The absolute maximum of n(x) = 1 - 2 · cos 2x, whose first derivative is n(0) = 0, exists at x = 0.5π on (0, 2π]. The value of the absolute maximum is 3.
How to find the absolute maximum of a differentiable function
A function is differentiable in a given interval if and only if its derivative exists for every value of the interval. To determine the absolute maximum of n(x), we need to integrate the given function, apply first derivative and second derivative test and finally evaluate n(x).
First, we integrate n'(x) in terms of x:
n(x) = 2 ∫ sin 2x dx = 2 · (- 0.5 · cos 2x) + C = - cos 2x + C
- cos 0 + C = 0
C = 1
Then, n(x) = 1 - 2 · cos 2x.
Now we proceed to apply first and second derivative tests:
First derivative test2 · sin 2x = 0
sin 2x = 0
2 · x = sin⁻¹ 0
2 · x = π ∨ 2π
x = 0.5π ∨ π
Second derivative testn''(x) = 4 · cos 2x
n''(π) = 4 · cos 2π
n''(π) = 4
There is an absolute minimum for x = π. [tex]\blacksquare[/tex]
n''(0.5π) = 4 · cos π
n''(0.5π) = - 4
There is an absolute maximum for x = 0.5π. [tex]\blacksquare[/tex]
Finally, we evaluate n(x) for x = 0.5π to determine the absolute maximum:
n(0.5π) = 1 - 2 · cos π
n(0.5π) = 3
The absolute maximum of n(x) = 1 - 2 · cos 2x, whose first derivative is n(0) = 0, exists at x = 0.5π on (0, 2π]. The value of the absolute maximum is 3. [tex]\blacksquare[/tex]
RemarkThe statement of the question is poorly formatted and reports several mistakes, correct form is introduced below:
If n'(x) = 2 · sin 2x and n(0) = 0. What is the absolute maximum of n(x) on (0, 2π]?
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Please help! I dont know how to do these :(
Answer:
t = 4 s
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+48t+64[/tex]
where:
h = height of the ball (in feet)t = time (in seconds)When the ball hits the ground, its height will be 0 ft.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t) &=0\\ \implies -16t^2+48t+64 & =0\\ -16(t^2-3t-4)& =0\\ t^2-3t-4 &=0\\ t^2+t-4t-4&=0\\ t(t+1)-4(t+1)&=0\\(t-4)(t+1)&=0\\ \implies t&=4, -1\end{aligned}[/tex]
As time is positive, t = 4 s (only).
Given
[tex]h = - 16 {t}^{2} + 48t + 64[/tex]
Where:- h= Height of ball (given in feet[ft]) and,
t= time (in seconds [s])
To find:-Time = (t)
SolutionWe know,
[tex] \text{When the ball hits the ground its height will be 0}[/tex]
[tex] \therefore h(t) = 0[/tex]
[tex] \implies - 16 t^{2} + 48t + 64 = 0 \\ \\ \fbox{taking - 16 as common multiple} \\ \\ \implies - 16(t {}^{2} - 3t - 4) = 0 \\ \\ \implies t {}^{2} - 3t - 4 = 0 \\ \\ \fbox {factorising the \: equation} \\ \\ \implies t {}^{2} - t - 4t - 4 = 0 \\ \\ \implies t(t + 1) - 4(t + 1) = 0 \\ \\ \implies(t - 4)(t + 1) = 0[/tex]
[tex] \tt{Either} \\ t - 4 = 0 \\ t = \red{ 4 } \\ \\ \tt{Or} \\ t + 1 = 0 \\ t = \red{ - 1}[/tex]
We know, Time cannot be negative.
So, Time (t) = 4 seconds
Which statement describes the value of the expression 7 times (24,672 - 589)?
168,581
________________________________________________________
SolveFollow PEMDAS
parenthesesexponentsmultiplicationdivisionadditionsubtractionAlways start with the top of the list, parentheses. Prioritize anything in parentheses.
[tex](24,672 - 589)[/tex]
start in hundreds place, then subtract from there.
[tex](24,672 - 589) = 24,083[/tex]
Next, multiply by 7.
[tex]24,083 * 7 = 168,581[/tex]
________________________________________________________
Questions?Ask in the comments box.
