these probabilities, what percent of all the games won against this opponent were games in which a left-handed pitcher was used?
Answers
Answer:
25%
Step-by-step explanation:
A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
Answers
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
Learn more about volume of cylender :
https://brainly.com/question/16134180
#SPJ4
Magnesium-27 has a half-life of 9.45 min. How many grams of a 200 g sample will remain after 120 min?
Round your answer to the nearest hundredth of a gram.
___ g
Answers
The mass of the atom of grams of a 200 g sample will remain after 120 min is 0.03g.
half life :
Half-life, in radioactivity, is the amount of time needed for one-half of a radioactive sample's atomic nuclei to decay.
here we use formula :
N/N₀ = (1/2)^t/t1/2
Where
N = no. of atoms after time t
N₀ = Number of atoms present originally
t = t Total time taken
t/2 = half life of the atom
N₀ =200 Gram
t = 120 minute
t/2 = 9.45 minute
then,
N/200 = (1/2)^120/9.45
N/200 = (1/2)^12.7
N = 200 * (1/2)^12.7
N = 0.03 gram
The mass of the atom of grams of a 200 g sample will remain after 120 min is 0.03g.
To know more about half life
https://brainly.com/question/24710827
#SPJ1
Help me pleaseeee the weekends almost over and it’s due like tomorrow :(
Answers
Actually half ques is not visible so
For Incap T-shirts, the cost of producing x t-shirts can be expressed as C=0.6x2+0.52x+3200.
The revenue they gain can be expressed as R=100x. What is the maximum profit (revenue subtract cost) they can make? In other words, what is the maximum value of R−C? Express your answer to 2 significant figures.
Answers
The maximum profit is $923.44 which is gotten when 83 T shirts are produced.
Given the function:
Profit = Revenue - Cost
Profit (P) = 100x - (0.6x²+0.52x+3200)
P = -0.6x² + 99.48x - 3200
The maximum profit is at dP/dx = 0, hence:
dP/dx = -1.2x + 99.48
0 = -1.2x + 99.48
1.2x = 99.48
x = 82.9
x ≅ 83
The maximum profit is at x = 83, hence:
P = -0.6(83)² + 99.48(83) - 3200
P = 923.44
Find out more at: https://brainly.com/question/19682087
A linear function contains the following points.
ху
0-1
38
What are the slope and y-intercept of this function?
A. The slope is
The y-intercept is (0, -1).
O B. The slope is -3.
The y-intercept is (0, -1).
O C. The slope is 3.
The y intercept is (0, -1).
O D. The slope is 3.
The y-intercept is (-1,0).
Answers
Answer:
The answer is C. The slope is 3 and y-intercept is (0,-1(
ANYONE...........help
Answers
Answer:
1 cmStep-by-step explanation:
Sides of the picture added margin:
l = 8 + 2xw = 5 + 2xA(margin) = 30 cm²Solution:
A(margin) = Total area - A(picture)(8 + 2x)(5 + 2x) - 5*8 = 304x² + 10x + 16x + 40 - 40 - 30 = 04x² + 26x - 30 = 02x² + 13x - 15 = 0x = (-13 + √(13² + 2*4*15))/4x = (-13 + 17)/4 x = 1 cmNote. The other root is ignored as negative.
Dania had discovered that three 4 inches diameter balls fitted exactly into the bottom of a cylindrical jar. She dropped the 4th ball on top of the three and poured water. If the height of the jar is 20 inches, determine the volume of water just enough to cover the 4 balls.
Answers
The volume of each ball is (32/3)π cubic inches, and the volume of water just enough to cover the four balls is also (32/3)π cubic inches.
First, let's calculate the volume of each ball. The diameter of each ball is given as 4 inches, so the radius (half the diameter) of each ball is 2 inches. The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V represents volume and r represents the radius.
For each ball, the volume is:
V = (4/3)π(2³)
V = (4/3)π(8)
V = (32/3)π cubic inches
Since there are three balls at the bottom of the jar, the combined volume of these three balls would be:
3 * (32/3)π = 32π cubic inches
Now, let's consider the fourth ball. Since it is dropped on top of the three balls, it will displace some water, and the volume of the water needed to cover the four balls will be equal to the volume of the fourth ball.
To find the volume of the fourth ball, we use the same formula:
V = (4/3)πr³
Since the diameter of the fourth ball is also 4 inches, its radius is 2 inches. Substituting this value into the formula, we get:
V = (4/3)π(2³)
V = (4/3)π(8)
V = (32/3)π cubic inches
Therefore, the volume of water required to cover the four balls is also (32/3)π cubic inches.
