Find all values of x where f '(x) = 0 for f(x) = arcsin(e^{2x} – 2x).
Answers
The only value of x where f'(x) = 0 is x = 0.
To find all values of x where f'(x) = 0 for the function f(x) = arcsin\((e²ˣ − 2x)\)\(
(e²ˣ − 2x)/tex], we'll first find the derivative f'(x), then solve for x when f'(x) = 0.
Find the derivative f'(x) using the chain rule:
f'(x) = (d(arcsin(u))/du) * (du/dx)
where u = (e²ˣ − 2x)
Find du/dx:
du/dx = d(e²ˣ − 2x)/dx = 2e²ˣ - 2
Find d(arcsin(u))/du:
d(arcsin(u))/du = 1/√(1 − u²)
Combine the derivatives using the chain rule:
f'(x) = (1/(1 − u²)) * (2e²ˣ - 2)
Substitute u back into the expression:
f'(x) = (1/√(1 − (e²ˣ − 2x)²)) * (2e²ˣ − 2)
Solve for x when f'(x) = 0:
(1/√(1 − (e²ˣ − 2x)²))*(2e²ˣ − 2)= 0
The only way this equation can equal zero is if the term (2e²ˣ − 2) equals zero:
(2e²ˣ − 2) = 0
2e²ˣ= 2
e²ˣ = 1
Recall that e^0 = 1, so:
2x = 0
x = 0
Therefore, the only value of x where f'(x) = 0 for the function f(x) = arcsin(e²ˣ − 2x) is x = 0.
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Related Questions
Riverside and Fresno are 36 cm apart on a map. The map has a scale of 2 cm = 15 miles. How many miles apart are Riverside and Fresno?
Answers
Answer:
270 miles
Step-by-step explanation:
36/2=18. So 18 times of 15 miles = 270
3w - 4z = 8 2w + 3z = -6 solve
Answers
Step-by-step explanation:
\(3w - 4z = 8 \\ 2w + 3z = - 6 \\ 3w = 8 + 4z \\ w = \frac{8}{3} + \frac{4z}{3} \\ 2( \frac{8}{3} + \frac{4z}{3} ) + 3z = - 6 \\ 5.33 + 2.67z + 3z = - 6 \\ 5.67z = - 11.33 \\ \)
\(z = - 1.99 = - 2 \\ w = \frac{8}{3} - \frac{8}{3} = 0\)
Help me with this please ASAP
Answers
Answer:
Im so sorry but I have no idea
Step-by-step explanation:
We define a graph’s degree sequence as a list of the degrees of all the vertices in the graph, in increasing order of degree. For example, the graph a b c d e f has degree sequence (0, 2, 2, 3, 3, 4) because there is one node with degree 0 (f), two nodes with degree 2 (a and e), two nodes with degree 3 (b and d), and one node with degree 4 (c). For each of the following, either list the set of edges of a tree with vertex set {a, b, c, d, e, f} that has the stated degree sequence, or show that no such tree exists. (a) (1, 1, 1, 3, 3, 3) (b) (1, 1, 1, 1, 3, 3) (c) (1, 1, 1, 1, 3, 4)
Answers
The edges of the tree are as follows:f - a, f - b, f - c, c - d, c - e, c - f, b - f, a - f, a - b.
Let the vertices be a, b, c, d, e, f with degree sequence (1, 1, 1, 1, 3, 3)
Since all vertices have a degree at most 3, the tree cannot have 6 vertices.
So, a tree with this degree sequence does not exist(c) (1, 1, 1, 1, 3, 4)
We can form a tree with this degree sequence as follows:Let the vertices be a, b, c, d, e, f with degree sequence (1, 1, 1, 1, 3, 4)
Vertex f must be the vertex of the highest degree in this graph, so we can make f the root of the tree.
The three children of f must have degrees 1, 1, and 3.
So, we label these vertices a, b, and c. The remaining vertex of degree 1 can be connected to any vertex of degree 1, let it be a.
Thus the tree can be represented as below. The edges of the tree are as follows:
f - a, f - b, f - c, c - d, c - e, c - f, b - f, a - f, a - b.
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Plzzzzz i need help!!!!!
Answers
Step-by-step explanation:
here is the anewer then change in fraction
Equations
1. Billy Banjo is trying to save money for a new banjo. The banjo costs $300. Mr. Banjo
makes $6 an hour.
a. How many hours will he need to work in order to pay for his banjo?
b. Write an equation for the situation and explain what each variable means.
Answers
Step-by-step explanation:
a. To find out how many hours Billy Banjo needs to work to pay for his banjo, we can set up the following equation:
$$ 6h = 300 $$
where "h" represents the number of hours Billy Banjo needs to work and 6 represents the amount of money he earns per hour.
