Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)
1.)f(x) = sin(x) + 4 0 < x < 2π
2.)f(x) = x + 2 sin(x), 0 < x < 2π
Consider the following function. 1.f(x) = (x + 7)2/3
(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)
(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) (x,y)
2.)f(x) = 3 − |x − 4| a.b,c
3.)f(x) = 6x + 1/2 a,b,c
4.) x^2/x^-81 a,b,c
Answers
There will be different critical numbers, increasing and decreasing of function and the relative maximum relative minimum of given functions.
How can we find the critical numbers, increasing and decreasing of function and the relative maximum relative minimum?For f(x) = sin(x) + 4, 0 < x < 2π:
(a) There are no critical numbers for this function.
(b) The function is increasing on the interval (0, π) and decreasing on the interval (π, 2π).
(c) The relative maximum occurs at x = π with y = 5, and the relative minimum occurs at x = 0 and x = 2π with y = 4.
For f(x) = x + 2 sin(x), 0 < x < 2π:
(a) The critical numbers are x = π/2 and x = 3π/2.
(b) The function is increasing on the intervals (0, π/2), (3π/2, 2π), and decreasing on the intervals (π/2, 3π/2).
(c) The relative maximum occurs at x = 3π/2 with y = 2π + 1, and the relative minimum occurs at x = π/2 with y = π + 1.
For f(x) = (x + 7)^(2/3):
(a) The critical number is x = -7.
(b) The function is decreasing on the interval (-∞, -7) and increasing on the interval (-7, ∞).
(c) The relative minimum occurs at x = -7 with y = 0.
For f(x) = 3 − |x − 4|:
(a) The critical number is x = 4.
(b) The function is decreasing on the interval (0, 4) and increasing on the interval (4, 8).
(c) The relative maximum occurs at x = 0 and x = 8 with y = 3, and the relative minimum occurs at x = 4 with y = 0.
For f(x) = 6x + 1/2:
(a) There are no critical numbers for this function.
(b) The function is increasing on the interval (-∞, ∞).
(c) There are no relative extrema for this function.
For f(x) = x^2/x^-81:
(a) The critical number is x = 0.
(b) The function is increasing on the interval (-∞, 0) and (0, ∞).
(c) The relative minimum occurs at x = 0 with y = 0.
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Related Questions
How many symmetry a rectangle have?
Answers
A rectangle has two lines of symmetry. A line of symmetry is a line that divides a figure into two parts that are mirror images of each other. In a rectangle, the two lines of symmetry are the lines that divide the rectangle into two congruent halves.
To see this, imagine folding a rectangle along one of its lines of symmetry. The two halves of the rectangle will be mirror images of each other, with corresponding sides and angles congruent. This means that the rectangle is symmetrical along this line.
The same is true for the other line of symmetry in a rectangle. When the rectangle is folded along this line, the two halves will again be mirror images of each other. As a result, the rectangle is symmetrical along both of its lines of symmetry.
In general, a rectangle has two lines of symmetry because it has four sides, and four is an even number. Shapes with an even number of sides can be divided into two equal parts by a line of symmetry. Shapes with an odd number of sides, on the other hand, cannot be divided into two equal parts in this way, and therefore do not have any lines of symmetry.
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The point P is on the unit circle. If the y-coordinate of P is -3/7
and P is in quadrant IV, then
T=
Question Help: Video
Submit Question
Answers
Answer: \(\bold{x=\frac{2 \sqrt{10}}{7}}\)
Step-by-step explanation:
\(\text { Let } p=\left(x,-\frac{3}{7}\right) \text { as given } y \text {-coordinate is }=-\frac{3}{7}\)
\(r=1 \ \ \text{(as $p$ is on unit circle)} \\$$\therefore x^{2}+y^{2}=1^{2}\)
\(\begin{aligned}&\Rightarrow x^{2}+\left(-\frac{3}{7}\right)^{2}=1 \Rightarrow x^{2}=1-\frac{9}{49}=\frac{40}{49} \\&\Rightarrow x^{2}=\pm \sqrt{\frac{40}{49}} \Rightarrow x=\pm \frac{2 \sqrt{10}}{7}\end{aligned}\)
\($$Since the point is in quadrant $4$ $\therefore \text{the} \ x$-coordinate will be positive$$\therefore x=\frac{2 \sqrt{10}}{7} \text$$\)
4V6+3v2
16
Simplified?
