Answers
Answer:
picturr is not visible to me
Related Questions
In Exercises 11-18, use analytic methods to find the extreme values of the function on the interval and where they occur. Identify any critical points that are not stationary points.
15. f(x) = sin(x + π/4), 0 ≤ x ≤ 7π/4
Answers
Answer:
Absolute maximum of 1 at x = pi/4 ; [tex](\frac{\pi}{4}, \ 1)[/tex]
Absolute minimum of -1 at x = 5pi/4 ; [tex](\frac{5\pi}{4} , \ -1)[/tex]
Local maximum of √2/2 at x = 0 ; [tex](0, \ \frac{\sqrt{2} }{2} )[/tex]
Local minimum of 0 at x = 7pi/4 ; [tex](\frac{7\pi}{4}, \ 0)[/tex]
No critical points that are not stationary points.
Step-by-step explanation:
[tex]f(x)=sin(x+\frac{\pi}{4} ), \ 0 \leq x\leq \frac{7 \pi}{4}[/tex]
Take Derivative of f(x):Let's start by taking the derivative of the function.
Use the power rule and the chain rule to take the derivative of f(x).
[tex]f'(x)=\frac{d}{dx} [sin(x+\frac{\pi}{4})] \times \frac{d}{dx} (x+\frac{\pi}{4})[/tex]The derivative of sin(x) is cos(x), so we can write this as:
[tex]f'(x)=cos(x+\frac{\pi}{4})\times \frac{d}{dx} (x+\frac{\pi}{4})[/tex]Now, we can apply the power rule to x + pi/4.
[tex]f'(x)=cos(x+\frac{\pi}{4} ) \times 1[/tex] [tex]f'(x)=cos(x+\frac{\pi}{4} )[/tex]Critical Points: Set f'(x) = 0Now that we have the first derivative of [tex]f(x)=sin(x+\frac{\pi}{4})[/tex], let's set the first derivative to 0 to find the critical points of this function.
[tex]0=cos(x+\frac{\pi}{4})[/tex]Take the inverse cosine of both sides of the equation.
[tex]cos^-^1(0) = cos^-^1[cos(x+\frac{\pi}{4})][/tex]Inverse cosine and cosine cancel out, leaving us with x + pi/4. The inverse cosine of 0 is equal to 90 degrees, which is the same as pi/2.
[tex]\frac{\pi}{2} = x +\frac{\pi}{4}[/tex]Solve for x to find the critical points of f(x). Subtract pi/4 from both sides of the equation, and move x to the left using the symmetric property of equality.
[tex]x=\frac{\pi}{2}- \frac{\pi}{4}[/tex][tex]x=\frac{2 \pi}{4}-\frac{\pi}{4}[/tex] [tex]x=\frac{\pi}{4}[/tex]Since we are given the domain of the function, let's use the period of sin to find our other critical point: 5pi/4. This is equivalent to pi/4. Therefore, our critical points are:
[tex]\frac{\pi}{4}, \frac{5 \pi}{4}[/tex] Sign Chart(?):Since this is a sine graph, we don't need to create a sign chart to check if the critical values are, in fact, extreme values since there are many absolute maximums and absolute minimums on the sine graph.
There will always be either an absolute maximum or an absolute minimum at the critical values where the first derivative is equal to 0, because this is where the sine graph curves and forms these.
Therefore, we can plug the critical values into the original function f(x) in order to find the value at which these extreme values occur. We also need to plug in the endpoints of the function, which are the domain restrictions.
Let's plug in the critical point values and endpoint values into the function f(x) to find where the extreme values occur on the graph of this function.
Critical Point Values:[tex]f(\frac{\pi}{4} )=sin(\frac{\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{\pi}{4} )=sin(\frac{2\pi}{4}) \\ f(\frac{\pi}{4} )=sin(\frac{\pi}{2}) \\ f(\frac{\pi}{4} )=1[/tex]There is a maximum value of 1 at x = pi/4.
[tex]f(\frac{5\pi}{4} )=sin(\frac{5\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{5\pi}{4} )=sin(\frac{6\pi}{4}) \\ f(\frac{5\pi}{4}) = sin(\frac{3\pi}{2}) \\ f(\frac{5\pi}{4} )=-1[/tex]There is a minimum value of -1 at x = 5pi/4.
Endpoint Values:[tex]f(0) = sin((0) + \frac{\pi}{4}) \\ f(0) = sin(\frac{\pi}{4}) \\ f(0) = \frac{\sqrt{2} }{2}[/tex]There is a maximum value of √2/2 at x = 0.
[tex]f(\frac{7\pi}{4} ) =sin(\frac{7\pi}{4} +\frac{\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(\frac{8\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(2\pi) \\ f(\frac{7\pi}{4} ) =0[/tex]There is a minimum value of 0 at x = 7pi/4.
We need to first compare the critical point values and then compare the endpoint values to determine whether they are maximum or minimums.
Stationary Points:A critical point is called a stationary point if f'(x) = 0.
