Answers
Yes you have the correct theorem.
The idea is to get everything to one side so we can form a function
\(\sin\left(e^{2x}\right) = 2x-1\\\\\sin\left(e^{2x}\right)-2x+1 = 0\\\\f(x) = \sin\left(e^{2x}\right)-2x+1\\\\\)
Afterward, we plug in x = 0 to find that
\(f(x) = \sin\left(e^{2x}\right)-2x+1\\\\f(0) = \sin\left(e^{2*0}\right)-2*0+1\\\\f(0) = \sin\left(1\right)+1\\\\f(0) \approx 1.84147\\\\\)
I set my calculator to radian mode, which is fairly common in many calculus courses.
Repeat for x = 1
\(f(x) = \sin\left(e^{2x}\right)-2x+1\\\\f(1) = \sin\left(e^{2*1}\right)-2*1+1\\\\f(1) \approx -0.10615\\\\\)
We see that f(x) changes in sign from positive to negative, when going from x = 0 to x = 1. Because f(x) is continuous, there must be at least one point in the road where it cuts through the x axis when f(x) = 0. This is the place where the intermediate value theorem kicks in.
Therefore, f(x) has at least one root on the interval 0 < x < 1. We don't know what the solutions are, or how many. We only know that at least one exists on this interval.
All of those ideas then extend back to the original equation. Since f(x) has at least one root, this must mean the original equation has at least one solution.
Related Questions
First if is an Eigenvector of the matrix A with Eigenvalue 4, will also be an Eigenvalue for any linear combination of the matrix A.
Answers
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.
What is matrix?
A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.
The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.
When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.
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Find the measure of each angle indicated:
?
959
Answers
Answer:
wdd
Step-by-step explanation:
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Answer:
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vv
Step-by-step explanation:
On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answers
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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Can you help me?! I would really appreciate it
Answers
Answer:
(3 , 8)
Step-by-step explanation:
Answer:
(3,8)
Step-by-step explanation:
the pattern of an ordered pair is (x,y). If x=3, and y=8, then you would get (3,8).
Find the equation of the lines in point-slope form with the
following properties.
passes through (3, 5) and (4, 7).
I NEED HELP!
Answers
Answer:
\(y-5=2(x-3)\)
Step-by-step explanation:
For this question, we just need to determine the slope, which is the: change in x / change in y
We can use the formal equation of: \(\frac{y_2 - y_1}{x_2 - x_1}\)
But the points given have a difference of one, in terms of the x-value, so the change in the y is simply the slope.
From (3, 5) -> (4, 7) the x changes by 1, the y changes by 2. So we know our slope is 2/1 or 2
the point-slope formula is simply: \(y-y_1=m(x-x_1)\)
where (x_1, y_1) are some point on the line, and m is the slope. Since we're given two points, we can use either, so let's just use (3, 5). This gives us the following: \(y-5=2(x-3)\)
Which construction is illustrated above?
O an angle congruent to a given angle
O the angle bisector of a given angle
O a perpendicular to a given line from a point on the line
O a line segment congruent to a given line segment
Answers
Answer:
The construction is a parallel line to a given line from a point not on the line.
Step-by-step explanation:
For a given figure,
To construct a parallel line
Step 1 : Draw transversal line through any point not on line which is given.
Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.
Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line
Step-by-step explanation:
ASAP simplify and show work.
1. (x^-6)^-3
2. (2x^4)(8x^15)
3. (xy^6)(xy)^3
4. a^4b^0(a^8)
5. (x^2)^2(5x^2)^3
Answers
1) Answer:
\({x}^{18} \)
2) Answer:
\( {16x}^{19} \)
3) Answer:
\( {x}^{4} {y}^{9} \)
4) Answer:
\(a ^{12} \)
5) Answer:
\(125 {x}^{10} \)
2x + 2x + 2 = 4x + 2
one solution
no solutions
all real solutions
0 x = 8
HELP
Answers
Answer:
no solution
Step-by-step explanation:
2x+2x+2=4x+2
4x+2=4x+2
4x-4x=2-2
0=0
Answer:
x=8
Step-by-step explanation:
34=34, always true
Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why.
Answers
We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.
How to find the value of x?We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:
cos(60°) = 4ft/x
solving for x:
x = 4ft/cos(60°) = 8ft
Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:
tan(60°) = y/4ft
y = 4ft*tan(60°)
Then using Pythagorean's theorem we get:
x = √( (4ft)² + (4ft*tan(60°))²)
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AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answers
When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.
We can use the Pythagorean theorem to find the length of AB:
AB^2 = AD^2 + BD^2
Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:
(8x)^2 = (x + 9)^2 + (7x - 9)^2
64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81
64x^2 = 50x^2 - 108x + 162
14x^2 + 108x - 162 = 0
Dividing the equation by 2, we get:
7x^2 + 54x - 81 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 7, b = 54, c = -81
x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)
x = (-54 ± √(2916 + 2268)) / 14
x = (-54 ± √5184) / 14
x = (-54 ± 72) / 14
Now we solve for x:
Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7
Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9
Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.
