The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).
To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.
We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).
To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have
lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.
However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have
lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.
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What is the difference in the interest that would have accrued if all of the money from question
#9 had only been in the savings account for the same 60 days?
We'll presume that the cash in question were initially split between two accounts since we don't know the answer to question #9: the amount that has been sitting in a savings account for 60 days is $78.00.
Where ought I to put my cash?Because the FDIC for savings accounts and the NCUA for community bank accounts guarantee all deposit made by consumers, savings are a secure location to put your money.
Is keeping money in a savings account wise?Savings accounts might assist you avoid overspending by keeping the money away from your spending account. You should save emergency cash in your bank account for easy access. Savings accounts keep money secure because the Deposit Insurance Corporation of the United States insures them for up to $250,000.
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X man can complete a work in 40 days.If there were 8 man more the work should be finished in 10 days less the original number of the man
Step-by-step explanation:
Original job = x men * 40 days = 40x man days to complete
now add 8 men = x+8 men
man days now is (x+8) (30) to complete job
so 40x = (x+8)(30)
40x = 30x + 240
10 x = 240
x = 24 men originally
A living room will be painted blue with white trim. The ratio of the surface area between the trim and the walls is 1:10. If 2 gallons of blue paint are used for the walls , how many pints of white pant do we need for the trim? (1 gallon = 8 pints).
2 gallons of blue paint are used for the walls, which cover 700 square feet.
What is surface area?
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
Let's call the surface area of the trim "T" and the surface area of the walls "W". We know that the ratio of T to W is 1:10, which means that:
T = (1/11) * W
We also know that 2 gallons of blue paint are used for the walls. Let's call the amount of white paint needed for the trim "P" (in pints).
We can use the fact that the total surface area of the room is equal to the surface area of the walls plus the surface area of the trim:
W + T = total surface area
Since T = (1/11) * W, we can substitute and simplify:
W + (1/11) * W = total surface area
(12/11) * W = total surface area
Now we can use the fact that 2 gallons of blue paint are used for the walls to find the surface area of the walls:
2 gallons = 16 pints
2 gallons = W / 350 (since 1 gallon covers 350 square feet)
W = 700 square feet
Now we can use the formula above to find the total surface area of the room:
total surface area = (12/11) * W
total surface area = (12/11) * 700
total surface area = 763.64 square feet
We know that the blue paint covers the walls, so we don't need to worry about that. We only need to find the amount of white paint needed for the trim. Let's call the amount of white paint needed per square foot of trim "p" (in pints). Then the total amount of white paint needed is:
P = p * T
We know that the ratio of the surface area between the trim and the walls is 1:10, so we can use that to find the surface area of the trim:
T = (1/11) * W
T = (1/11) * 700
T = 63.64 square feet
Now we just need to find the amount of white paint needed per square foot of trim. Since the trim is white, we don't need to worry about coverage, so we just need to find the surface area of the trim in square pints:
P = p * T
P = p * 63.64
Finally, we know that 1 gallon of paint is equal to 8 pints, so we can convert the total amount of white paint needed from pints to gallons:
P = p * 63.64
P / 8 = gallons of white paint needed
Putting it all together, we get:
2 gallons of blue paint are used for the walls, which cover 700 square feet.
The total surface area of the room is (12/11) * 700 = 763.64 square feet.
The surface area of the trim is (1/11) * 700 = 63.64 square feet.
The total amount of white paint needed is P = p * 63.64.
The amount of white paint needed in gallons is P / 8.
We don't know the value of p, so we can't solve for P directly. However, we do know that the ratio of the surface area between the trim and the walls is 1:10. This means that the surface area of the trim is 1/11 of the total surface area of the room.
Therefore, we can solve for p as follows:
T = (1/11) * W
63.64 = (1/11) * 700
p = P / T
p = P / 63.64
Hence, 2 gallons of blue paint are used for the walls, which cover 700 square feet.
