Answers
Answer:
Step-by-step explanation:
Given function is,
f(x) = [tex]x\sqrt{x}[/tex]
We can rewrite this function as,
f(x) = [tex]x^{\frac{3}{2}}[/tex]
a). Domain of the function is [0, ∞)
Derivative of the function in this domain,
f'(x) = [tex]\frac{3}{2}x^{(\frac{3}{2}-1)}[/tex]
= [tex]\frac{3}{2}x^{\frac{1}{2}}[/tex]
Since, f'(x) > 0 in the interval [0, ∞)
Function is increasing in the interval [0, ∞)
b). For local maxima and local minima,
Second derivative of the function,
f"(x) = [tex]\frac{3}{2}(\frac{1}{2})x^{\frac{1}{2}-1}[/tex]
= [tex]\frac{3}{4}x^{-\frac{1}{2}}[/tex] > 0
So the function should have a local minima.
But the function is continuous in the interval x ≥ 0,
There is no local minima (only absolute minima).
c). Since, second derivative is undefined at x = 0,
There are no inflection points.
d). Since, f"(x) > 0 in the interval [0, ∞)
Concavity of the curve is UPWARDS.
Related Questions
A line with slpoe 3 passes through the point (0.10). What is the y-coordinate of the point on the line with x-coordinate 2
Answers
Answer:
When x-coordinate x = 2, the value of the y-coordinate is: y = 16
Please also check the graph.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven
The point (0, 10)
The slope m = 3
The value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
We have given the point (0, 10)
It means:
at x = 0, y = 1 0
Therefore, the y-intercept b = 10
so substituting b = 10 and m = 3 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y = 3x+10[/tex]
Therefore, the equation of a line with slope 3 passes through the point (0, 10) will be:
[tex]y = 3x+10[/tex]
Now, substituting x = 2 in the equation
[tex]y = 3x+10[/tex]
y = 3(2) + 10
y = 6+10
y = 16
Therefore, when x-coordinate x = 2, the value of the y-coordinate is: y = 16
Please also check the graph.
Find the area of the structure.
Answers
Answer:
8/9 in squared
Step-by-step explanation:
because one block is 1/9, and there are 8
Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coordinates of point U.
Answers
Answer:
(0, -1)
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram RSTU, RS // TU and RU // ST
Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:
Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5
Slope of ST = (2 - 4) /[6 - 3] = -2/3
Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)
Slope of TU = (y - 2) /[x - 6]
Slope of RU = Slope of ST
(y - 1) / (x + 3) = -2/3
3y - 3 = -2x -6
2x + 3y = -6 + 3
2x + 3y = -3 (1)
Slope of RS = Slope of TU
0.5 = (y - 2) /[x - 6]
0.5x - 3 = y - 2
0.5x - y = 1 (2)
Solving 1 and 2 simultaneously gives:
x = 0, y = -1
Therefore the coordinates of U = (0, -1)
An equilateral triangle has a side length of 12sqrt(3) inches. What is the length of the altitude of the triangle?
HELP ASAP
Answers
Answer:
18 inches.
Step-by-step explanation:
Let x inches be the altitude of the triangle.
By Pythagoras Theorem,
[6sqrt(3)]^2 + x^2 = [12sqrt(3)]^2
108 + x^2 = 432
x^2 = 324
x = 18
So the altitude of the triangle is 18 inches.
What is the best estimate
4.79 + 13.02
Answers
Answer:
17.81, but I would estimate 17.80 so it doesnt look exact.
Step-by-step explanation:
Consider the following pieces of identification a person might have in order to apply for a credit card:
B : Applicant present a birth certificate
D: Applicant presents a drivers license
M applicant presents a marriage license
Write Logical expressions
1. The applicant must present either a birth certificate, a drivers license or a marriage license.
2. The applicant must present any two of the following forms of identification: birth certificate, drivers license, marriage license
3. Applicant must present either a birth certificate or both a drivers license and a marriage license
Answers
Answer:
B v D v M ;
(B ٨ M) V (B ٨ D) V (M ٨ D) ;
B V (D ٨ M)
Step-by-step explanation:
Given :
B : Applicant present a birth certificate
D: Applicant presents a drivers license
M applicant presents a marriage license
1.)
This means that any one of the three must be presented :
Birth certificate OR Driver's license OR Marriage certificate
B v D v M
2.)
This means any two combination of the three certificates :
(birth certificate and marriage certificate) OR (birth certificate and driver's license) OR (marriage certificate and driver's license)
(B ٨ M) V (B ٨ D) V (M ٨ D)
3.)
That is birth certificate alone will suffice or a driver's incense and a marriage certificate
B V (D ٨ M)
Seven more than three times a number is thirty-one. Write an equation
and solve for the unknown number.