200
g of fertiliser is required for a plot of land
that has an area of 8 m?. Find
(i) the amount of fertiliser needed for a plot of
land that has an area of 14 m²,
(ii) the area of land that can be fertilised by
450 g of fertiliser
Answer:
(i) 350 g; (ii) 18 m². This is done by using proportion
Step-by-step explanation:
I need help please with this 1 problem
Answer:
See below, please
Step-by-step explanation:
We know
[tex]f(x) = {x}^{2} + 3x - 7[/tex]
[tex]g(x) = 3x + 5[/tex]
[tex]h(x) = 2 {x}^{2} - 4[/tex]
Hence
[tex]f(g(x))[/tex]
[tex] = {(3x + 5)}^{2} + 3 \times (3x + 5) - 7[/tex]
[tex] = (9 {x}^{2} + 30x + 25) + (9x + 15) - 7[/tex]
[tex] = 9 {x}^{2} + 39x + 33[/tex]
[tex]h(g(x))[/tex]
[tex] = 2 \times {(3x + 5)}^{2} - 4[/tex]
[tex]2 \times (9 {x}^{2} + 30x + 25) - 4[/tex]
[tex] = 18 {x}^{2} + 60x + 50 - 4[/tex]
[tex] = 18 {x}^{2} + 60x + 46[/tex]
[tex](h - f)(x)[/tex]
[tex] = h(x) - f(x)[/tex]
[tex] = (2 {x}^{2} - 4) - ( {x}^{2} + 3x - 7)[/tex]
[tex] = {x}^{2} - 3x + 3[/tex]
[tex](f + g)(x)[/tex]
[tex] = f(x) + g(x)[/tex]
[tex] = ( {x}^{2} + 3x - 7) + (3x + 5)[/tex]
[tex] = {x}^{2} + 6x - 2[/tex]
Item
Small pizza (plain) $8.99
Large pizza (plain) $13.99
Each topping $0.75
Anna ordered a large pizza
with 2 toppings. What was the total cost of her pizza Show your equation and the total cost
Part B
Anna gave the clerk two 10- dollar bill. She received $4.51 in change. Anna said the clerk was incorrect and should have given her 14.51. Who is correct Explain your answer and include an equation or example using money to support your answer.
Answer:
$15.49
Step-by-step explanation:
0.75 x 2 = 1.5
1.50 + 13.99 = 15.49
The clerk is correct; Anna only gave 20 dollars (10x2). 20 - 15.49 = 4.51, which then would be the correct change.
Prove algebraically that the difference between the squares of any two consecutive
odd numbers is always a multiple of 8
Answer:
See below ↓
Step-by-step explanation:
Let the odd integers be :
2x + 12x + 3Solving
(2x + 3)² - (2x + 1)²4x² + 12x + 9 - 4x² - 4x - 18x + 8 = 8(x + 1)On substituting any value for 'x', the value will be a multiple of x.Examples
8(1) + 8 = 16 = 8 x 28(2) + 8 = 24 = 8 x 38(3) + 8 = 32 = 8 x 4Answer:
Let one odd number be (2n + 1)
Therefore, its consecutive odd number is (2n + 3)
Difference between the two squares of these numbers:
[tex]\begin{aligned}\sf (2n+3)^2-(2n+1)^2 & = \sf (4n^2+12n+9)-(4n^2+4n+1)\\ & = \sf4n^2+12n+9-4n^2-4n-1\\ & = \sf 8n+8\\ & = \sf8(n+1)\end{aligned}[/tex]
Thus proving that the difference between the squares of any two consecutive odd numbers is always a multiple of 8.
What is the difference between surface area and lateral surface area?
Answer:
Surface area is the sum of all areas/faces of a solid, INCLUDING bases.
Lateral surface area is the surface area of a solid WITHOUT bases.
hope this helps :)
A. Find the perimeter of each figure
(Math) [please answer this correctly] thank you
A tank in the shape of a hemisphere has a radius of 3 feet. If the liquid that fills the tank has a density of 88.2 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
4988 pounds
Step-by-step explanation:
Volume of Hemisphere
4/3 x π x r^3 = 4/3 x 3^3 x π = 4/3 x 27π = 36π = Volume of Sphere
To calculate volume of Hemisphere = 36π / 2 = 18π foot^3
Weight of the liquid
88.2 pounds / foot^3 means that every cubic foot weighs 88.2 pounds so
88.2 pounds x 18π = 4987.5925 which to the nearest pound = 4988 pounds.
Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts x stickers in each bag. After filling 4 bags, they have used a total of 44 items.:Draw a diagram for the story and find the unknown amount.