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Find a negation for each of the statements in (a) and (b). (a) This vertex is not connected to any other vertex in the graph. No vertex is connected to any other vertex in the graph. All vertices are connected to all other vertices in the graph. This vertex is connected to at least one other vertex in the graph. All vertices are connected to at least one other vertex in the graph. This vertex is connected to all other vertices in the graph.
(a) Negation: C) This vertex is connected to at least one other vertex in the graph. (b) Negation: D) This number is related to at least one even number.
(a)
A) Some vertex is connected to some other vertex in the graph.
B) At least one vertex is not connected to any other vertex in the graph.
C) This vertex is connected to at least two other vertices in the graph.
D) There exists at least one vertex that is not connected to at least one other vertex in the graph.
E) This vertex is connected to some other vertices in the graph, but not necessarily to all of them.
(b)
A) This number is related to at least one odd number.
B) There exists at least one number that is not related to any even number.
C) All numbers are related to at least one even number.
D) This number is not related to at least one even number.
E) All numbers are related to at least one even number.
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Complete question:
Find a negation for each of the statements in (a) and (b).
(a) This vertex is not connected to any other vertex in the graph.
A) No vertex is connected to any other vertex in the graph.
B) All vertices are connected to all other vertices in the graph.
C) This vertex is connected to at least one other vertex in the graph.
D) All vertices are connected to at least one other vertex in the graph.
E) This vertex is connected to all other vertices in the graph.
(b) This number is not related to any even number.
A) This number is not related to any odd number.
B) All numbers are related to at least one even number.
C) All numbers are not related to any even number.
D) This number is related to at least one even number.
E) No number is related to any even number.
5. Paul practiced playing the pia
for hour on Friday. He pract
for the same amount of time
on Saturday. How long did P
practice on Saturday? Answer gets 90 points
Paul practiced playing the piano for one hour on Friday and for the same amount of time on Saturday. Therefore, he practiced for 1 hour on both days.
Describe Time?Time is a concept used to measure the duration or sequence of events, actions or processes, and to organize them into a coherent and meaningful structure. It is a fundamental aspect of the physical universe and an essential element of human experience, enabling us to make sense of our environment and our lives.
The measurement of time is typically based on the movement of objects or the cycles of natural phenomena, such as the rotation of the Earth on its axis, the orbit of the Moon around the Earth, or the vibrations of an atomic oscillator. Time is commonly expressed in units such as seconds, minutes, hours, days, weeks, months, and years.
In addition to its scientific and practical applications, time also plays an important role in culture, language, and philosophy. It has been the subject of extensive debate and speculation throughout history, with questions about its nature, meaning, and relationship to other concepts such as causality, free will, and eternity.
Paul practiced playing the piano for one hour on Friday and for the same amount of time on Saturday. Therefore, he practiced for 1 hour on both days.
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Paul practiced playing the piano for one hour on Friday and for the same amount of time on Saturday. Therefore, he practiced for 1 hour on both days.
Describe Time?Time is a concept used to measure the duration or sequence of events, actions or processes, and to organize them into a coherent and meaningful structure. It is a fundamental aspect of the physical universe and an essential element of human experience, enabling us to make sense of our environment and our lives.
The measurement of time is typically based on the movement of objects or the cycles of natural phenomena, such as the rotation of the Earth on its axis, the orbit of the Moon around the Earth, or the vibrations of an atomic oscillator. Time is commonly expressed in units such as seconds, minutes, hours, days, weeks, months, and years.
In addition to its scientific and practical applications, time also plays an important role in culture, language, and philosophy. It has been the subject of extensive debate and speculation throughout history, with questions about its nature, meaning, and relationship to other concepts such as causality, free will, and eternity.
Paul practiced playing the piano for one hour on Friday and for the same amount of time on Saturday. Therefore, he practiced for 1 hour on both days.
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Show your solution ( 3. ) C + 18 = 29
Answer:
Show your solution ( 3. ) C + 18 = 29
Step-by-step explanation:
To solve the equation C + 18 = 29, we want to isolate the variable C on one side of the equation.
