The main answer is that the function f(x) = -2cos(x) - x is decreasing on the open interval (-π/2, π/2) and increasing on the open interval (π/2, 3π/2).
To explain step-by-step, we need to find the critical points of the function by taking the derivative. The derivative of f(x) with respect to x is given by f'(x) = 2sin(x) - 1.
To determine where the function is increasing or decreasing, we set f'(x) equal to zero and solve for x: 2sin(x) - 1 = 0
sin(x) = 1/2
x = π/6, 5π/6 + 2πn
The critical points are at x = π/6 + 2πn and x = 5π/6 + 2πn, where n is an integer.
Now we check the intervals between the critical points to determine if the function is increasing or decreasing.
On the interval (-π/2, π/6 + 2πn), the derivative f'(x) is negative, indicating that the function is decreasing.
On the interval (π/6 + 2πn, 5π/6 + 2πn), the derivative f'(x) is positive, indicating that the function is increasing.
Therefore, the function f(x) = -2cos(x) - x is decreasing on the open interval (-π/2, π/2) and increasing on the open interval (π/2, 3π/2).
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create a video explaning the solution of this problem.
help me create a script and the answer for the problem thank you!
The grounded ends of the guy wires are 15 meters apart.
How to calculate tie valueUsing the Pythagorean theorem, we can calculate the length of the base (distance between the grounded ends of the guy wires).
Let's denote the length of the base as 'x.'
According to the problem, the height of the tower is 20 meters, and the length of each guy wire is 25 meters. Thus, we have a right triangle where the vertical leg is 20 meters and the hypotenuse is 25 meters.
Applying the Pythagorean theorem:
x² + 20² = 25²
x² + 400 = 625
x² = 225
x = √225
x = 15
Therefore, the grounded ends of the guy wires are 15 meters apart.
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Jake is buying a sweater with a price of $30 shown on the tag. The store is having a sale that will reduce the price by 30%. Sales tax of 5% will be added to the final purchase price. What is Jake’s total cost for the sweater? (I ALREADY KNOW THE ANSWER. BUT I NEED THE WORK FOR THE ANSWER TO SHOW MY TEACHER) (the answer is $22.05)
Reducing
30-30*0.3=
21
21+21*0.05=22.05
Need help ASAP!!!!
Answer the question using a table of values.
The graphic at the end shows the graph of the absolute value function.
How is the function graphed?
The following is the function:
y=−2³√x−1+2
To graph this, we must first identify some points on the line, which requires evaluating the line in a variety of x values.
Replace the value 2 of x in f(x)=-8x-1+2
x is replaced with 2 f(2)=-8+2 f(2)=-6.
Evaluation in x = 3 results in:
y = -8√(3)-1+2
The vertex points (1,2), (2,-6), and (3,-9.31) can be used to graph the square root.
Once you have accumulated enough data points, you may plot them using absolute value functions to create the graph you see below in this case.
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The midpoint of AB is M(-4,0). If the coordinates of A are (-6,6), what are the coordinates of B?
Answer:
(-2,-6) is your answer..
hope this helped you
please mark as the brainliest (ㆁωㆁ)
An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. If one student is randomly selected from this class, what is the probability of getting a freshman
The probability of randomly selecting a freshman from the class is approximately 0.5455 or 54.55%.
To calculate the probability of randomly selecting a freshman from the class, we need to determine the total number of freshmen in the class and divide it by the total number of students in the class.
Given information:
Freshman males: 9
Freshman females: 15
Total number of freshmen: 9 + 15 = 24
To find the probability of selecting a freshman, we divide the number of freshmen by the total number of students:
Total number of students:
Freshman males: 9
Freshman females: 15
Sophomore males: 8
Sophomore females: 12
Total number of students = 9 + 15 + 8 + 12 = 44
Probability of selecting a freshman = Number of freshmen / Total number of students
Probability of selecting a freshman = 24 / 44
Simplifying the fraction:
Probability of selecting a freshman ≈ 0.5455
Therefore, the probability of randomly selecting a freshman from the class is approximately 0.5455 or 54.55%.
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Solve for xxx.
x=x=x, equals
Answer:
since traingleABC~ADE
AB/BD=BC/DE
9/15=3/X
9X=15×3
X=15×3/9=5
The value of x is 5 units.
We need to solve for x, from the given figure.
What is the similarity of the triangles?Two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional.
Now, in ΔABC and ΔADE
∠B=∠D=90°
∠EAD=∠CAB (common angles)
So, from AA similarity ABC~ADE
Then, AB/AD=BC/DE
9/15=3/x
9X=15×3
X=15×3/9=5 units
Therefore, the value of x is 5 units.
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use natural logarithms to solve the equation 3e^2x+5=27
The solution to the equation 3e^(2x) + 5 = 27 is x = 1.36.
