First take note of the domain of f(x) ; the square root term is defined as long as x - x ² ≥ 0, or 0 ≤ x ≤ 1.
Check the value of f(x) at these endpoints:
f (0) = 0
f (1) = 0
Take the derivative of f(x) :
[tex]f(x)=8x\sqrt{x-x^2}=8x\left(x-x^2\right)^{\frac12}[/tex]
[tex]\implies f'(x)=8\left(x-x^2\right)^{\frac12}+4x\left(x-x^2\right)^{-\frac12}(1-2x)=4\left(x-x^2\right)^{-\frac12}\left(2\left(x-x^2)\right)+x(1-2x)\right)=\dfrac{4(3x-4x^2)}{\sqrt{x-x^2}}[/tex]
For x ≠ 0, we can eliminate the √x term in the denominator:
[tex]x\neq0\implies f'(x)=\dfrac{4\sqrt x (3-4x)}{\sqrt{1-x}}[/tex]
f(x) has critical points where f '(x) is zero or undefined. We know about the undefined case, which occurs at the boundary of the domain of f(x). Check where f '(x) = 0 :
√x (3 - 4x) = 0
√x = 0 or 3 - 4x = 0
The first case gives x = 0, which we ignore. The second leaves us with x = 3/4, at which point we get a maximum of max{f(x) } = 3√3 / 2.
Please help due today
Our fathers brought forth on this continent a new nation.
How do I solve this quadratic using the square root property
Answer: x=2−2√3,2+2√3
Step-by-step explanation:
I know how to solve this problem
Asap need help fast pls!!!!!!
Answer:
i think its 20 too, tho good luck
Step-by-step explanation:
ian charges $15 per hour to landscape. if ian hired for more then six hours, he will reduce the cost by $1.50 per hour. write an expression to show the total cost of hiring ian for h hours if he landscapes for more then six hours?
Answer:
87
Step-by-step explanation:
87 because 15 times 6 equals 90 but take away the 1.50 from eah hou and you get 87
can someone help me with this?
Answer:
everything on the right, multiply by 4, and everything on the left, divide by 4
Step-by-step explanation:
The way to get from 8 to 2 is by dividing by 4. the same thing with the opposite side, but instead of multiplying, divide.
☁️ My answer is in the picture attached.
☁️ Authentic Answer
☁️ 좋은 하루 되세요 !!
[tex]-HunnyPeachy[/tex]
Anyone know this?? Thanks
9514 1404 393
Answer:
x = 4
Step-by-step explanation:
The figure is a rhombus when the sides are the same length.
21 -x = 2x +9
12 = 3x . . . . . . . . add x-9 to both sides
4 = x . . . . . . . . . . divide by 3
which is an equation of line L?
I need help pls help me
Answer:
Allison
Step-by-step explanation:
Allison:
2^6 = 64
Chris:
3³ = 27
Hannah:
4² = 16
Steve:
18^1 = 18
Answer:
Allison
Step-by-step explanation:
Allison
[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64
Chris
[tex]3^{3}[/tex] = 3 x 3 x 3 = 27
Hannah
[tex]4^{2}[/tex] = 4 x 4 = 16
Steve
[tex]18^{1}[/tex] = 18 = 18
What is the surface area of this square pyramid
Which is the cost of the minimum spanning tree of the weighted graph using Kruskal's Algorithm?
28
30
31
40
9514 1404 393
Answer:
(a) 28
Step-by-step explanation:
Kruskal's algorithm has you identify the shortest edge at each stage, including in the tree any identified edge that does not form a cycle. Here, we can start with AB, then add DF, EH, HG, BG, AC, CD and that covers the entire graph.
Starting at E, the node list is EHGBACDF. The cost is ...
3 +4 +5 +1 +6 +7 +2 = 28
__
In the attached, the minimum-cost spanning tree is highlighted in red.
How many almonds in the cup? (1/4 cup) Help me
Answer:
The amount of almonds in the fourth cup are 40
Four fewer than triple the sum of x and 3 is 17
Answer:
4- 3(x -3) =17 x =10
Step-by-step explanation:
A) 79.2
C) 11.9
B) 8.9
D) 11.6
Answer:
789
Step-by-step explanation:
Annie had 24 more paper clips than Paul.Paul had 20% fewer paper clips than Annie. How many paper clips do they have altogether help
Answer:
43.20
Step-by-step explanation:
100%=24
1%=24÷100=0.24
100+80=180
180%=0.24×180=43.20
can someone help pls?
try googling it thats what I would do. I think it would be 1/6 tho
NEEDED ASAP PLEASE. 22-32 will give brqinliest no trolls
please help me(i'm not smart so i don't get this at all T-T)
Answer:
Step-by-step explanation:
6x4=24+1=25 75/25=3 .
oh and btw go back to high school
12 pieces ! ( > < )
for future reference, this will be a lot easier to do than using points !! so simple :))
use your calculator to divide the large number by the small number !! that should give your answer
and remember if a fraction is out of four think of it like quarters or 25 cents :3
so 75 divided by 6.25 is 12 !!
good job !!! ♡♡
3/4
of 7 please answer quick
Answer:
5 and 1/4
Step-by-step explanation:
7*3/4= 3/4 of 7.