Answer:
x=8
Step-by-step explanation:
Answer:
44 items in 4 bags means there are 11 items in each bag (44/4).
each bag has 3 erasers + x stickers. So, 3 + x = 11
subtract three from each side of the equation to isolate the variable (x):
3+x-3=11-3
x=8
PLEASE HELP 20 POINTS AND BRAINLIEST TO WHOEVER ANSWERS FIRST
sketch the region enclosed by the lines x=0 x=6 y=2 and y=6 find the area of the region
Answer:
24 units²
Step-by-step explanation:
Given:
Region enclosed by the line x = 0, x = 6, y = 2 and y = 6.To find:
SketchAreaThe area enclosed by these lines can be expressed as:
[tex]\displaystyle \large{\int_0^6 \int_2^6 dy dx }[/tex]
For:
[tex]\displaystyle \large{\int_2^6 dy}[/tex]
Recall:
[tex]\displaystyle \large{\int_a^b dy = [y]_b^a = a-b}[/tex]
Therefore:
[tex]\displaystyle \large{\int_2^6 dy = [y]_2^6 = 6-2 = 4}[/tex]
Now we we have:
[tex]\displaystyle \large{\int_0^6 4dx}[/tex]
Recall:
[tex]\displaystyle \large{\int_a^bk dx = [kx]_a^b = kb-ka}[/tex]
for k = constant
Therefore:
[tex]\displaystyle \large{\int_0^6 4 dx = [4x]_0^6 = 4(6)-4(0) = 24}[/tex]
Hence, the area of region is 24 units²
Dakota deposited $500 in an account earning 10% interest compounded annually,
To the nearest cent, how much interest will she earn in 3 years?
Answer:
he will get 150$
Step-by-step explanation:
you times 500 to 0.1 then times that by 3
Help PLEASE
(explanation included please.)
Answer:
x = 12.714
Step-by-step explanation:
Vertical angles sum to 180 degrees
8x-12 + 6x + 14 = 180
solve for x = 12.714
Suppose a triangle has two sides of length 42 and 35, and that the angle
between these two sides is 120°. Which equation should you solve to find the
length of the third side of the triangle?
A. c²=422+352-2(42)(35)sin120°
sin 35
B.
sin42
120
=
b
OC.
2²=42²+35²-2(42)(35)cos120°
D. c=42+352(42)(35)cos120°
Answer:
The correct option is C because it shows the accurate cosine rule
Equation to get the third side : [tex]c = \sqrt{(42^2 +35^2 -2\times 42\times35\times cos(120\degrees ))}[/tex]
The correct option is C.
Given, that sides of triangle are 42 cm and 35 cm .
The third side can be found using the Law of Cosines,
[tex]c^2 = a^2 +b^2 - 2ab\times cos(C)[/tex]
where C is the angle opposite the third side (c) .
For the given side lengths, then the third side can be found .
Here,
a = 42
b = 35
∠C = 120°
Substitute the values,
[tex]c = \sqrt{(42^2 +35^2 -2\times 42\times35\times cos(120\degrees ))}[/tex]
[tex]c = \sqrt{1764 + 1225 + 1470} \\c = \sqrt{4456}\\c = 66.75[/tex]
Hence the third side is of 66.75 units.
The correct option is C .
Know more about cosine law,
https://brainly.com/question/30766161
#SPJ5
Find all values of k for which the equation 3x^2−4x+k=0 has no solutions.
Answer:
k>1 1/3
Step-by-step explanation:
i have rsm too bro
The given equation has no solution when K is any real number and k>12
We have given that
3x^2−4x+k=0
△=b^2−4ac=k^2−4(3)(12)=k^2−144.
What is the condition for a solution?If Δ=0, it has 1 real solution,
Δ<0 it has no real solution,
Δ>0 it has 2 real solutions.
We get,
Δ=k^2−144 here Δ is not zero.
It is either >0 or <0
Δ<0 it has no real solution,
Therefore the given equation has no solution when K is any real number.
To learn more about the solution visit:
https://brainly.com/question/1397278
please help i am not smart
Answer:
Step-by-step explanation:
Number of shells she had in the begining = 40
Number of shells collected in the morning and at noon = 6 + 3 = 9
Now the number of shell at the end = 40 + 9 = 49
Icreased shells = 49 - 40 = 90
[tex]\text{Percentage increase = $\dfrac{49- 40}{40}*100$}[/tex]
[tex]=\dfrac{9}{40}*100\\\\\\= 22.5 \ \%[/tex]
Which measure of spread is least affected by the long tail in the
graph?
Vehicle A
>
0
1
2
2
3
5
6
0)
7
CO
9
4
Repairs per Vehicle
MAD
IQR
Range
Answer:
IQR
Step-by-step explanation:
I got it right :)
Five 1/4-2 5/7 needed by 3:30
Three baseball players are playing catch. Rosanne is 6.4 meters south of Lillian and 5.2
meters west of Jenna. How far does Lillian need to throw the ball to get it to Jenna? If
necessary, round to the nearest tenth.
meters
Submit
Answer:
8.2 meters
Step-by-step explanation:
This problem will form a Right angle triangle.
Where;
6.4 m and 5.2 m are the adjacent and opposite sides of the triangle while the distance that Lillian needs to throw the ball to get it to Jenna is the hypotenuse of the right angle triangle. Thus;
h = √(6.4² + 5.2²)
h = √68
h = 8.2
If f(x) = x-3/x and g(x) = 5x-4, what is the domain of (f•g)(x)?