Since f'(x) is zero at both of the critical points, there are no critical points that are not stationary points.
cube m holds a maximum of 64 unit cubes. each unit cube has an edge length of 1/2 centimeter. what is the length of cube m?
Answers
Answer:
136 or 34
Step-by-step explanation:
not sure if its right because my math is bad
PLS ANWSER QUICK TIMED ASSIGNMENT
Which equation represents a circle with a center at (2,-8) and a radius of 11
(x-8)^2+(y+2)^2=11
(x-2)^2+(y+8)^2=121
(x+2)^2+(y-8)^2=11
(x+8)^2+(y-2)^2=121
Answers
The second one, because when you square the right side of the equation you get 11 which is your radius. On the right side you get 2,-8 when you solve for the radius. aka solve for x and y
Select ALL the true statements
Answers
Answer:
2 and 5 because dilation always have the same angles and they can increase and decrease in size
Step-by-step explanation:
But I am not sure so if I am wrong I am sorry I did a test like this
Perform the function compositions
Answers
Answer:
1. 4x^2-24x^2+37
2.16x^4+8x^2-2
Step-by-step explanation:
Tova has 17 marbles. The types of marbles she has are aggies, comets, and cats eyes. She has twictas many aggies as comets. She has 1 more cats eye than comets. She has 8 aggies. How many cats eyes does tova have?
Answers
Answer:
Tova has 5 cat's eyes.
Step-by-step explanation:
Use simple math to figure out the amounts. If she had twice as many aggies as comets, and the amount of aggies is 8, she had 4 comets. She had one more cat eye than comets. That means that she had 5 cat's eyes.
Answer: Tova has 5 cat's eyes.
Solve the system of equations.
2x−9y=14
x=−6y+7
Answers
Answer:{x,y}={7,0}
i hope this is right :)
Step-by-step explanati
Answer:
Step-by-step explanation:
Directions : Find the indicated term of each arithmetic sequence.
Question :14th term: a = 4; d = -5
Answers
Answer:
The 14th term is -61.
Step-by-step explanation:
T(n) = 9-5n
T(14) = 9 - 5 * 14 = 9 - 70 = -61
Needdd helpp noww please
Giving extra points
Answers
Answer:
b
20
10
Step-by-step explanation:
the process of finding factors
Answers
Christina is buying a new rug for her bedroom. The rug's length is 8 yards, 2 feet, and 4 inches long. The rug's width is 1/4 of its length. What is the perimeter of the rug?
Answers
Answer:
20 yards, 6 feet
Step-by-step explanation:
Width of the rug is [tex]\frac{1}{4}[/tex] of the length:
[tex]\frac{1}{4}[/tex] × 8 yards = 2 yards
[tex]\frac{1}{4}[/tex] × 2 feet = [tex]\frac{1}{2}[/tex] foot = 6 inches
[tex]\frac{1}{4}[/tex] × 4 inches = 1 inch
P = 2( l + w )
2 × l = 16 yards, 4 feet, 8 inches
2 × w = 4 yards, 1 foot, 2 inches
P = 20 yards, 5 feet, 12 inches = 20 yards, 6 feet
f(x) =2x+8 when x=-2, x=0, and x=5.
Answers
Answer:
f(-2)=4, f(0)=8, f(5)=18
Step-by-step explanation:
f(x)=2x+8
f(-2)=2(-2)+8
f(-2)=-4+8
f(-2)=4
f(0)=2(0)+8
f(0)=0+8
f(0)=8
f(5)=2(5)+8
f(5)=10+8
f(5)=18
twice a number k plus the quantity s minus 2
Answers
Answer:
2k+s-2
im assuming
I need help figuring out what: f(r-2)=6x+7 is
Answers
Answer:
f(r-2) = 6r -5
Step-by-step explanation:
f(r-2) is another notation for x = r-2
so we’ll plug in r-2 for x and solve:
f(r-2) = 6(r-2)+7
f(r-2) = 6r -12 +7
f(r-2) = 6r -5
56) A tire retailer plans to sell
$100,000 worth of tires in
January. Planned reductions are
$15,000; planned inventory for
January Ist is $300,000 and for
January 31st is $350,000. As of
January 8th, the retailer has
ordered $15,000 for January
delivery. What is the open-to-
buy for the rest of the month?
Answers
Answer:
/
Step-by-step explanation:
#4
Write an equation in slope-intercept
form to represent the line
perpendicular to 6y = 9 - x with
y-intercept 2
O y = -6x + 2
O y = 2x + 9
Answers
Answer:
A, y= -6x + 2
Step-by-step explanation:
1. Put the equation into slope intercept form
6y = 9 - x
y= -1/6x + 9/6
The slope of equation 1 is -1/6
2. A perpendicular line is the inverse slope of our firsy equation. (-1/6)^-1 = -6.
3. The y intercept of a line in slope intercept form is the b value in the equation as written:
y=mx+b
Therefore, if m=-6 and b=2, our equation is
y= -6x + 2
The edge length of a cube is changing at a rate of 10 in/sec. At what rate is the cube's volume changing when the edge length is 3 inches?
Answers
Given:
The edge length of a cube is changing at a rate of 10 in/sec.