Answers
Answer:
195/8v or 24.375v
Step-by-step explanation:
The names of the months of the year are cut from a calendar and put into a bag. A month with more than 5 letters in its name is drawn. What is the probability of the complement of the event? Express your answer as a fraction in simplest form.
Answers
Answer: \(\frac{7}{12}\)
Step-by-step explanation:
First, we need to find how many months have more than 5 letters in their name. There are 7 months with >5 letters and 12 months total.
✓ January
✓ February
✗ March
✗ April
✗ May
✗ June
✗ July
✓ August
✓ September
✓ October
✓ November
✓ December
Next, we will divide the wanted outcomes by the total outcomes.
\(\displaystyle \frac{\text{wanted outcomes}}{\text{total outcomes}} =\frac{\text{more than 5 letters}}{\text{all months}}=\frac{7\;\text{months}}{12\;\text{months}} =\frac{7}{12}\)
The linear correlation coefficient for a set of paired variables is r=0.897. what proportion of the variation in y acn be explained by the linear relationship between x and y?
Answers
About \(80.5\%\) of the variation in y can be attributed to the linear relationship with x.
Used the concept of correlation coefficient that states,
The proportion of the variation in y that can be explained by the linear relationship between x and y can be determined by squaring the correlation coefficient
Given that,
When paired variables are considered, the linear correlation coefficient is,
\(r=0.897\)
Hence the proportion of the variation in y explained by x is,
\(r^2 = (0.897)^2\)
\(r^2 = 0.804609\)
This means that about \(80.5\%\) of the variation in y can be attributed to the linear relationship with x.
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Animals at a dog shelter a 24 pound bag of dog food will feed 36 dogs a day. how many dogs would you expect to feed with a 16- pound of dog food?
Answers
Answer: 24 dogs
Step-by-step explanation:
24 lb 16 lb
-------- = -------------
36 dogs x dogs
24x = 576
x = 24
Quincy Jackson sells motorcycles. He earns a 10 percent commission on the first $5,000 and 15 percent on all sales over $5,000. How much cornmission will he earn on $19,000 in sales?
Answers
Answer:
total commission= $2,600
Step-by-step explanation:
Giving the following information:
He earns a 10 percent commission on the first $5,000 and 15 percent on all sales over $5,000.
First, we need to structure the total commission formula:
total commission= 0.10*x + 0.15*y
X= sales up to $5,000
Y= sales from $5,001 to infinity
Now, sales for $19,000 sales:
total commission= 0.1*5,000 + 0.15*14,000
total commission= $2,600
helpppp What is the value of y? Triangle A B C has right angle C with side A C labeled 5. Angle A is 60 degrees and its opposite side B C is labeled y. The long leg is labeled y and the short leg is labeled 5. Enter your answer, as an exact value, in the box.
Answers
Answer:
\( 5\sqrt{3} \)
Step-by-step explanation:
here
tan(60)= p/b
\( \sqrt{3 } = \frac{y}{5} \)
\(y = 5\sqrt{3} \)
PLEASE HELP complete the construction a perpendicular line to segment AB through point P.
Answers
Answer:
.
Step-by-step explanation:
sorry i can't help
Which of the following measures can be precisely located on the graph of a skewed distribution without doing any calculations? Variance Standard deviation Mode Mean Median
Answers
In a skewed distribution, the median can be precisely located on the graph without doing any calculations.
So, the correct answer is E.
The median represents the middle value in the data set, separating the distribution into two equal parts. Unlike the mean, it is not affected by extreme values, making it a more accurate representation of central tendency for skewed distributions. The mode, which indicates the most frequent value, can also be identified on the graph.
However, variance and standard deviation, both measures of dispersion, require calculations to be determined and cannot be precisely located on the graph without additional information.
Hence, the answer of the question is E.
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How many Cube Bs will fit into Cube A? Enter the max amount.
Answers
Answer:
8
Step-by-step explanation:
The answer is 8 because 1/2 times 1/2 times 1/2 is 1/8, which means that 8 B cubes can fit into cube A.
Factor each quadratic expressionx^2-2x-15
Answers
When we are factoring a quadratic function, we are trying to reverse the following equation
\((x+a)(x+b)=x^2+(a+b)x+ab\)Now, comparing the right-hand side of the above equation and the one given in the problem we see that
\(\begin{gathered} a+b=-2 \\ ab=-15 \end{gathered}\)This means the question simplifies to "what are the two numbers that if I add them I get -2 and if I multiply them I get -15? "
Well, If we set a = -5 and b = 3, then
\(\begin{gathered} -5+3=-2 \\ -5\cdot3=-15 \end{gathered}\)Hence, our expression factors to
\((x-5)(x+3)\)Which of the following coordinates are exactly 5 units from (2, -1)? Select all that apply.