Answers
Answer:
As an equation, (we'll use x as the variable), that word problem is 3x+7=31.
To solve we'd subtract 7 from both sides to isolate 3x, which gives us 3x=24. Now, to isolate x(unknown number) we would divide both sides by 3. When you divide both sides by 3, you'd get x=8.
The Chandlers are moving across the country. Mr. Chandler leaves 4 hours before Mrs. Chandler. If he averages 70mph and she averages 80mph, how many hours will it take Mrs. Chandler to catch up to Mr. Chandler?
Answers
Answer:
It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.
Step-by-step explanation:
Given that:
Speed of Mr. Chandler = 70 mph
Distance covered in 4 hours = 70 * 4 = 280 miles
Let,
h be the number of hours.
y be the total distance covered.
y = 70h + 280
Speed of Mrs. Chandler = 80 mph
y = 80h
For catching up, the distance would be same.
80h = 70h + 280
80h - 70h = 280
10h = 280
Dividing both sides by 10
[tex]\frac{10h}{10}=\frac{280}{10}\\h=28[/tex]
Hence,
It will take 28 hours for Mrs. Chandler to catch up with Mr. Chandler.
Jolie purchased a concert ticket on a web site. The original price of the ticket was $110. She used a coupon code to receive a 15% discount. The web site applied a 10% service fee to the discounted price. Jolie’s ticket was less than the original price by what percent?
Answers
Answer:
10 percent
Step-by-step explanation:
i took a test
In 2010, the population of Alabama was about 4.8 million. This is an increase of about 7.5% over the population of Alabama in 2000. If this trend continues, predict the population of Alabama in 2030 and 2040.
Answers
Answer:
alabama is 7.85 million
Step-by-step explanation:
What is cos 60°?
60
2
1
90'
309
3
O A.
O B. 2
С.
0
D.
OE.
E.
< PREVIOUS
Answers
Answer:
B but sorry 4 the time tho
The measure of the trigonometric relation cos 60° = 1/2
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
A = cos 60°
And , cos θ = adjacent / hypotenuse
So , cos 60° = 1/2
Hence , the measure of cos 60° = 1/2
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
#SPJ7
A band expects to put 16 songs on their next CD. The band writes and records 37.5% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD?
Answers
answer:
- this is multi-step problem
16 X 1.375 = 22 songs (37.5% was added)
22 X .5 = 11 songs (50% was removed)
final answer: 11 songs.
Are these triangles similar?
Answers
pretty sure its no, the number on the outside arent the same meaning both areas wont add up.
Can someone please help me solve this
Answers
Answer:
[tex]m\angle1=75^{\circ}[/tex]
Step-by-step explanation:
Solution 1:
[tex]m\angle1[/tex] is formed by a point that is on the circle. The angle encompasses an arc of [tex]150^{\circ}[/tex] and thus the measure of the angle formed is [tex]\frac{150}{2}=\fbox{$75^{\circ}$}[/tex].
Solution 2:
Since [tex]\angle 1[/tex] is adjacent to a line and encompasses an arc, we can set up the following proportion:
[tex]\frac{150}{360}=\frac{m\angle 1}{180}[/tex]
Solving, we get [tex]m\angle 1=\fbox{$75^{\circ}$}[/tex].
_ divided by 4= _ remaider 5
Answers
Answer:
20 / 4 =5
Step-by-step explanation:
I think
write the following numbers in order from least to greatest . -1, 1.75, -1.75, -2, -2 1/2, -5/2, 9/4 I NEED HELP ASAP PLEASE
Answers
Step-by-step explanation:
-5/2
-2
-1.75
-1
1/5
1.75
9/4
Mark as brainlist . kindly
what is 8÷530 TYPE FAST
Answers
Answer:
0.0150
Step-by-step explanation:
8÷530
0.0150
it is correct
4(b-3)=6 put the steps in Oder to solve the equation from first to last
Answers
Answer:
B= 9/2 Hope this helped
Let's solve your equation step-by-step.
4(b−3)=6
Step 1: Simplify both sides of the equation.
4(b−3)=6
(4)(b)+(4)(−3)=6(Distribute)
4b+−12=6
4b−12=6
Step 2: Add 12 to both sides.
4b−12+12=6+12
4b=18
Step 3: Divide both sides by 4
The value of b in the expression 4(b - 3) = 6 is 4.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, 4(b - 3) = 6 and we have to solve for b.
4(b - 3) = 6.
4b - 12 = 6. (distributive law a(b+c) = ab + ac).
4b = 6 + 12. (constants change sign when moved to the other sides).
4b = 16.
b = 16/4.
b = 4.
learn more about numerical expression here :
https://brainly.com/question/29199574
#SPJ2
Which angle is congruent to p
Answers
Answer: angle q is congruent to angle p
Step-by-step explanation:
congruent means same size shape, ect....