To know more about volume here
https://brainly.com/question/11168779
#SPJ4
pleaseeee help I only have 3 more days left and if I don’t get it done i won’t pass
Answers
Which is the name of a rat with endpoint A?
Answers
Answer:
AB
Step-by-step explanation:
A ray has one endpoint and the rest is a line, so AB would be the only answer that would make sense in this situation (because it's starting from A and B is a point on the ray).
Please help me solve for x =
I message my teacher she said the side are not equal to each other, they are proportional ( please help me awnser)
Answers
Answer:
x = 13
Step-by-step explanation:
Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:
\(\frac{ML}{NM} = \frac{ST}{PS}\)
\(\frac{8}{10} = \frac{x - 1}{x + 2}\)
Cross multiply:
8(x + 2) = 10 (x - 1)
8x + 16 = 10x - 10
Subtract 8x from both sides:
8x - 8x + 16 = 10x - 8x - 10
16 = 2x - 10
Add 10 to both sides:
16 + 10 = 2x - 10 + 10
26 = 2x
Divide both sides by 2:
\(\frac{26}{2} = \frac{2x}{2}\)
13 = x
Verify whether x = 13 is the correct value:
\(\frac{ML}{NM} = \frac{ST}{PS}\)
\(\frac{8}{10} = \frac{x - 1}{x + 2}\)
\(\frac{8/2}{10/2} = \frac{4}{5}\)
\(\frac{x -1}{x+2} = \frac{13 - 1}{13 + 2} = \frac{12}{15} = \frac{12 / 3}{15 /3} = \frac{4}{5}\)
This shows the proportional relationship between \(\frac{ML}{NM} = \frac{ST}{PS}\), and that ΔNML and ΔPST are indeed similar right triangles.
Therefore, the correct answer is x = 13.
Passes through (2, 3) and has slope of -1/2
Answers
Answer:
y=(-1/2)x + 2
Step-by-step explanation:
classic example.
The sum of the measures of two exterior angles of a triangle is 264. What is the measure of the third exterior angle?
Answers
given, the sum of two exterior angles is 264 degrees. let the third angle be x degree. so the third exterior angle is 96 degrees.
Cedric has a sealed bag of 5000 marbles, but he cannot
see inside of the bag. Some of the marbles are orange, and
some of the marbles are green.
Cedric pulls 10 marbles from the bag without putting any
back in. He pulls 8 orange marbles and 2 green marbles.
Cedric estimates that there are 4000 orange marbles and
1000 green marbles in the container.
What could Cedric do to make a better estimate of the number of marbles in each bag? why? Explain your answer
Answers
Cedric could conduct further random samplings to get a better estimate of the number of marbles in each bag.
To make a better estimate of the number of marbles in each bag, Cedric could perform additional random samplings and use the results to refine his estimates.
The larger the sample size, the more accurate the estimates are likely to be.
For example, Cedric could pull out another 10 marbles from the bag and record the number of orange and green marbles.
If he gets similar results as his initial sampling (i.e., mostly orange marbles), then his estimate of 4000 orange and 1000 green marbles may be more reliable.
However, if he gets a different distribution of colors in the second sampling, he may need to adjust his estimates accordingly.
Learn more about the random samplings here:
https://brainly.com/question/31523301
#SPJ1
Question 3 Find whether the vectorrs are parallel. (-2,1,-1) and (0,3,1)
a. Parallel
b. Collinearly parallel
c. Not parallel
d. Data insufficient
Answers
To determine whether the vectors (-2,1,-1) and (0,3,1) are parallel, we need to compare their direction. If they have different directions, they are not parallel. the correct answer is option c) Not parallel.
To check if two vectors are parallel, we can compare their direction vectors. The direction vector of a vector can be obtained by dividing each component of the vector by its magnitude. In this case, let's calculate the direction vectors of the given vectors.
The direction vector of (-2,1,-1) is obtained by dividing each component by the magnitude:
Direction vector of (-2,1,-1) = (-2/√6, 1/√6, -1/√6)
The direction vector of (0,3,1) is obtained by dividing each component by the magnitude:
Direction vector of (0,3,1) = (0, 3/√10, 1/√10)
Comparing the direction vectors, we can see that they are not equal. Therefore, the vectors (-2,1,-1) and (0,3,1) are not parallel. Hence, the correct answer is option c) Not parallel.