(3, 4)
(5, 3)
(-2, 2)
(-3, -1)
20 Brainly points!
Answers
Answer:
-3-1
Step-by-step explanation:
The given planes intersect in a line. Find parametric equations for the line of intersection. [Hint: The line of intersection consists of all points (x, y, z) that satisfy both equations. Solve the system and designate the unconstrained variable as t .]
x + 2y + z = 1, 2x+5y + 32 = 4
Answers
The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t
To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:
1. x + 2y + z = 1
2. 2x + 5y + 32 = 4
Step 1: Solve for x from equation 1:
x = 1 - 2y - z
Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4
Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:
Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30
Step 4: Designate z as the parameter t:
z = t
Step 5: Substitute z with t in the expression for y:
y = 2t - 30
Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t
Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t
Note that we can choose any value of z for the parameter t, since z is unconstrained.
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put these in order starting from the smallest 0.72,4/5,0.799,9/10
Answers
Answer:
0.72 ; 0.799 ; 0.8 ; 0.9
Step-by-step explanation:
4/5 = 0.8
9/10 = 0.9
Ascending order:
0.72 ; 0.799 ; 0.8 ; 0.9
First compare the tenth places. If tenth places are same, compare hundredth places
0.72, 0.799, 4/5 and 9/10
A seagull is 23 meters above the surface of the ocean. What is its elevation?
Answers
Answer: 23 meter
Step-by-step explanation:
meters "above"
elevation means the distance above sea level
Pamela’s age is two times Jiri’s age. The sum of their age is 15. What is Jiri’s age?
Answers
Answer: Jiri is 5, Pamela is 10
Step-by-step explanation:
Pamela age: x
Jiri age: y
x = 2y
x + y = 15
plug in the x value
2y + y = 15
combine
3y = 15
y = 5
solve for x
x = 2(5)
x = 10
check your answer
10 + 5 = 15
Explain why each statement is true. 5 + 2 + 3 = 5 + (2 + 3)
Answers
Answer:
Associative property of addition. Grouping different addends does not change the sum.
Step-by-step explanation:
5 + 2 + 3 = 5 + (2 + 3)
10 = 5 + (5)
10 = 10
Pls. Help find these answers?!
Answers
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
Write thee answer in form a^b
4^3 x 8^2 = ?
Answers
Answer:
\(2^{12}\)
Step-by-step explanation:
\(4^3=(2^2)^3=2^6 \\ \\ 8^2=(2^3)^2=2^6 \\ \\ 2^6 \times 2^6=2^{6+6}=2^{12}\)
identify the solution of the compound inequality x − 2 > 4 or 5x ≥ 35 and the graph that represents it.
Answers
To find the solution of the compound inequality x − 2 > 4 or 5x ≥ 35, we need to solve each inequality separately and then combine their solutions using the OR operator.
Solving x − 2 > 4, we add 2 to both sides to get x > 6.
Solving 5x ≥ 35, we divide both sides by 5 to get x ≥ 7.
The solution of the compound inequality x − 2 > 4 or 5x ≥ 35 is the set of all values of x that satisfy at least one of the inequalities, which is x > 6 or x ≥ 7.
To graph this solution, we draw a number line and mark the points 6 and 7 with open circles (because they are not included in the solution). Then we shade the region to the right of 6 and/or to the right of 7, as shown below:
<---o---o=========>
6 7
The open circles indicate that 6 and 7 are not included in the solution, because x can be any value greater than 6 or any value greater than or equal to 7, but not both at the same time.
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the problem is x > 6 or x ≥ 7. To explain this solution, we need to solve each inequality separately and then combine the results.
First, we solve x − 2 > 4 by adding 2 to both sides to get x > 6.
Next, we solve 5x ≥ 35 by dividing both sides by 5 to get x ≥ 7.
To combine the results, we take the union of the two solutions, which gives us x > 6 or x ≥ 7. This means that any value of x that is greater than 6 or equal to 7 will satisfy the original compound inequality.
The graph that represents this solution is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.
the solution to the compound inequality x − 2 > 4 or 5x ≥ 35 is x > 6 or x ≥ 7, and the graph that represents it is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.