To find:
The rate by which cube's volume changing when the edge length is 3 inches.
Solution:
We have,
[tex]\dfrac{da}{dt}=10\text{ in/sec}[/tex]
We know that, volume of cube is
[tex]V=a^3[/tex]
Differentiate with respect to t.
[tex]\dfrac{dV}{dt}=3a^2\dfrac{da}{dt}[/tex]
Substituting [tex]\dfrac{da}{dt}=10[/tex] and a=3, we get
[tex]\dfrac{dV}{dt}_{a=3}=3(3)^2(10)[/tex]
[tex]\dfrac{dV}{dt}_{a=3}=3(9)(10)[/tex]
[tex]\dfrac{dV}{dt}_{a=3}=270[/tex]
Therefore, the volume increased by 270 cubic inches per sec.
Define a variable, write an inequality, and solve the problem : Four less than nine times a number is greater than eleven more than two times the same number.
Answers
Answer:
x > 15/7
Step-by-step explanation:
four less than nine times a number:
9x - 4
Eleven more than two times the same number:
2x + 11
Thus:
9x - 4 > 2x + 11
7x > 15
x > 15/7
I hope this helps you :)
Write the fractional equivalent (in reduced form) to each number
10
0.125 =
0.16
Answers
0.125 —> 1/8
0.16 —> 4/25
x+y =783
10x+7y=6459
Answers
9514 1404 393
Answer:
(x, y) = (326, 457)
Step-by-step explanation:
Use the first equation to make an expression for y that can be substituted into the second.
y = 783 -x
10x +7(783 -x) = 6459
3x = 978 . . . . . . . . . . . . subtract 7(783) = 5481
x = 326 . . . . . . . . . . . . . divide by 3
y = 783 -326 = 457
The solution is (x, y) = (326, 457).
Write the number 7,070,000,000 in scientific notation.
Answers
Answer:
7.07 x 10^9
Hope this Helps!! Have a fabulous day!
~PumpkinSpice1
Answer:
7.07 x 10^9
Step-by-step explanation:
hope it helps!
simplify the given involving the indicated division.
Answers
I NEED HELP PLZ
Write an equation in point slope and slope-intercept that includes the points (0, 0) and (9, -3).
Answers
The spinner in a game based on chance has 25 equal sectors. The prize is worth $50, and the cost to play is $2.50. A player wins if the arrow lands on the sector he or she chose.
Which table shows the correct outcomes for a player who plays the game one time?
Answers
Answer:
________________ WIN _____ LOSE
Outcome(x) ______ $47.50 ____ - $2.50
PROBABILITY P(x) _____ __________
Step-by-step explanation:
Given that :
The cost of play = $2.50
The winning price = $50
Hence, if a player emerges victorious or wins; the net amount won is :
Winning price - cost of play
$50 - $2.50 = $47.50
If the player loses :
Then he wins $0
Net amount lost equals :
Amount won - cost of play
$0 - $2.50 = - $2.50
________________ WIN _____ LOSE
Outcome(x) ______ $47.50 ____ - $2.50
PROBABILITY P(x)
Answer:
Win Lose
47.50 -2.50
Step-by-step explanation:
Got it right on the test.
You start at (2, 5). You move left 5 units and right 8 units. Where do you end?
Answers
Answer:
(5,5)
Step-by-step explanation:
left 5 is -5 and right 8 is +8.
-5+8=3
2+3=5
When talking about left and right, you change the x-coordinate, when up and down, y-coordinate.
Overall, (5,5)
Answer:
5,5
Step-by-step explanation:
since we are not changing the height of the point and just moving side to side, the y intercept does not change. Once you move 5 units to the left, your new point is -3,5 but then when you move 8 to the right it switches to positive again and the new point is 5,5
Please help me!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
70
Step-by-step explanation:
4060/58=70
8)Four added to twice a number yields. Find the number.
Answers
Answer:
X=-2
Step-by-step explanation:
Let no =X
So 2x+4=0
2x=-4
X=-4/2
X=-2
So the answer is -2
ILL GIVE BRAINLIEST FOR BEST AWNSER!!!
A football player kicks a ball with a force of 50 N
How does the impulse above change if he doubles the amount of time that his foot is in contact with the ball?
Answers
Answer: AP= 30 kgm/s c) Calculate the final velocity of the object, if it was initially at rest. A 0.5kg baseball experiences a 10N force for a duration of 0.1s.
Step-by-step explanation:
45×(−10)×45 STEP explanation
Answers
Answer:
-20,250
Step-by-step explanation:
PEMDAS
Multiply left to right
45 * -10 * 45
45* -10
-450 * 45 =
-20,250
05.01)A poster is shown below: A rectangle is shown. The length of the rectangle is labeled 18 inches. The width of the rectangle is labeled 6 inches. What are the dimensions if the poster is enlarged by a factor of seven over two ? 42 in by 126 in 3 in by 9 in 9 in by 12 in 21 in by 63 in
Answers
Answer:
21 in by 63 in
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
I took the quiz!!!!