Learn more about vectors here:
https://brainly.com/question/24256726
#SPJ11
Can someone please help me on this problem and show work pleasee I’m having trouble doing this!!!
Answers
Let’s start by stating the formula for the area of a rectangle,
A=LW
the letter a represents area, l represents length, and w represents width.
Next let’s substitute known values.
A=x(x+10)
Next let’s use the distributive property
A=(x(x))+(10(x))
Now simplify.
A=x^2 + 10x
So the equation for the area of this rectangle is A=x^2+10x
I believe this is the most simplified answer, please tell me if I am wrong and I will redo my work.
x^2 + 10x
Find x.
A.2.14
B.10
C.22.8
D.35
Answers
A is your answer just multiply it by 14 then add it by 5 it looks as if all sides are equal.
roman has a certain amount of money. if he spends $15, then he has 14 of the original amount left. how much money did roman have originally?
Answers
Roman has a certain amount of money. if he spends 15, then he has 14 of the original amount left. Roman had originally 20.
To find out how much money Roman had originally, you can follow these steps:
Step 1: Let the original amount of money be "x".
Step 2: According to the problem, if Roman spends $15, he has 1/4 of the original amount left.
So, after spending 15, he has (1/4)x left.
Step 3: Since he spent $15, we can write the equation as: x - 15 = (1/4)x.
Step 4: To solve for x, first multiply both sides of the equation by 4 to get rid of the fraction:
4(x - 15) = 4(1/4)x => 4x - 60 = x.
Step 5: Subtract "x" from both sides:
4x - x - 60 = 0 => 3x - 60 = 0.
Step 6: Add 60 to both sides:
3x = 60.
Step 7: Divide both sides by 3 to find the value of x:
x = 60 / 3 => x = 20.
for such more question on Roman number
https://brainly.com/question/30778051
#SPJ11
El terreno donde se encuentra una cancha
de fútbol mide 88 metros de ancho y 112
de largo ¿Cuál es su área? ¿Es su superficie
mayor a una hectárea?
Answers
hectarea we xdddddddddddd
Determine the solution to the equation for x
Answers
Answer:
9/5
Step-by-step explanation:
because I know I pass the test
you guess that lebron james would score 35 points during the game. he actually scored 28. find your percent error.
Answers
The error Percentage is 20%
What is Percentage?
A percentage is a component of a whole stated as a number between 0 and 100 rather than as a fraction. All of anything is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the fraction of the entire by the whole itself and multiply by 100.
Solution:
We gussed that LeBron James would score 35 points, but he only scored 28 points
So, the difference was of 7 points (35-28)
Error Percentage = 7/35 * 100
Error Percentage = 1/5 *100
Error Percentage = 20%
To learn more about Percentage from the given link
https://brainly.com/question/843074
#SPJ4
A group of 12 students goes on a school field trip, 6 are in third grade. which fraction is equivalent to 6 12
Answers
The fraction which is equivalent to 6/12 is 1/2
What does a fraction mean?
In the first place, fraction is a numerical quantity or relationship where one number is expressed in terms of another.
In order to determine the equivalence of 6/12 in fraction , we need reduce 6/12 to the lowest term, since 6 is common to 6 and 12 and that 6 divided by gives 1 and 12/6 gives 2, which means that we are left 1/2
The correct fraction which is equivalent to 6/12 is 1/2
Find out more about fraction on:https://brainly.com/question/5243429
#SPJ1
Full question:
A group of 12 students goes on a school field trip, 6 are in third grade. which fraction is equivalent to 6/12?
(A) 1/3
(B)1/4
(C) 1/6
(D) 1/2
Compute the effective annual rate of interest at which $ 2,000
will grow to $ 3,000 in seven years if compounded quarterly Express
the final answer as a % rounded to 2 decimal places .
Answers
The formula for calculating the effective annual rate of interest with quarterly compounding is:
(1 + r/4)^4 - 1 = A/P
where r is the quarterly interest rate, A is the final amount, and P is the principal.
In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.
So we have:
(1 + r/4)^4 - 1 = 3000/2000
(1 + r/4)^4 = 1.5
1 + r/4 = (1.5)^(1/4)
r/4 = (1.5)^(1/4) - 1
r = 4[(1.5)^(1/4) - 1]
To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:
effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%
Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.
For more questions like interest visit the link below:
https://brainly.com/question/18096283
#SPJ11