We can start by subtracting 18 from both sides of the equation:
C + 18 - 18 = 29 - 18
Simplifying the left side of the equation:
C = 29 - 18
C = 11
Therefore, the solution to the equation C + 18 = 29 is C = 11.
Find X using the picture of the triangles below.
Answer:
x = 37.5
Step-by-step explanation:
the top triangle has 2 congruent sides and is therefore isosceles with base angles being congruent, then
base angles = (180 - 75) ÷ 2 = 105 ÷ 2 = 52.5
the angle on the left of the outer triangle is right , then
x + 52.5 = 90 ( subtract 52.5 from both sides )
x = 37.5
this is just a quick addition to the superb reply above by "jimrgrant1"
Check the picture below.
Write the function for the table in standard form?
I tried to work out the problem and got y = -x^2 -6x + 2 not sure if that is correct. Please see steps on the attached file.
The value of the quadratic equation in the standard form is y = -x² -6x + 2.
What is quadratic equation?y = ax² + bx + c, where a, b, and c are constants and an is not equal to 0, is a quadratic equation in standard form. A parabolic function's vertex, axis of symmetry, and intercepts with the x- and y-axes are all expressed by the quadratic equation in standard form. While the positions of the vertex and intercepts are determined by the factors b and c, the direction and form of the parabola are determined by the coefficient a. Every quadratic equation may be changed into standard form by applying the quadratic formula or the square method, which simplifies the analysis and comparison of various functions.
The standard form of the quadratic equation is given by:
y = ax² + bx + c
Substituting the values of x and y from the table we have:
For (-4, 10):
10 = a(-4)² + b(-4) + c
10 = 16a - 4b + c......(1)
For (-3, 11):
11 = a(-3)² + b(-3) + c
11 = 9a -3b + c......(2)
For (-2, 10):
10 = 4a - 2b + c .........(3)
Equation 1 can be written as follows:
10 = 16a - 4b + c
c = 10 - 16a + 4b
Substitute the value of c in equation 2 and 3:
11 = 9a -3b + c
11 = 9a - 3b + 10 - 16a + 4b
1 = - 7a + b .........(4)
And,
10 = 4a - 2b + c
10 = 4a - 2b + 10 - 16a + 4b
0 = -12a + 2b
12a = 2b
b = 6a .......(5)
Substitute the value of b in equation 4:
1 = - 7a + 6a
1 = -a
a = -1
Substitute the value of a in equation 5:
b = -6
Now, substitute the value of a and b in equation 1:
10 = 16a - 4b + c
10 = 16(-1) - 4(-6) + c
10 = -16 + 24 + c
10 = 8 + c
c = 2
Substituting the value in the quadratic equation we have:
y = -x² -6x + 2
Hence, the value of the quadratic equation in the standard form is y = -x² -6x + 2.
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Suppose that we are testing H0: µ = µ0 versus H1: µ > µ0. Calculate the P -value for the following observed values of the test statistic (round all answers to 4 decimal places.
(a)z0 = 2.35,
(b)z0 = 1.53,
(c)z0 = 2.00,
(d)z0 = 1.85,
(e)z0 = -0.15.
Please show steps will rate Life Saver
The p-values for the observed values of the test statistic are 0.0094, 0.0628, 0.0228, 0.032 and 0.4404.
To calculate the p-value for each observed value of the test statistic, we need to find the area under the standard normal distribution curve to the right of each z-score. This is because the alternative hypothesis is one-tailed, with the inequality sign pointing to the right (i.e., H1: µ > µ0). Here are the steps to calculate the p-value for each observed value:
For z0 = 2.35, the area to the right of the z-score can be found using a standard normal distribution table or calculator. The area is 0.0094, which is the p-value.
For z0 = 1.53, the area to the right of the z-score is 0.0628, which is the p-value.
For z0 = 2.00, the area to the right of the z-score is 0.0228, which is the p-value.