To solve the equation 3e^(2x) + 5 = 27 using natural logarithms, we can follow these steps:
Step 1: Subtract 5 from both sides of the equation:
3e^(2x) = 22
Step 2: Divide both sides of the equation by 3:
e^(2x) = 22/3
Step 3: Take the natural logarithm (ln) of both sides of the equation:
ln(e^(2x)) = ln(22/3)
Step 4: Apply the property of logarithms that states ln(e^a) = a:
2x = ln(22/3)
Step 5: Divide both sides of the equation by 2:
x = ln(22/3)/2
Using a calculator, we can evaluate ln(22/3) to be approximately 2.72.
Therefore, x = 2.72/2 = 1.36.
So, the solution to the equation 3e^(2x) + 5 = 27 is x = 1.36.
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a(n) variable is characterized by infinitely uncountable values and can take any value within interval.
The correct answer is a countable variable is characterized by infinitely uncountable values and can take any value within interval.
A random variable is with an unknown value or a function that gives values to each of the results of an experiment.
Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.
Continuous random variables have an endless number of possible values and can represent any value that falls within a given range or interval.
An experiment that measures the amount of rain that falls in a city over the course of a year or the average height of a random group of 25 people are two examples of continuous random variables.
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Solve the set of the equations using Gauss-Seidal Method (three iterations) and calculate the percentage approximate error for all x's at each iteration. Initial guess is X1 = X2 = x3 = 1.000: -8x₁ + x₂ - 2x3 = -20 -2x₁-6x₂x3 = -38 -3x₁-x₂7x3 = -34
Using the Gauss-Seidel method with 3 iterations and an initial guess of X₁ = X₂ = X₃ = 1.000, the solution is -8X₁ + X₂ - 2X₃ = -20, -2X₁ - 6X₂X₃ = -38, and -3X₁ - X₂ + 7X₃ = -34 is X₁ ≈ -2.000, X₂ ≈ 4.000, and X₃ ≈ -2.571.
To solve the set of equations using the Gauss-Seidel method, we begin with an initial guess of X₁ = X₂ = X₃ = 1.000. Then, we perform three iterations to refine the solution.
In each iteration, we update the values of X₁, X₂, and X₃ based on the given equations. After the first iteration, we obtain X₁₁, X₂₁, and X₃₁. In the second iteration, we update X₁ to X₁₂, X₂ to X₂₂, and X₃ to X₃₂. Finally, in the third iteration, we calculate X₁₃, X₂₃, and X₃₃.
After three iterations, we find that X₁ ≈ -2.000, X₂ ≈ 4.000, and X₃ ≈ -2.571. These values represent the approximate solution to the given set of equations using the Gauss-Seidel method.
To calculate the percentage approximate error for each iteration, we compare the new values with the previous ones. By using the formula: error = |(new value - previous value) / new value| * 100, we can calculate the percentage error for each x at each iteration.
Therefore, by comparing the values obtained at each iteration with the previous ones, we can compute the percentage approximate error for X₁, X₂, and X₃.
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PLZZZZZZZZZ HELPPPPP
Answer:
Step-by-step explanation:
(-3,0)
(0,2)
(6,6)
Will the solution to the following equation be positive or negative?
b ÷ -2 = 5
positive
negative
Answner:
negative
Step-by-step explanation:
I hope it can help.
Answer:
negative
Step-by-step explanation:
numbers with same sign, multiplied or divided, equal a positive number
numbers with different signs, multiplied or divided, equal a negative number
,,,,,,,,,hi help pls
1st one to answer gets brainliest
Answer:
C - Sarah reads 4 pages in the morning and 6 pages at night for two days.
Step-by-step explanation:
(4+6)*2
(10) - C is the only one where they (do) something that equals 10, and does it twice.
A - (6+2)*4
B - 4 + (6*2)
D - (4 + 6) + 2
what geometric shape forms the hole that fits an allen wrench
Answer:
A hexagon
Step-by-step explanation:
A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.
The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.
The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.
The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.
The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.
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x*7/3=1 i don't understand this question
A scale factor of 1 or 100% would make the new image be a b an enlargement q reduction the same image Od none of these
A scale factor of 1 or 100% would make the image the same image. ( option C) is the answer.
A laminar boundary layer velocity profile is approximated by u / U = [ 2 − ( y / δ ) ] ( y / δ ) u/U=[2−(y/δ)](y/δ) for y ≤ δ y≤δ, and u = U u=U for y > δ y>δ. (a) Show that this parabolic profile satisfies the appropriate boundary conditions.
To show that the given parabolic velocity profile satisfies the appropriate boundary conditions, we need to verify that it satisfies the continuity and the no-slip conditions.