We can solve this equation by dividing both sides by 6, giving us:
$$ h = \frac{300}{6} $$
$$ h = 50 $$
Therefore, Billy Banjo needs to work 50 hours in order to pay for his $300 banjo.
b. The equation $6h = 300$ represents the situation where Billy Banjo is trying to save money for a new banjo that costs $300, and he earns $6 per hour. The variable "h" represents the number of hours Billy Banjo needs to work in order to pay for the banjo. The left side of the equation, $6h$, represents the amount of money Billy Banjo earns in "h" hours, while the right side of the equation, 300, represents the cost of the banjo he is trying to save up for. By setting these two expressions equal to each other, we are able to solve for the value of "h," which represents the number of hours Billy Banjo needs to work in order to pay for his banjo.
select the appropriate reagents for the transformation at −78 °c.
Answers
For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.
What reagents are suitable for -78 °C transformations?At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.
Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.
The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.
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1.0000÷16
solution pls pls help me
Answers
Answer:
0.0625
Step-by-step explanation:
emma buys a gift basket online for 30% off the list price. she has to pay $5.50 for shipping. the total charge is $45.20. what is the list price of the gift basket?
Answers
The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.
Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.
This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.
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Approximately how many pounds of sand will it take to fill the sandbox. (URGENT)
Answers
Answer:
E
Step-by-step explanation:
becuase 16 divided by 0.5 is 32 then 32x42=1344
Sorry if im late or got it wrong :)
Answer:
B
Step-by-step explanation:
I check my answer many times
Can someone help me with
Answers
Answer:
x=28
Step-by-step explanation:
All angles in any triangle must equal 180
50+3x-10+2x=180
add similar numbers
40+5x=180
-40 -40
5x=140
/5 /5
x=28
Here is a regular polygon with 9 sides
Work out the side of an exterior angle
Thanks
Answers
Answer:
40
Step-by-step explanation:
The number of sides also represents the number of angles.
Now, to find the measure of one angle we will need to find the sum of angles first and to do that, we use this very simple formula:
(n-2)*180 (n is the count of interior angles)
7*180 = 1260 and to find the measure of one angle we divide the sum with the number of angles:
1260/9 = 140
now, since the sum of an interior angle and an exterior angle is 180:
180-140 = 40 is the size of one exterior angle
There's an easier way too, just divide the sum of exterior angles by the number of angles
360/9 = 40
PLEASE Help ASAP!!!!!!!!!!!!!!!!!!!!!Tyson has a 50$ gift card to use at a store. He does not have additional money to spend at the store. Tyson will purchase a belt that costs $8 and x number of shirts that cost 15$ each. The function f(x) = 42-15x models the balance on the gift card after Tyson makes the purchases. What is the most appropriate domain of the function?
Answers
Answer:
multiply that what my teacher said do
Step-by-step explanation:
A(n) _____ leader is an individual who grows into the leadership role, often out of necessity.
a. appointed
b. autocratic
c. democratic
d. emergent
e. laissez-faire
Answers
The correct answer is d. emergent.
An emergent leader is an individual who grows into the leadership role naturally, often due to circumstances or necessity. They are not appointed or assigned to the position of leadership but rather emerge from the group or organization based on their skills, qualities, or actions.
Emergent leaders may possess certain qualities or demonstrate their competence and ability to guide and influence others. They gain recognition and respect from their peers, leading to their emergence as leaders within the group or organization.
This type of leadership often occurs in situations where formal leadership structures may be absent or ineffective, and individuals step up to take charge based on their capabilities and the needs of the group.
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Equation 1: C = 1.29x
Equation 2: C = 21 + 0.99x
what is the y intercept of the line for each question?
Answers
Answer:
Eq1 - 0
Eq2 - 21
Step-by-step explanation:
For Equation 1, the y-intercept is 0, since there is no constant term in the equation.
For Equation 2, the y-intercept is 21, which represents the fixed cost or the cost incurred even when the production is zero.
Answer:
021Step-by-step explanation:
The y-intercept is basically the constant.
In the first equation, there's no constant term, so the intercept is 0.
In the second equation, the constant term is 21.
∴ The y-intercepts are 0 and 21, respectively.
2. What is the value of x? Show your work. Answer:
Answers
The value of x=4.
To solve the equation 2x + 3 = 11 and find the value of x, we can use inverse operations and isolate x on one side of the equation. The goal is to get the variable, x, by itself on one side of the equation, with all the constants on the other side.
First, we can subtract 3 from both sides of the equation to isolate the term with the variable on one side, as follows:
2x + 3 - 3 = 11 - 3
2x = 8
Next, we can divide both sides of the equation by 2 to isolate the variable x:
2x/2 = 8/2
x = 4
Therefore, the solution to the equation 2x + 3 = 11 is x = 4, since this value of x makes the equation true.