Therefore, x = 9/7.
Substituting this value back into AB = 8x:
AB = 8 * (9/7) = 72/7 ≈ 10.29
Rounding to 2 decimal places, the length of AB is approximately 10.29 units.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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Find a function whose graph is a parabola with vertex (3, -2) and that passes through the point (4, 3).
I don't understand can someone help please
Answers
Answer:
\(y=5(x-3)^2+2\)
Step-by-step explanation:
\(y=a(x-h)^2+k\\y=a(x-3)^2-2\\\\3=a(4-3)^2-2\\3=a(1)^2-2\\3=a-2\\5=a\\\\y=5(x-3)^2+2\)
By using the vertex form of a parabola, we were able to plug in the vertex (h,k)=(3,-2) and then eventually our point (x,y)=(4,3) to solve for "a" to get the final function.
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
Answer: 171 attendees
Step-by-step explanation:
I answered another similar question by you earlier, so I really hope you read through this explanation, as I will go far in depth. It's important you learn to do this so as not to simply skate through homework, then struggle with assessment.
For this problem, you have to find something called a unit price.
A unit price is the price in dollars per thing.
In this case, the price in dollars for the whole group is $132 for many things, 66 attendees.
Because 66 attendees costs $132, to find out how much money a single attendee costs, simply divide $132 by 66 to get 2$ for 1 attendee.
With this information, it is very straightforward to determine the number of attendees for $342. Simply divide $342 by $2 to get 171 attendees.
I really hope it helps :) and please, let me know if you want me to explain in more depth, the unit you are currently in is a fundamental part of early math, and it is important you understand it.
Find the volume of the cylinder. Round your
answer to the nearest tenth.
Answers
Formula of volume of a cylinder: V=Bh
V= (3.14 (10)^2) 16
10x10 = 100
(3.14 x 100) 16
(314 x 16)
V = 5,024
Help me please with my IXL GEOMETRY
Answers
Answer:
7.5
Step-by-step explanation:
hey hope this helps and is right
(Diversifying Portfolios MC)
worth points)
Name of Stock Symbol High Low Close
Stock A
105.19 103.25 103.38
Stock B
145.18 143.28 144.05
A
B
Last year, an investor purchase
difference in overall loss or ga
O The difference in overall gain is $207.00.
O The difference in overall loss is $207.00.
O The difference in overall loss is $200.70.
O The difference in overall gain is $200.70.
shares of stock A at $90 per share and 75 shares of stock B at $145 per share. What is the
ween selling at the current day's high price or low price?
Answers
The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.
To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.
Stock A:
High price = $105.19
Low price = $103.25
Close price = $103.38
Stock B:
High price = $145.18
Low price = $143.28
Close price = $144.05
The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.
To calculate the selling prices, we need to multiply the number of shares by the respective selling price.
Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50
Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50
Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50
Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00
Now, let's calculate the difference in overall gain or loss:
Difference in overall gain = Selling price at the high price - Selling price at the low price
= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)
= $16,148.00 - $15,908.50
= $239.50
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What is the difference between intersecting, perpendicular, and parallel?
Answers
Answer:
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Step-by-step explanation:
Answer:
Perpendicular lines are when two lines intersect each other at 90 degrees, parallel are when the two lines never touch, and also have the same slope, and then intersecting is when two or more lines cross each other in a plane.
Step-by-step explanation:
Proportionality yes or no - show work
X y
____ ____
6 -2
7 -1
8 0
9 1
Answers
No, the relationship on the table is not proportional
How to determine if the relationship is proportionalFrom the question, we have the following parameters that can be used in our computation:
x y
____ ____
6 -2
7 -1
8 0
9 1
On the table of values, we can see that:
The values of x increase by 1 i.e. 6, then 7, then 8 and finally 9 As these values of x increase by 1, the values of y increase by 1 also i.e. -2, then -1, then 0 and finally 1Using the above as a guide, we have the following:
The relationship is not a proportional relationship
This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)
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Which excerpt from "The Treasure of Lemon Brown" would provide strong evidence that Greg feels upset and resentful
at the beginning of the story?
O The dark sky, filled with angry, swirling clouds, reflected Greg Ridley's mood as he sat on the stoop of his building.
His father's voice came to him again, first reading the letter the principal had sent to the house, then lecturing
endlessly about his poor efforts in math.
O Report cards were due in a week, and Greg had been hoping for the best. But the principal had ended the suspense
early when she sent the letter saying Greg would probably fail math if he didn't spend more time studying.
O There was a room a few feet from the door, and from where he stood in the entrance, Greg could see a squarish
patch of light on the floor. He entered the room, frowning at the musty smell
. It was a large room that might have beer
someone's parlor at one time.
O From this spot he could see the blinking neon sign over the bodega on the corner. He sat a while, watching the sign
blink first green then red, allowing his mind to drift to the Scorpions, then to his father.