Continuity Condition: At the boundary y = δ, the velocity profile should be continuous. For y ≤ δ, we have u/U = 2 - (y/δ), and for y > δ, we have u/U = 1. Evaluating the velocity profile at y = δ, we get: u/U = 2 - (δ/δ) = 2 - 1 = 1. Therefore, the velocity profile is continuous at y = δ, satisfying the continuity condition. No-Slip Condition: At the solid surface y = 0, the velocity should be zero. For y ≤ δ, we have u/U = 2 - (y/δ), and when y = 0, we get: u/U = 2 - (0/δ) = 2 - 0 = 0.
Therefore, the velocity profile satisfies the no-slip condition at y = 0. Hence, the parabolic velocity profile u/U = 2 - (y/δ) for y ≤ δ, and u = U for y > δ satisfies the appropriate boundary conditions.
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Product going toward health care x years after 2006 . According to the model, when will 18.0% of gross domestic product go toward health care? According to the model, 18.0% of gross domestic product will go toward health care in the year (Round to the nearest year as needed.)
According to the model, 18% of gross domestic product will go toward health care in the year 2026.
To find the year when 18% of gross domestic product (GDP) will go toward health care according to the given model, we need to solve the equation:
f(x) = 18
where f(x) represents the percentage of GDP going toward health care x years after 2006.
Given the model f(x) = 1.4 ln(x) + 13.8, we can substitute 18 for f(x):
1.4 ln(x) + 13.8 = 18
Subtracting 13.8 from both sides:
1.4 ln(x) = 4.2
Dividing both sides by 1.4:
ln(x) = 3
To solve for x, we can exponentiate both sides using the base e (natural logarithm):
e^(ln(x)) = e^3
x = e^3
Using a calculator, the approximate value of e^3 is 20.0855.
Therefore, according to the model, 18% of GDP will go toward health care in the year 2006 + x = 2006 + 20.0855 ≈ 2026 (rounded to the nearest year).
According to the model, 18% of gross domestic product will go toward health care in the year 2026.
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Complete question is below
The percentage of gross domestic product (GDP) in a state going toward health care from 2007 through 2010, with projections for 2014 and 2019 is modeled by the function f(x) = 1.4 In x + 13.8, where f(x) is the percentage of gross domestic product going toward health care x years after 2006. According to the model, when will 18% of gross domestic product go toward health care?
According to the model, 18% of gross domestic product will go toward health care in the year (Round to the nearest year as needed.)
Which model represents 2.36 ÷ 4? A. Three groups of three tenths and four hundredths B. Three groups of five tenths and nine hundredths C. Four groups of three tenths and six hundredths D. Five groups of five tenths and nine hundredths
Answer:
Five groups of five tenths and nine hundredths
Step-by-step explanation:
Mathematically;
2.36 divided by 4 = 0.59
So we want to select from the options, the best representation of this
That will be
0.5 + 0.09
so our answer is 5 groups of five tents and nine hundredths
The model which represents 2.36 ÷ 4 is; Choice D: Five groups of five tenths and nine hundredths
We must perform the division 2.36 ÷ 4 first so that we have;
2.36 ÷ 4 = 0.59The result, 0.59 can then be written in words as; Five tenths and 9 Hundredths.
Ultimately, the model. which represents the expression 2.36 ÷ 4 is; Choice D: Five groups of five tenths and nine hundredths.
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What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is $2\sqrt{6}$ centimeters
The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.
What is the ratio of sides for the 30°-60°-90° triangle?The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x
where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.
Calculation:It is given that the triangle is a right triangle with angles 30°-60°-90°
For such a triangle, the ratio of side lengths is x: x\(\sqrt{3}\):2x
we have the length of the hypotenuse is \(2\sqrt{6}\)
So, 2x = \(2\sqrt{6}\)
⇒ x = \(\sqrt{6}\)
So,
the other length of the other leg is x√3 = √6 × √3 = 3 √2
Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.
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21 m
15 m
Which is closest to the length of XY?
Answer:
18.0 i think
Step-by-step explanation:
1. Construct E from the ciphertext xhBBpWdotCf!uJE = 24 2 -16 -4 -20 -6 -21-8 2 23 29 3 28 10
To construct E from the given ciphertext xhBBpWdotCf!uJE, we need to use the given numbers as the key to decrypt the message. The numbers represent the positions of the letters in the alphabet, where A=1, B=2, C=3, and so on.
Starting with the first number 24, we look for the 24th letter in the alphabet which is X. Similarly, we decrypt the remaining numbers and get the following letters: h, B, B, p, W, d, o, t, C, f, !, u, J, and E.
Therefore, the decrypted message E can be constructed from the given ciphertext xhBBpWdotCf!uJE.
To do this, follow these steps:
1. Write down the given ciphertext: xhBBpWdotCf!uJE
2. Write down the given series of numbers: 24 2 -16 -4 -20 -6 -21 -8 2 23 29 3 28 10
3. For each character in the ciphertext, find its corresponding ASCII value.
4. Add the corresponding number from the series to the ASCII value of each character.
5. Convert the resulting ASCII values back to characters.
6. Combine the characters to form the plaintext (E).
Following these steps, you'll be able to construct the plaintext E from the given ciphertext and the series of numbers.