Answer: x cannot equal 4/5 (3rd choice)
Step-by-step explanation:
f(g(x)) = f(5x-4)
plug 5x-4 into all values of x in the f(x) equation
f(5x-4)= ((5x-4) - 3))/ (5x-4)
f(5x-4) = (5x-7)/(5x-4)
set denom = 0 and solve for x to find domain
5x-4 = 0
5x = 4
x = (4/5)
x cannot equal (4/5)
How do you quarter pi
Answer:
I think its this answer I believe 0.7853982 if this is correct can u mark me brainliest
What is the surface area of the figure below
Answer: Its 120 cm
Step-by-step-explenation:
All you have to do is multiply
3x2=6
6x5=30
30x4=120
EZ QUESTION, FREE BRAINLIEST
The maximum possible area is 36 square units.
Answer:
36sq Units at max? i think
Step-by-step explanation:
Have a good day!
#ViolentJax~
Mrs. Vance decided to buy dress shirts for her two sons. She bought her older son a blue shirt for $9.91, and she bought her younger son a white shirt for $9.68. How much did she spend in all
Hope the picture will help you
Answer: $19.59
Step-by-step explanation:
9.91 + 9.68 = 19.59
I need help I really don't get this ?
Answer:
466,207,795.2 cm^3
Step-by-step explanation:
The equation to find both, the volume of the sphere and cube, are given.
The sphere:
V = [tex]\frac{4}{3}[/tex]πr^3
the radius is 7 ft therefore
V = [tex]\frac{4}{3}[/tex]π7^3
The problem says to use 3 for pie therefore
V = [tex]\frac{4}{3}[/tex](3)7^3
7 to the power of three is
V = [tex]\frac{4}{3}[/tex](3)343
[tex]\frac{4}{3}[/tex] and 3 cancel each other out to equal 4
V = 4 × 343
V = 1,372 ------> volume of sphere
______________________________________________
The cube:
V = Legth × width × height
V = 12 × 12 × 12
V = 1,728 ------> volume of cube
_______________________________________________
Total volume:
1,372 + 1,728 = 3,100 ft^3
But the question asks for the mesurement in centimeters so convert feet to centimeters using a calculator :)
3,100 ft^3 = 87,782,080 cm^3
Isaiah earned a score of 61 on Exam A that had a mean of 78 and a standard deviation
of 10. He is about to take Exam B that has a mean of 200 and a standard deviation of
50. How well must Isaiah score on Exam B in order to do equivalently well as he did
on Exam A? Assume that scores on each exam are normally distributed.
Answer:
isaiah must get a score of 115
What is the surface area of the triangular prism shown?
A triangular prism. The triangle faces have base 14 meters and height 24 meters. The rectangular bottom has dimensions 10 meters by 14 meters. The height of the prism is 25 meters.
558 m2
976 m2
1,680 m2
1,750 m2
Answer: 726 meters²
Step-by-step explanation:
We will need to find the area of five shapes. The base, the top/bottom, and the two triangle sides.
The area of a triangle is B * H / 2. Since we have two congruent triangles, I will not be dividing by two.
14 * 24 = 336 meters²
-> This value is for both of the triangle faces
The rectangular bottom is L * W
14 * 10 = 140 meters²
The two rectangles for the top and bottom will also be L * W. Since these are congruent, I will find the area of one and multiply it by two.
10 * 25 = 250 meters²
Now I will add them all together for the total surface area:
336 + 140 + 250 = 726 meters²
-> I don't see this as an option choice listed. I will review my work, but I am currently confused on the options they provide.
What is the least common denominator for the fractions 1/3 and 1/6
Answer:
least common denominator=6
Step-by-step explanation:
For the fractions, 1/3 and 1/6th, 3*2=6. making the fraction 2/6 and leaving the other the same 1/6th.
There's a picture with all the info
Answer:
3 un wer
8 lnter
12 jin
Step-by-step explanation:
of the corret anwer
Factor.
x^2 4x +4
(x + 2)^2
(x+4)^2
(2 – 2)^2
(2 – 4)^2
Answer: The answer is [tex](x+2)^2[/tex]
Step-by-step explanation:
Because [tex](x+2)^2[/tex] means [tex](x+2)(x+2)[/tex]
So we use the foil method to factor
First: [tex]x*x=x^2[/tex]
Outside: [tex]x*2=2x[/tex]
Inside: [tex]2*x=2x[/tex]
Last: [tex]2*2=4[/tex]
So we now write the following equation [tex]x^2+2x+2x+4[/tex]
Simplfied [tex]x^2+4x+4[/tex]
