The correct format of the question is
If f(x)= [tex]\frac{1}{3}x^3 -4x^2+12x -5[/tex] and the domain is the set of all x such that 0≤x≤9 , then the absolute maximum value of the function f occurs when x is
Answer:
The absolute maximum value of the function F(x) occurs when x is 9
Step-by-step explanation:
F'(x) = [tex]x^2 -8x +12= 0[/tex]
= (x-6)(x-2) = 0
x = 2,6
so we have boundary points 0 , 9 and 2,6
The value of function at these four points
x = 0 2 6 9
F(x) = -5 17/3 -5 22
So the absolute maximum value of the given function is x = 9 and F(x) is 22.
The absolute maximum value of the function f occurs when x is 9 and this can be determined by differentiating f(x) and then equating it to zero.
Given :
[tex]\rm f(x)=\dfrac{1}{3}x^3-4x^2+12x-5[/tex]The domain is the set of all x such that 0≤x≤9In order to determine the absolute maximum value of function f(x), differentiate f(x) and then equate it to zero.
[tex]\rm f'(x)=\dfrac{1}{3}\times(3x^2)-8x+12[/tex]
Now, equate the above equation to zero.
[tex]x^2-8x+12 = 0[/tex]
Factorize the above quadratic equation.
[tex]x^2-6x-2x+12=0[/tex]
x(x - 6) - 2(x - 6) = 0
(x - 6)(x - 2) = 0
Now, determine the value of f(x) at x = 0, 2, 6, 9
f(0) = -5
f(2) = 1/3.(8) - 4(4) + 12(2) - 5
f(2) = 17/3
f(6) = 72 - 144 + 72 - 5
f(6) = -5
f(9) = 243 - 324 + 108 - 5
f(9) = 22
So, the absolute maximum value of the function f occurs when x is 9.
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Mary makes 3 1/2 cookies in 1/4 of an hour. How many cookies can she make in 1 hour?
Answer:
14
Step-by-step explanation:
3.5 × 4 = 14
4 is how many 1/4s there are in 1
Answer:
1/4 of a minute is 15mins
You have to do 3 1/2 × 4
So 7/2 × 4/1 is 28/2 which is 14
So every hour she makes 14 cookies
8 (x + 5) + 4 = 60
........
Answer:
or, 8×x+ 40+4= 60
or,8x+44=60
or,8x= 60- 44
or,8x= 16
or,x= 16/8
or,x= 2
:. x= 2
Step-by-step explanation:
first we have to multiply . if there is plus we have to do minus .then it came answer .then we can divide and we can get the value of x
Sophia earns 40 points every time she shops at a grocery store. She needs a total of 2,680 points to receive a free prize. So far, she has earned 1,280 points. How many more times will Sophia have to shop at the grocery store in order to earn the additional points she needs for a free prize? Let t represent the number of times Sophia visits the store. Which of the following equations best represents the solution to the above question?
The answer is B 1280+40t = 2680 it's on my test
You have $3.50 made up in quarters and nickels. In total, you have 26 coins. How many of each coin do you have?
Answer:
15 nickels and 11 quarters
i need help with my homework
How many solutions does the following equation have?
7(y + 3) = 5y +8
Choose 1 answer:
A
No solutions
B
Exactly one solution
Infinitely many solutions
What’s the area for this shape??????