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Solve the pair of simultaneous equations and leave the answer as a fraction in
its lowest term. 2x − 3 = y, x+ y= 8
Answer:
x = 11/3 = 3 2/3
y = 13/3 = 4 1/3
Step-by-step explanation:
Here, we want to solve the system of equations simultaneously
x + y = 8
2x -3 = y
From the second equation, we have an equation for y
we can simply proceed to substitute this into the first equation
x + 2x - 3 = 8
3x - 3 = 8
3x = 8 + 3
3x = 11
x = 11/3
Recall;
y = 2x - 3
y = 2(11/3) - 3
y = 22/3 - 3
y = (22-3(3))/3
y = (22-9)/3 = 13/3
A 1971 Indian Motorcycle is worth 30 times its original cost. Today it is worth $3000. How much did it originally cost in 1971?
Answer: $100
Step-by-step explanation:
3,000 divided by 30 is 100
Answer: 100
Step-by-step explanation: divide 3,000 by 30
Name any two 2D shapes which are not polygons.Insert the diagrams of these shapes to support your answer.
please hurry
Answer:
Circle and Semi-circle are 2D but not polygons.
Picture to shwo answer:
hey...... what's the answer,
\( \sqrt{256 \times 256} \)
Answer:
That would just equal 256.
Hope this helps
Answer:
256
hope it helps...........
Which table of ordered pairs represents a proportional relationship?
Х
-3
-4
-5
y
3
2
1
0
Х
-1
-3
-5
y
1
3
5
х
-2.
4
-6
y
-5
-7
-9
ở
х
-2
-3
-4
-1
-2
Answer
The right table is the second one it presents proportional relationship
Step-by-step explanation:
The ordered pairs that represent a proportional relationship are:
X Y
-1 1
-3 3
-5 5
Option B is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
From table B.
X Y
-1 1
-3 3
-5 5
We can make a proportional equation as:
y ∝ x
y = kx
Now,
From the table,
(-1, 1), (-3, 3), and (-5, 5)
It is in the form of (x, y).
So,
y = kx
1 = k (-1)
k = -1
We see that,
y = -1(x)
y = -1 x 3 = -3
y = -1 x 5 = -5
This is true for table B.
Thus,
The ordered pairs that represent a proportional relationship is:
X Y
-1 1
-3 3
-5 5
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please help i don’t understand
Answer:
well i dont either
Step-by-step explanation: i'm
weird
How do you solve for x in an angle?
To solve for x at an angle, you must first understand what type of angle you are working with. If the angle is a right angle, you can use the Pythagorean theorem to solve for x. If the angle is an obtuse angle, you can use the law of cosines to solve for x. If the angle is an acute angle, you can use the law of sines to solve for x.
How to solve for x at a right angle?To solve for x at a right angle using the Pythagorean theorem, you must have the lengths of the two neighboring sides of the triangle. The sum of the squares of the two sides is equal to the square of the hypotenuse, according to the Pythagorean theorem. By rearranging the components and solving for x, this equation may be used to find x.
How to solve for x at an obtuse angle?To use the law of cosines to solve for x at an obtuse angle, you must know the lengths of all three sides of the triangle. According to the law of cosines, the square of one side's length equals the sum of the squares of the other 2 sides minus twice the product of the other 2 sides multiplied by the cosine of the obtuse angle. You can use this equation to solve for x by rearranging the terms and solving for x.
How to solve for x in an acute angle?To apply the law of sines to solve for x in an acute angle, you should first know the lengths of the triangle's two sides as well as the acute angle's measurement. According to the law of sines, the ratio of one side's length to the sine of the opposite angle equals the ratio of the other side's length to the sine of the acute angle. By rearranging the terms and solving for x, you may use this equation to solve for x.
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fill in the blank. ___ the vertical line that splits the parabola in half.
The vertical line that splits the parabola in half is called the "axis of symmetry."
The line of symmetry that divides a parabola in half as "The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola".
A parabola is an approximately U-shaped, mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form. A parabola's general equation is written as y = a(x - h)² + k or x = a(y - k)²+ h. Vertex here is indicated by (h, k).
Therefore, The vertical line that splits the parabola in half is called the "axis of symmetry."
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The term that fills in the blank is axis of symmetry.
When graphing a parabola, the vertical line that splits the parabola in half is called the axis of symmetry. The axis of symmetry is a vertical line that passes through the vertex of the parabola. It divides the parabola into two symmetrical halves.
The equation of the axis of symmetry can be found using the formula x = -b/2a, where a and b are coefficients of the quadratic equation in standard form.
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