Helppppppppppppppppppppppp please
Answers
Answer:
A
Step-by-step explanation:
Two Squares
There are 2 squares at the top and bottom. All sides = 3
2* s^2
2 * 3^2
2 * 9
18
Middle Figure.
Triangles
There are many ways to solve this. I think the most easily understood is to break it into 2 triangles and a rectangle.
Base of both triangles = 5 + 5 = 10
The height of each triangle = (7 - 3)/2 = 4/2 = 2. You divide by 2 because there are 2 bases -- one in each triangle.
Area = 1/2 * 2 * 10 = 10
But there are 2 of them so the total area is 20
Rectangle
The length of the rectangle = 5 + 5 = 10
The width = 3
Area = 30
Total
Total Area = 2 squares + 2 triangles + 1 rectangle
Total Area = 18 + 20 + 30 = 68
At a multi screen movie theater two movies begin at 10 AM the first movie is shown every two hours the second movie is on every three hours what time will both movies be shown together again
Answers
Answer:
¯\_(ツ)_/¯
Step-by-step explanation:
enter the value of 3/4 + 7/12 - ( -4 )
Answers
Answer:
16/3 or 5.33
Step-by-step explanation:
3/4+7/12+4/1= 16/3 = 5.33
Answer:
Step-by-step explanation:
Exact Form:
16/3
Decimal Form:
5.3....
Mixed Number Form:
5 1/3
need help asap please
Answers
Answer:
[tex]\displaystyle yes[/tex]
Step-by-step explanation:
By the way Angle-Angle-Side Triangle Postulate, this would be enough information as proof of using the Angle Bisectour Theorem.
I am joyous to assist you at any time.
Write the rule for the transformation.
Answers
Here is an example,
Original Coordinates:
S (-5,3)
X (-4,-2)
U (-2,-1)
New"moved" coordinates:
S(5,-3)
X (4,2)
U (2,1)
Please help, don’t understand
Answers
The sales tax of 8% on a purchase of $12 is
A. $0.86
B. $0.96
C. $1.06
D. $1.60
Answers
Please help me guys
2+2
Answers
Answer:
Step-by-step explanation:
2 plus 2 is four (4)
A bell pepper has 3 grams of sugar per serving.
An apple has 18 grams of sugar per serving.
Which statement is true?
For an equal number of servings, the apples will have six times as much sugar.
There will always be more sugar in 10 servings of bell peppers than a smaller number of servings of apples.
For an equal number of servings, the apples will always have 15 more grams of sugar.
The amount of sugar in two servings of bell peppers is 36 grams.
Answers
Answer:
For an equal number of servings, the apples will have six times as much sugar.
Step-by-step explanation:
process of elimination. All the other answer choices are incorrect and this one checks out.
Just answer Number 5, I got the rest.
Any spam will be reported/deleted.
Answers
Answer:
30
Step-by-step explanation:
so one of them is 90, one of them is 60
180-150 = 30
so 30
I will give brainliest to whoever helps, I really need this. pls pls help! thanks!!
Answers
Answer:
[tex]\mathrm{1.}\; m=\mathrm{N/A};\: \mathrm{none}; \: x=14\\\mathrm{2.}\; m=0;\: (0,-5); \:y=-5\\\mathrm{3.}\; m=2;\:(0, -6); \: -2x+y=-6\\[/tex]
Step-by-step explanation:
Problem 1:
The slope of a vertical line is always undefined.The y-intercept of a line occurs when [tex]x=0[/tex]. In this line, [tex]x[/tex] is defined already as [tex]14[/tex] and therefore there is no y-intercept.The equation of a vertical line is [tex]x=n[/tex], where [tex]n[/tex] is some constant.Problem 2:
The slope of a horizontal line is always [tex]0[/tex].The y-intercept of a line occurs when [tex]x=0[/tex]. In this line, [tex]y[/tex] is declared as 5 for [tex]x\in \mathrm{R}[/tex]. Therefore, the y-intercept is [tex](0, -5)[/tex].The equation of a horizontal line is [tex]y=n[/tex], where [tex]n[/tex] is some constant.Problem 3:
The slope of a line given two points can be found using [tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]. In this case, the slope is [tex]\frac{11-(-1)}{5-(-1)}=\frac{12}{6}=2[/tex].The y-intercept occurs when [tex]x=0[/tex]. Using the equation we found (refer below), plug in [tex]x=0[/tex] to get the y-coordinate of the y-intercept.In slope-intercept form, the equation of a line is written as [tex]y=mx+b[/tex]. Using [tex]m=2[/tex] and any coordinate this line passes through, we find the equation of this line to be [tex]y=2x-6[/tex]. Rearranging this in standard form ([tex]ax^2+bx+c[/tex]), we get [tex]-2x+y=-6[/tex].