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Please help me with these two :/
Answers
Exponential growth, starts at 2, asymptote at y = 0 what is the equation?
Answers
According to the problem, the initial condition is 2, which means the coefficient of the exponential must be 2, so the given situation can be model by the following equation
\(f(x)=2(2)^x\)PLEASE HELP I WILL MARK BRAINLIEST SHOW WOrK HOW YOU GOT IT
Answers
Answer:
7 . 8.9
8 . 19.5
9 . 9.9
10 .12.6
Step-by-step explanation:
7.x=11tan39
8.x=28cos46
9.x=8tan51
10.x=31sin24
side opposite of mentioned angle is opposite
longest side in triangle is hypotenuse
the side subtended by the angle is the adjacent
A Ferris wheel has a radius of 218 feet. What is the
total distance covered if the Ferris wheel makes 6
rotations? Write an exact answer in terms of Pi.
Answers
The total distance covered by the Ferris wheel after 6 rotations is 2616π feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.
Perimeter = 2π * radius = 2π * 218 feet = 436π
For 6 rotations:
Total distance covered = 6 * 436π = 2616π
The total distance is 2616π feet
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Please help I need it I’ll give Brainly please
Answers
Answer:
35.7
Step-by-step explanation:
So to find voulme you would mutiple and we have the two number 11.9 and 3 so you would do 11.9x35.7 this equals 35.7 i hope this helps you.
Answer:
V= 35.7 cubic inches
Step-by-step explanation:
Multiply your length, width and height figures together, giving you a total in cubic inches (in3) Divide the total by 1728 (as there are 1728 cubic inches in a cubic foot
11.9 x 3 = 35.7
The triangles in the figure below are similar.
image b125a080d0e9444e9eebf9b6644403df
Which proportion is correct?
A.
x20=96
x
20
=
9
6
B.
x20=915
x
20
=
9
15
C.
2015=x6
20
15
=
x
6
D.
x20−x=156
x
20
−
x
=
15
6
Answers
The perimeter of the triangle is 12 in.
What is perimeter of similar triangle?
The perimeter of similar triangle is equal to the ratio of the similar sides of the triangle. The ratio of two similar perimeters of two similar shapes is equal to the ratio of the lengths of their corresponding sides.
Here, perimeter of triangle PQR = sum of all the side
=12+20+16
=48
The ratio of the corresponding side = 12/3
=4/1
Hence, the perimeter of triangle xyz = ?
perimeter of triangle PQR /perimeter of triangle xyz =4/1
48/x =4/1
x = 48/4
=12
Hence, the perimeter of triangle xyz = 12
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Zack wants to map an abandoned line of reasoning. Which shape should Zack use? (a) line with one arrowhead. (b) orange oval. (c) green rectangle. (d) red
Answers
Zack should use a line with one arrowhead to map an abandoned line of reasoning.
A line with one arrowhead is commonly used in diagrams to represent the direction of a process or flow of information. In the case of mapping an abandoned line of reasoning, the line can be used to show the original train of thought that was pursued but later abandoned.
The arrowhead can indicate the point at which the reasoning was abandoned or diverted. Therefore, using a line with one arrowhead would be the most appropriate shape for Zack to use. The other shapes listed (orange oval, green rectangle, red) do not provide a clear representation of a line of reasoning and would not be suitable for this purpose.
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write an explicit formula for an, the nth term of the sequence 24,16,8
Answers
Answer:
f(n) = 32 - 8n
Step-by-step explanation:
24, 16, 8, 0
f(n) = 24 - 8 x (n-1)
f(n) = 32 - 8n
How many different ways are there to arrange the letters of the word PRISM?
Enter your answer in the box.
ways
Answers
Answer:
5! (5 factorial) or 120 ways
Step-by-step explanation:
You can arrange P different ways. R can be arranged only 4 different ways because Pwill be in one of the spots. Next, you can arrange "I" 3 different ways because P and R are already arranged in 2 spots, meaning you cant put "I" there. Next, S can be arranged in 2 different ways for the same reason. And lastly, M can only be arranged in 1 different way because the other spots are taken.
You can put it in any order. For example, M could be arranged 5 ways and P could be arranged in 1 way. You will still get 120 ways
Hopefully this helped. The explanation might be a bit confusing but I tried my best. I'm not good with explaining my solutions but I always try
Answer:
120
Step-by-step explanation:
took the test and i got it right