Answer:
40cm²
Step-by-step explanation:
The formula of a trapezium is: A=1/2(a+b)h
The values are: a=6, b=10 and h=5
Therefore, to calculate the area: A=1/2(6+10)5
Hence, the area of the trapezium is A=40cm²
3x-1/5 = 2x+3/7
[tex]3x - 1 \div 5 = 2x + 3 \div 7 \\[/tex]
Answer:
123
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\textsf{Given expression:}\\[/tex]
[tex] \rm{ \frac{3x - 1}{5} = \frac{2x + 3}{7} } \\ [/tex]
[tex]\textsf{By, doing cross multiplication, we get}\\[/tex]
[tex] \rm\longmapsto \:7(3x - 1) = 5(2x + 3) \\ [/tex]
[tex] \rm\longmapsto \:21x - 7 = 10x + 15 \\ [/tex]
[tex] \rm\longmapsto \:21x - 10x = 15 + 7 \\ [/tex]
[tex] \rm\longmapsto \:11x = 8 \\ [/tex]
[tex] \rm\therefore \:x = \frac{8}{11} . \\ [/tex]
[tex]\textsf{Hence, the value of x will be $\frac{8}{11}$ respectively.}\\[/tex]
Find two numbers with a sum of 14 and a difference of 4:
Answer:
First number --> x
Second number --> y
x + y = 14 --> x = 14 - y
x - y = 4
so
14 - y - y = 4
14 - 2y = 4
2y = 10
y = 5
so
x = 14 -5
x = 9
The slope of the line below is 2. Write the point-slope equation for the line
using the coordinates of the labeled point.
pls help
37a + 45b +1 3c + 26d + 27
which one is the term?
i literally have no idea but hope you don't mind if i get your points!?
Use the diagram to find lengths. BP is the perpendicular bisector of AC. CQ is the perpendicular bisector of BD. AB = BC = CD.
Answer:
hhhhhh i have no idea
Step-by-step explanation:
sorrrrrrryyyyyyyyyyy
Answer:
PC = 8
Step-by-step explanation:
Bisectors split things into equal parts. The bisector PB made AP and PC equal. So AP = 8, AP = PC, 8 = PC
Solve for r using literal equations methods
Answer:
option 4
Step-by-step explanation:
Liana is studying the activity of nurse sharks. She starts at a position that is 25 feet below sea level. She rises 9 feet, then descends 12 feet to take a photo of a sleeping shark. Find her position relative to sea level when she took the photo.
Answer:
I believe the answer is -28
Step-by-step explanation
I gotchu bro
The answer is -28 because Liana starts at 25 below sea level (which is the same thing as -25) If she rises 9 feet, then you know to add because she is going up so your just gonna add. Next she descends 12 feet, so she went down, so subtract. So i know the answer is going to be -28 because -25+9 is -16, then imma subtract -16 and 12 so, -16 - 12= -28. There ye go
PLEASE HELP 15 POINTS...PLEASE HELP
Answer:
-4
Step-by-step explanation: it is intercepting the -4 so i think -4 is the right answer
Answer:-4
Step-by-step explanation:
it bc the line crosses on -4
Y=7e^6x -5x^3 + 30 find Y
Answer:
reorder 7e^6x and -5x^3
y=-5x^3 +7e^6x +3e
Step-by-step explanation:
Now thats if its 7e to the power of 6x
Find the value of g when 5g + 6 equals 2g + 15.
Answer:
g=3
Step-by-step explanation:
5g+6=2g+15
3g=9
g=3
A rain barrel can hold 72 gallons of water. As it rained last week, water entered the
barrel at a rate of 2 gallons every 6 hours. At this rate, how long will it take the rain
barrel to fill?
(show how you hit the answer if you can)
Answer: Correct me if I’m wrong but I think it’s 216 hours
Step-by-step explanation: every 24 hour you get 8 gallons so do 24 x 10 you get 240 hours and that gets you 80 gallons so you minus 8 gallons so take off 24 hours and you get your answer
S= CB-7, for C.
What is the Answer to this?
Answer:
C = (S + 7) / B
Step-by-step explanation:
S = CB - 7
S + 7 = CB
C = (S + 7) / B
Hope this helps!
Darnell is underwater 20 feet below sea level. His friend is on a hill 32 feet above sea level. How far apart are the two friends?
Answer:
52 feet apart
Step-by-step explanation:
20 + 32 = 52
Answer:
52 feet
Step-by-step explanation:
20 + 32 = 52
Pedro makes a base monthly salary of $1500. As a vendor, he must sell $20000 worth of items per month. He also makes a 4% commission on all sales beyond the monthly quota. If Pedro sold $26000 worth of items this month, what is his total salary for the month including base salary and commission to the nearest dollar?
Answer:
$2540
Step-by-step explanation:
Given parameters:
Base salary of Pedro = $1500
Amount of commission on sales = 4%
Sales = $26000
Unknown:
His total salary including base salary and commission = ?
