Answer:
Step-by-step explanation:
Let the smaller number = x
Let the larger number = x + 1
(4,5)
(5,6)
(6,7)
(7,8)
(8,9)
(9,10)
(10,11)
(11,12)
twice a number k plus the quantity s minus 2
Answer:
2k+s-2
im assuming
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
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.
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?
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.
Jesus has a total of $80 in his savings account he is withdrawing $10 from his savings account each week write an equation indicating his withdrawal from his savings account
Help and please show all your work I need this ASAP
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?
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.
ksdfjsbjgdfg f sndm f
Answer:
Nice
Step-by-step explanation:
Answer:
hahhhh funny one nice :-)
Manny rolls a number cube labeled 1-6 and spins a spinner with four equal sections, labeled 1, 2, 3, and 4. If both numbers are odd, he wins. Otherwise, Gabriel wins. Use a list to find the sample space. Then find the probability that Gabriel wins.
a.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
b.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
c.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
d.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
Answer:
b
Step-by-step explanation:
Answer:
b.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
Step-by-step explanation:
IT'S B
45×(−10)×45 STEP explanation
Answer:
-20,250
Step-by-step explanation:
PEMDAS
Multiply left to right
45 * -10 * 45
45* -10
-450 * 45 =
-20,250
Please help me!!!!!!!!!!!!!!!!!!!!
Answer:
70
Step-by-step explanation:
4060/58=70
Needdd helpp noww please
Giving extra points
Answer:
b
20
10
Step-by-step explanation:
A rectangle is 2 meters long and 50 centimeters wide. What is its perimeter, in centimeters?
Answer:
250 centimeters
Step-by-step explanation:
2 meters into centimeters is 200 so 200+50=250
Answer:
100cm
Step-by-step explanation:
8)Four added to twice a number yields. Find the number.
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
You start at (2, 5). You move left 5 units and right 8 units. Where do you end?
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
Y’ALL PLEASE HELP ME ON MY TEST PLEASE I’VE BEEN STRUGGLING TO UNDERSTAND THE CLASSES AND MY TEACHER WONT EVEN EXPLAIN ANYTHING JUST SAY “I don’t know what you want me to do.” LIKE EXPLAIN PLEASE. SOMEONE PLEASE JUST HELP ME ON MY TEST
Answer:
1. 4320
2. 248
3. -180
4. 1/8
Three printing companies were rated on their performance using a percentage scale. This graph shows how they were
rated.
Printing Company Ratings
100
KEY
Q = Quicky Printing Company
80
R = Reliable Printers, Inc.
S = Superior Printing, Inc.
60
Rating Scale (%)
20
Q
S
Printing Company
Which company was rated the best?
a. There is insufficient information to determine which company was rated best.
Mark this and return
Save and Exit
Next
Submit
Answer:
D All three companies were rated to be equal
Step-by-step explanation:
got it right on EDG2020
Select ALL the true statements
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
Please help me out, I don’t usually ask for answers but this will mean the world too me
Write the fractional equivalent (in reduced form) to each number
10
0.125 =
0.16
2(3x+10)=6x+20 does this equation have one solution or many ? Explain why
Answer:
2(3x+10) = 6x+20
6x+20 = 6x+20
6x = 6x
x = x
This has an infinite amount of solutions
Step-by-step explanation:
Please help 30 points plus brainlyist who does first
Determine which expressions can be simplified further, and which cannot. Sort the expressions into the correct
category
2x + 3y
Can Be Simplified
Cannot Be Simplified
x + x
4r +
7y + 1
4y + 4x
y + 2y
Answer:
Step-by-step explanation:
expresion can be simplified is they have like terms such as
x+x=2x
y+2y=3y
expresions can NOT be simplified if they have difrerent variables or just one number suchh as
2x+3y
7y+1
4y+4x
I do not know what is 4r+
Answer:
can - y +2y
9x+6x
4x+x
can't 4y+4x
7y+1
2x+3y
Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability the fourth defective engine will be found on the second trial?
Answer:
0
Step-by-step explanation:
From the given information;
Let x be the number of trails on which the [tex]r^{th}[/tex] defective occurs.
Let the probability that an occurrence of a defective be p = 0.10
Suppose x is a random variable that follows a negative binomial distribution with parameters r and p.
Then the probability mass function of X can be expressed as:
[tex]P(X=x) = \bigg (^{x-1}_{r-1} \bigg)p^r (1 - p) ^{x-r} \ \ \ \ ; x=r, \ r+1 , \ r+2 , ...[/tex]
[tex]P(X=x) = \bigg (^{x-1}_{r-1} \bigg)(0.10)^r (1 - 0.10) ^{x-r}[/tex]
[tex]P(X=x) = \bigg (^{x-1}_{r-1} \bigg)(0.10)^r ( 0.90) ^{x-r} \ \ ... \ \ (1)[/tex]
We are to find the probability of the fourth defective engine will be found on the second trial.
i.e. r = 4 and x = 2
[tex]P(X=2) = \bigg (^{2-1}_{4-1} \bigg)(0.10)^4 ( 0.90) ^{2-4}[/tex]
[tex]P(X=2) = \bigg (^1}_{3} \bigg)(0.10)^4 ( 0.90) ^{-2}[/tex]
[tex]P(X=2) = \bigg (\dfrac{1!}{3!(1-3)!} \bigg)(0.10)^4 ( 0.90) ^{-2}[/tex]
[tex]\mathbf{P(X=2) = 0}[/tex]
40 coins = 7.75 how many are quarters
the process of finding factors
Consider the function. f(x) = 2x(x - 1)
What are the values of
f(0)=
f(3)=
f(-4)=
Answer:
3
Step-by-step explanation:
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?
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
One-eighth of a number is -4,200.
What is the number?
-42,800
-37,800
-33,600
-42,000
Answer:
33,600
Step-by-step explanation:
take -4200 and multiply it by 8. You'd do this since the equation to get -4200 is
x(1/8) = -4200
multiply both sides by 8 to get rid of the fraction and you get x=33,600
Directions : Find the indicated term of each arithmetic sequence.
Question :14th term: a = 4; d = -5
Answer:
The 14th term is -61.
Step-by-step explanation:
T(n) = 9-5n
T(14) = 9 - 5 * 14 = 9 - 70 = -61
simplify the given involving the indicated division.
Write the number 7,070,000,000 in scientific notation.
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!