For z0 = 1.85, the area to the right of the z-score is 0.0322, which is the p-value.
For z0 = -0.15, the area to the right of the z-score is 0.5596. However, since the alternative hypothesis is one-tailed with the inequality sign pointing to the right, we need to subtract this area from 1 to get the p-value. Therefore, the p-value is 1 - 0.5596 = 0.4404.
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Each license plate in a certain state has five characters (with rep Here are the possibilities for each character. Character Possibilities The digits 1, 2, 3, or 4 The 26 letters of the alphabet The 26 letters of the alphabet The 10 digits 0 through 9 Fifth The 10 digits 0 through 9 How many license plates are possible in this state? First Second Third Fourth
The state in question is using a five-character license plate system, with each character having 36 possible combinations. Multiplying the possible combinations of each character gives us a total of 60,466,176 possible license plates.
What is multiplication?Multiplication is an iterative process of addition where the multiplier is the quantity of times the multiplicand is added to itself. When a number is multiplied, it is multiplied by itself a predetermined amount of times.
This implies that each license plate will have five distinct characters, each of which can be any of the following: the 26 characters of the alphabet, the digits 1, 2, 3, or 4, or the numbers 0 through 9. It provides us with a total of 5 characters, each of which has 36 different potential combinations (4 digits + 26 letters + 10 digits).
The number of character combinations is multiplied to determine the total number of potential license plates. In this instance, the result is 36 times itself.
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270,400 license plates are possible from the combinations of each character given in the question.
What are Combinations?Combinations are used to calculate the number of ways a certain number of items can be selected from a given set of items.
To calculate the total possible license plates in the state, we need to consider the total number of possible combinations of the five characters.
For the first character, there are four possible digits (1, 2, 3, or 4).
For the second character, there are 26 letters of the alphabet. (A-Z)
For the third character, there are again 26 letters of the alphabet.
For the fourth character, there are 10 possible digits (0 through 9).
For the fifth character, there are again 10 possible digits.
We can calculate the number of possible license plates by multiplying the number of possibilities for each character.
4 x 26 x 26 x 10 x 10 = 270,400 possible license plates.
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Factor the polynomial completely:
78¹ - 148³ - 560s²
Answer: 2s²(39 - 74s - 280s)(s - 2)(s + 7/2)
Step-by-step explanation:
To factor the polynomial 78s - 148s³ - 560s² completely, we can first factor out a common factor of 2s²:
2s²(39 - 74s - 280s)
Then, we can factor the quadratic expression inside the parentheses using the quadratic formula:
s = [-(-74) ± √((-74)² - 4(39)(-280))] / 2(39)
s = [74 ± √(54724)] / 78
s = [74 ± 2√13681] / 78
s = [74 ± 2×117] / 78
Therefore, the roots of the quadratic expression are:
s = 2 or s = -7/2
Substituting these values back into the factored expression, we get:
2s²(39 - 74s - 280s) = 2s²(39 - 74(2) - 280(2)) = -1240s²
2s²(39 - 74s - 280s) = 2s²(39 - 74(-7/2) - 280(-7/2)) = 2450s²
So the completely factored form of the polynomial is:
2s²(39 - 74s - 280s)(s - 2)(s + 7/2)
what is the length of h in the following composite figure? all angles are right angles. 5 m 3 m 4 m 2 m
The length of h in the attached composite figure where all the angles are right angles is equal to 4m.
In the attached diagram of composite figure,
All are right angles.
Composite figure consist two rectangles,
Upper and lower rectangles.
length of the upper rectangle is equal to 5m
Width of the upper rectangle is equal to 'h' m
Width of the lower rectangle is equal to 2m
Length of each dash '-' mark is equals to 1m.
length of 'h'm is equals
= 2 m + 2 dash marks
= 2m + 2m
= 4m
Therefore, the length of the h in the composite figure ( attached diagram ) is equals to 4m.