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Note: The complete question is - What is the value of x in the equation 2x + 3 = 11? Show your work.
in a bag of marbles, 1 2 are red, 1 4 are blue, 1 6 are green, and 1 12 are yellow. you pick a marble without looking. what color marble are you most likely to choose?
Answers
bund to the nearest tenth
2. 84 is 60% of what number?
What is that answer
Answers
Answer:
140
Step-by-step explanation:
84/140 = 60/100
if 3A =2b=5c, then find A:B:C
Answers
Answer:
10:15:6
Step-by-step explanation:
let 3A=2B=5C
then,A=1/3,B=1/2,=1/5
therefore:A:B:C=1/3,1/2,1/5
10:15:6/30=10:15:6
Last week, gas cost $2.50/gallon. This week, gas cost $3.20/gallon. What was in the
percent change (increase)?
Answers
Answer:
28%
Step-by-step explanation:
plz can i get brainliest;)
prime between number of 1234 to 1352
Answers
prime between number of 1234 to 1352 are 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327
Find the median of this data set: 4, 9, 1, 3, 7, 1
Answers
The median is 3.5
Hope this helped
(*^▽^*)
Write the equation of the line that passes through the given point and has the given slope. (-2,-11) slope=
4
Answers
Answer:
y = 4x - 19
Step-by-step explanation:
Find the y-intercept
y = mx + b
-11 = 4 * -2 + b
-11 = -8 + b
-19 = b
Now, rewrite the equation
y = 4x - 19
Please let me know if I got something wrong!
what is the value when 18times of the difference of 15 and 12 divided by 6
Answers
If the two figures are congruent, which statement is true?
A. BCDA ≅ FEHG
B. ABCD ≅ EFGH
C. BADC ≅ EFGH
D. ADCB ≅ HGFE
Answers
Answer:
A
Step-by-step explanation:
the order of letter should resemble the same shape
Tyler's brother earns a commission. He makes 6.5% of the amount he sells. Last week, he sold $900 worth of shoes.
How much was his commission?
Answers
Answer:
He earns $58.5
Step-by-step explanation:
i did the math
with similar triangles, the corresponding angles are equal. T/F
Answers
True. With similar triangles, the corresponding angles are equal. This property is one of the fundamental characteristics of similar triangles.
Similar triangles are triangles that have the same shape but possibly different sizes. They have corresponding angles that are equal, meaning that the angles in one triangle match the angles in the other triangle. This correspondence allows us to establish proportional relationships between the corresponding sides of the triangles.
The corresponding angles of similar triangles are equal because the angles are determined by the shape and orientation of the triangles, rather than their size. If two triangles have the same shape, their corresponding angles will be equal regardless of their size or position.
This property is the basis for many geometric proofs and calculations involving similar triangles. It allows us to solve problems involving proportions, ratios, and scaling.
By knowing that the corresponding angles of similar triangles are equal, we can confidently apply the principles of similarity to find missing side lengths, determine unknown angles, or establish relationships between different parts of the triangles.
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Which expression represents the number -2i(5- i) + (17- 8i) rewritten in a + bi
form?
O 15-18i
O 15-2i
O 19 - 18i
O 11 + 8i
Answers
Answer:
(a) 15 -18i
Step-by-step explanation:
You want the simplified form of the expression -2i(5- i) + (17- 8i).
Complex numbersFor many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.
-2i(5- i) + (17- 8i) = -10i +2i² +17 -8i
= -2 +17 +(-10 -8)i
= 15 -18i
__
Additional comment
Your scientific or graphing calculator can probably help you evaluate such expressions.
50+100x=300+75x can someone solve this ?
Answers
Answer:
50+100x=300x+75x
Step 1: Simplify both sides of the equation.
50+100x=300x+75x
100x+50=(300x+75x)(Combine Like Terms)
100x+50=375x
100x+50=375x
Step 2: Subtract 375x from both sides.
100x+50−375x=375x−375x
−275x+50=0
Step 3: Subtract 50 from both sides.
−275x+50−50=0−50
−275x=−50
Step 4: Divide both sides by -275.
\(\frac{-275x}{-275}\) = \(\frac{-50}{-275}\)
x= \(\frac{2}{11}\)
Multiply: -6 x 1 II don't get it!!!
Answers
The multiplication we need to make is:
\(-6\times1\)To answer this question we need to use the following rules for multiplications with signs:
\(\begin{gathered} (+)\times(+)=+ \\ (-)\times(-)=+ \\ (+)\times(-)=- \\ (-)\times(+)=- \end{gathered}\)We can see that in our expression we have the last case: a negative number multiplied by a positive number. In this case, the negative number is -6 and the positive number is 1.
So, we know from the rule that the result will be negative.
And finally, we multiply just the numbers: 6 by 1 is 6.
In summary, the result is:
\(-6\times1=-6\)Answer: -6
Answer:
-6
Step-by-step explanation:
hope this helps