Answer:
Step-by-step explanation:
2. Moore has 20 songs. His friend bought him M more
songs. Write an expression that shows how many songs
Moore has now.
Answer:
20+m
Step-by-step explanation:
Answer:
20+m=?
Step-by-step explanation:
if moore already has 20 songs and his freind brought m more books then we would need to find the total amount of books more has now.
3392 divided by 56 x 986 -34 help
Answer:
59,689.43 (rounded)
Step-by-step explanation:
I cN explain how to get to the answer if you'd like
If −6n=−48
then n=
HELP PLEASE
Answer:
8
Step-by-step explanation:
Can anyone help me plz?
Answer:
[tex] y = \frac{1}{4}x + 1 [/tex]
Step-by-step explanation:
Line is passing through the points (0, 1) & (4, 2)
Slope of line = (2 - 1)/(4 - 0) = 1/4
y-intercept (b) = 1
Equation of line in slope-intercept form is given as:
[tex]y = mx + b \\ \\ y = \frac{1}{4}x + 1 [/tex]
Answer:
[tex]y = \frac{1}{4}x + 1[/tex]
Step-by-step explanation:
Slope intercept form allows one to write an equation for a line from only the y-intercept and the slope, so we need to identify those two things.
The slope is simply [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]=>[tex]\frac{2-1}{4-0}[/tex]=> 1/4
The slope intercept is the y value when x = 0, and since we have the point (0,1), the y-intercept must be 1
The equation is: y = mx + b where m is the slope and b is the intercept so the final equation is:
[tex]y = \frac{1}{4}x + 1[/tex]
Which statement is true help
Answer:
The correct one is 6 is 3 times as many as two.
Step-by-step explanation:
R1 663 200 in words?
Answer:
one million six hundred sixty-three thousand two hundred
Step-by-step explanation:
Suppose that 93% of approximately 1000 total dogs sold by a shelter are up-to-date on their shots. Administration plans to take an SRS of 40 dogs sold by the shelter to see what proportion of the dogs sampled are up-to-date on their shots. What are the mean and standard deviation of the sampling distribution of the proportion of dogs who are up-to-date on their shots? Choose 1 answer:
Answer: μp^ = 0.93
σp^ = √0.93(0.07)/40
Step-by-step explanation:
A cylindrical drinking glass has a base radius of 3.2 centimeters and a height of 14.0 centimeters. Given that 1 cubic centimeter is equivalent to
1 milliliter, how many milliliters of water does the glass hold when it is full? Round your answer to the nearest millimeter.
ml (Only enter the number, no words.)
Answer:
450 ml.
Step-by-step explanation:
Volume of a cylinder:
The volume of a cylinder is given by:
[tex]V = \pi r^2h[/tex]
In which r is the radius and h is the height.
A cylindrical drinking glass has a base radius of 3.2 centimeters and a height of 14.0 centimeters.
This means that [tex]r = 3.2, h = 14[/tex]
How many milliliters of water does the glass hold when it is full?
Radius and height are measured in centimers, so the volume will be in cubic centimeters, which is the same as milliliter. So
[tex]V = \pi(3.2)^2*14 = 450.3[/tex]
Rounding to the nearest millimeter, the answer is 450 ml.
Officer
De La Cruz wrote950 tickets last
year. Fourteen percent of those were for parking
violations. How many tickets were for parking
violations?
A 13
B. 133
C. 120
D. 160
Answer:
The asnwer is B. 133
Step-by-step explanation:
14X950=13,300
13,300/100=133
Please guys helppp ;( F(x)=mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and b
Answer:
I think the answer is m= -1/3 b=7/3
Explanation:
so first, you need to make equations using the info that the question gave.
f(-2)= m(-2)+b f(4)= m(4)+b
= -2m+b =4m+b
f(-2)= 3 f(4)= 1
-2m+b= 3 4m+b=1 -(2)
b= 3+2m -(1)
substitute (1) into (2) : 4m+(3+2m)=1
4m+2m+3=1
6m=1-3
6m= -2
m= -2/6
m= -1/3
Substitute m= -1/3 into (2)
4(-1/3) + b=1
-4/3 +b =1
b= 1+ 4/3
b= 7/3
Therefore, m= -1/3 b=7/3
and that's how you do it
i need help with this
Answer:
b≈41.95
Step-by-step explanation:
A bag of potatoes weighs 15 pounds. How many kilograms is this?
Answer:
6.8 kg
Step-by-step explanation:
1 pound = 0.4536 kg
15(0.4536) = 6.804