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The above question is incomplete, the complete question is:
What is the length of h in the following composite figure? All angles are right angles.
5 m
4 m
3 m
2 m
Diagram is attached.
Answer:
4 m is ur answer
Step-by-step explanation:
hope this helps
3. The total number of Democrats and Republicans in the US House of Reps during the 115th
year was 434. There were 46 fewer Democrats than Reps. How many were there of each
party?
Answer:
Step-by-step explanation:
subtract 434-46
Y=3x-4 4x+3y=1 what does X and y equal?
Answer:
{y,x}={-1,1}
to leave and take
Selected values of a continuous function f are given in the table above. Which of the following statements could be false? (A By the Intermediate Value Theorem applied to f on the interval (2,5), there is a value c such that f (c) = 10. (B) By the Mean Value Theorem applied to f on the interval (2,5), there is a value c such that f' (c) = 10. c) By the Extreme Value Theorem applied to f on the interval (2,5), there is a value c such that f(c) f (x) for all w in (2,5). Let f be the function defined by f (x) = r - 6x2 + 9x + 4 for 0 < 3 < 3. Which of the following statements is true? А ) f is decreasing on the interval (0,1) because f' (2) < 0 on the interval (0,1). f is increasing on the interval (0, 1) because f'(x) < 0 on the interval (0,1). f is decreasing on the interval (0, 2) because f" (c) < 0 on the interval (0,2). f is decreasing on the interval (1,3) because f' (2) < 0 on the interval (1, 3).
The values of a continuous function f are given which are false is By the Mean Value Theorem applied to f on the interval (2,5), there is a value c such that f' (c) = 10. So, the correct option is statement (B). Let f be the function defined by f (x) = r - 6x2 + 9x + 4 for 0 < 3 < 3 then f is decreasing on the interval (1,3) because f' (2) < 0 on the interval (1, 3). So, the correct option is D).
For continuous function f the statement (B) is false. Although the Mean Value Theorem guarantees the existence of a point c such that f'(c) = (f(5)-f(2))/(5-2) = 2, there is no guarantee that this value will be exactly 10.
When f (x) = r - 6x2 + 9x + 4 for 0 < 3 < 3 is statement (D) is true. We have f'(x) = -12x + 9, which is negative for x in the interval (1,3). Therefore, f is decreasing on this interval. Statement (A) is false, as f'(2) = 3 is positive, so f is increasing on the interval (0,1).
Statement (B) is also false, as f'(x) is not negative on the interval (0,1). Statement (C) is false, as f" (x) = -12 is negative everywhere, so f is concave down on the entire interval (0,3).
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find the value of the derivative (if it exists) at
each indicated extremum
Answer:
The value of the derivative at (2, 3) is zero.
Step-by-step explanation:
Given function:
[tex]g(x)=x+\dfrac{4}{x^2}[/tex]
To differentiate the given function, use the power rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\textsf{Rewrite\;the\;function\;using\;the\;exponent\;rule\;\;$a^{-n}=\dfrac{1}{a^n}$}:[/tex]
[tex]\implies g(x)=x+4x^{-2}[/tex]
Apply the power rule:
[tex]\implies g'(x)=1+(-2) \cdot 4x^{-2-1}[/tex]
[tex]\implies g'(x)=1-8x^{-3}[/tex]
[tex]\implies g'(x)=1-\dfrac{8}{x^3}[/tex]
An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (2, 3).
To determine the value of the derivative at the minimum point, substitute x = 2 into the differentiated function.
[tex]\begin{aligned}\implies g'(2)&=1-\dfrac{8}{2^3}\\\\&=1-\dfrac{8}{8}\\\\&=1-1\\\\&=0\end{aligned}[/tex]
Therefore, the value of the derivative at (2, 3) is zero.
6u^2+17u-10
factor please
Answer:
(2u - 1) (3u + 10)
Step-by-step explanation:
Let's Check
(2u - 1) (3u + 10)
6u² + 20u - 3u + 10
6u² + 17u + 10
So, (2u - 1) (3u + 10) is the correct answer.