Solution:
His total salary;
Total salary = Base Salary + (percent on commission x sales)
Total salary = $1500 + ([tex]\frac{4}{100}[/tex] x $26000)
Total salary = $1500 + $1040
Total salary = $2540
Express the inequality using interval notation x ≤ -4 or x ≥ 3
Y+5= -3/4x Select the slope and y-intercept of the linear equation.
Answer:
Slope: -3/4
y-intercept: (0,-5)
Step-by-step explanation:
Hope it helps!
For the school's sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres left over. How many litres of lemonade were sold?
Given :
For the school's sports day, a group of students prepared 12 1/2 litres of lemonade. At the end of the day they had 2 5/8 litres left over.
To Find :
How many litres of lemonade were sold.
Solution :
Initial amount of lemonade, I = 12 1/2 = 25/2 litres.
Final amount of lemonade, F = 2 5/8 = 21/8 litres.
Amount of lemonade sold, A = I - F
A = 25/2 - 21/8 litres
A = 9.875 litres
Therefore, 9.875 litres of lemonade were sold.
Hence, this is the required solution.
Suppose that 2000 is placed in an account that pays 13% interest compounded each year. Assume that no withdrawals are made from the account. Do not do any rounding.
A:Find the amount in the account at the end of 1 year.
B: Find the amount in the account at the end of 2 years.
The amount will be $2260 in the account at the end of 1 year. The amount will be $2553.8 in the account at the end of 2 years.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
A = P(1+r/100)ⁿ
Where:
A = the future value of the investment or loan
P = the principal investment or loan amount
r = the interest rate (decimal)
n = the number of compound periods
As per the question, the given data will be:
p = $2000
r = 13%
t = 1 year
To calculate the amount in the account at the end of 1 year.
A = P(1+r/100)ⁿ
Substitute the values of p,r, and t in the formula,
A = 2000(1 + 13/100)¹
A = 2000(1 + 0.13)¹
A = 2000(1.13)
A = $2260
To calculate the amount in the account at the end of 2 years.
A = 2000(1 + 13/100)²
A = 2000(1 + 0.13)²
A = 2000(1.13)²
A = $2553.8
Thus, the amount will be $2260 in the account at the end of 1 year. The amount will be $2553.8 in the account at the end of 2 years.
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Darrell is interested in getting a puppy and goes to the local animal shelter. He finds a puppy that he likes and begins the process of making the purchase. Because they want to neuter the puppy, Darrell has to sign a contract and pay for the puppy and then leave the puppy there until Monday while the puppy is in surgery. When Darrell returns on Monday, he finds out that the puppy did not survive the surgery and died over the weekend. Darrell's heart is broken, but he wants to enforce the contract. Will he win?
Answer:
The answer is "yes".
Step-by-step explanation:
In this question, the given statement is true because, for the dogs, its standard neutering age is six to nine months, so long as they would be safe puppies as young as eight weeks can be neutered.
The Male dog neutralization avoids disease of the testicles or reduces the risk of other conditions like a prostatic disease. Its tangled male dog may also have less motivation to go about, which may assist with certain behavioral problems. It can decrease aggressive behavior in many dogs.PLEASE ANSWER
How many terms are in the expression 5 - 3c + 21?
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
i think of a number add 3 to it and multiply the results by 6
Answer:45
Step-by-step explanation:
Answer:
43
Step-by-step explanation:
25+(3*6)=43
Solve the system using substitution y=2x+10 y=x+8
Answer:
x = -2
Step-by-step explanation:
x+8 = 2x +10
-2x + x = 10-8
-x = 2
divide both side by -1
answer -- x = -2
:( this is due by the end of the day! 20 points!! right answer please
Answer:
∠c=90°, ∠b=47.5°, a=85°
Step-by-step explanation:
∠c is inscribing a semicercle so is half of the intercepted arc and the whole circle is 360 , half will be 180 and the angle will be 90°
∠b is inscribing a 95°arc so is half of that 95/2=47.5°
arc a is part of a semicircle so is 180-95 =85°