Answers
Answer:
I just took my test on edge and it’s a
Find the reciprocal of the number 2/7
Answers
Answer:
7/2
Step-by-step explanation:
The reciprocal is basically just flipping the fraction upside down. Reciprocal is also called inverse.
The point G(-5, -4) is translated 1 unit left. What are the coordinates of the resulting point, G′?
Answers
X- intercept: right/left
Y- intercepy: up/down
Since it is translated 1 unit left, you need to subtract 1 from the x-intercept:
(-5-1,-4)
Solve, and you get
(-6,-4) for your final answer.
Solve the problem algebraically 4∣x+9∣−2>10
Answers
Answer:
x is (-infinite, -12) and (-6, infinite)
Step-by-step explanation:
Meaning that x is less than -12 and greater than 6. I think...
PLEASE HELP ME WITH THESE 2 MATH QUESTIONS
Answers
y = 4^x and y = log_4x are inverses of each other is true.
The transformation that takes the graph of the function f(x) = e^x to
f(x) = -e^x - 2 is a reflection about the x-axis followed by a vertical shift downward by 2 units.
We have,
To show that y = 4^x and y = log_4x are inverses of each other, we need to show that:
The domain of 4^x is (−∞, ∞), and the range is (0, ∞).
The domain of log_4x is (0, ∞), and the range is (−∞, ∞).
For any x in the domain of 4^x, we have log_4(4^x) = x.
For any x in the domain of log_4x, we have 4^(log_4x) = x.
These conditions are indeed satisfied,
So y = 4^x and y = log_4x are inverses of each other.
The graph of f(x) = e^x can be transformed into the graph of f(x) = -e^x - 2 using the following transformations:
- Reflection about the x-axis:
f(x) → -f(x)
This will reflect the graph of f(x) = e^x about the x-axis so that it is now below the x-axis.
- Vertical shift downward by 2 units:
f(x) → f(x) - 2
This will shift the graph downward by 2 units, so that it is now centered at (-∞, -2).
Therefore,
y = 4^x and y = log_4x are inverses of each other is true.
The transformation that takes the graph of the function f(x) = e^x to
f(x) = -e^x - 2 is a reflection about the x-axis followed by a vertical shift downward by 2 units.
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please solve the question attached
Answers
1. Based on the producer theory, an increase in the demand for labor (L) would be caused by An increase in the productivity of labor, A decrease in the wage rate and A decrease in the rental rate of capital.
2. Missing variables in this simple producer theory would include The technology used to produce output, The preferences of consumers and Quality of labor and capital.
What more should you know about the producer thoery?In the standard producer theory, a producer minimizes costs for a given level of output.
This involves choosing the optimal mix of inputs, such as labor (L) and capital (K), to produce the desired output (y).
The cost function is represented by C = wL + rK, where w is the wage rate (cost of labor) and r is the rental rate (cost of capital).
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trouve trois nombres entiers consécutifs dont la somme vaut 513
Answers
Answer:
170, 171, 172
Step-by-step explanation:
x + x + 1 + x + 2 = 513
3x + 3 = 513
3x = 510
x = 170
x + 1 = 171
x + 2 = 172
In the Special Right Triangle below, solve for the value of y. Y = _____ (keep your answer in simplest radical form)
Options
5
5√2
10
10√2
Answers
Answer:
Value of Y = 5√2 units
Step-by-step explanation:
Given:
Perpendicular = X
Base = Y
Hypotenuse = 10
Find:
Value of Y
Computation:
Cos θ = Base / Hypotenuse
Cos 45 = Y / 10
1/√2 = Y / 10
Value of Y = 5√2 units
Julie thinks this will mean the prices will be reduced to $0 after the four reductions because 4 x
25% = 100%.
Explain why Julie is wrong
Answers
Answer:
4x25/100=1
Step-by-step explanation:
How I came up with it
4÷100=25
25÷25=1
Julie will only get a 1% discount
Hope it helps
Express 75 as a product of its prime factors write the prime factors in ascending order and give your answer in index form
Answers
Step-by-step explanation:
75 = 3 x 5 x 5 in prime factorization
Answer:
Step-by-step explanation:
3x5x5
On a bus, the lady sitting in front of me silently passed gas, but why did my mom (who was sitting next to me) silently ask me "did you pass gas" and accuse me??
Answers
Answer: lol she was lowkey trying to call out the lady in front of you without directly addressing her. Or she was just trying to mess with you cuz that's how moms are
Step-by-step explanation:
Go step by step to reduce the radical.
Square Root 200
Answers
Answer:
10 root 2
Step-by-step explanation:
root 200 = root 2 × root 100 = 10 root 2
Write the value of the underline digit.
0.496 the underline number is 9
Answers
Answer:
0.090
Step-by-step explanation:
In the number 0.496, the number 9 is in the hundredths place.
0.496
The value of 9 in 0.496 is 9 hundredths, or 0.090.
Hope this helps.
Answer: 9 hundredths or 0.09