I will mark you brainiest!
In the diagram, ∠AFG and ∠CGF are what type of angles?
A) same side interior angles
B) corresponding angles
C) alternate interior angles
D) alternate exterior angles
E) vertical angles
Wildlife biologists inspect 144 deer taken by hunters and find 23 of them carrying ticks that test positive for Lyme disease.
a) Create a 90% confidence interval for the percentage of deer that may carry such ticks. (Round to one decimal place asneeded.)
b) If the scientists want to cut the margin of error in half, how many deer must they inspect?
For part A the 90% confidence interval for the percentage of deer carrying ticks that test positive for Lyme disease is (0.106, 0.214), or 10.6% to 21.4% (rounded to one decimal place). And for part b cut the margin of error in half, we need to quadruple the sample size.
How to solve?
a) To create a 90% confidence interval for the percentage of deer carrying ticks that test positive for Lyme disease, we can use the following formula:
CI = p ± z×(√(p×(1-p)/n))
where:
p is the sample proportion of deer carrying ticks that test positive for Lyme disease (p = 23/144 = 0.16)
z× is the critical value for a 90% confidence level, which is approximately 1.645 (from a standard normal distribution table)
n is the sample size (n = 144)
Substituting these values into the formula, we get:
CI = 0.16 ± 1.645×(√(0.16×(1-0.16)/144))
CI = 0.16 ± 0.054
Therefore, the 90% confidence interval for the percentage of deer carrying ticks that test positive for Lyme disease is (0.106, 0.214), or 10.6% to 21.4% (rounded to one decimal place).
b) To cut the margin of error in half, we need to quadruple the sample size. Since the original sample size was 144, we need to inspect 4×144 = 576 deer.
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prove that the absolute value of x-y is greather than the absolute value of x minus the absolute value of y
Using the properties of absolute value function, proved that |x - y| > |x| - |y| is true for all x and y.
To prove that |x - y| > |x| - |y|, we can consider two cases
Case 1
x >= 0 and y >= 0
In this case, |x - y| = x - y and |x| - |y| = x - y. So we have
|x - y| = x - y
| x | - | y | = x - y
Substituting these expressions into the original inequality, we get:
x - y > x - y
This inequality is true for all x and y where x >= 0 and y >= 0, since the difference between x and y is always greater than or equal to zero.
Case 2
x < 0 and y < 0
In this case, |x - y| = -(x - y) and |x| - |y| = -x + y. So we have:
|x - y| = -(x - y)
| x | - | y | = -x + y
Substituting these expressions into the original inequality, we get
-(x - y) > -x + y
Simplifying both sides, we get
y - x > -x + y
Adding x to both sides, we get
y > 0
This inequality is true for all x and y where x < 0 and y < 0, since both x and y are negative and the difference between x and y is always less than or equal to zero.
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HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU
Answer:
[tex]\textsf{To\;add\;(or subtract)\;in\;Scientific\;Notation,\;you\;must\;have\;the\;same\;$\boxed{\sf power\;of\;10}$\:.}\\\textsf{Then\;you\;can\;$\boxed{\sf add\;or\;subtract}$\;the\;coefficients\;and\;$\boxed{\sf keep}$\;the\;power\;of\;10.}[/tex]
[tex]\textsf{To\;multiply\;in\;Scientific\;Notation,\; you\;must\;$\boxed{\sf multiply}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf add}$\;the\;powers\;of\;10.}[/tex]
[tex]\textsf{To\;divide\;in\;Scientific\;notation,\;you\;must\;$\boxed{\sf divide}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf subtract}$\;the\;powers\;of\;10.}[/tex]
Step-by-step explanation:
To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add or subtract the coefficients and keep the power of 10.
Example expression:
[tex]2.3 \times 10^3 +3.2 \times 10^3[/tex]
Factor out the common term 10³:
[tex]\implies (2.3 +3.2) \times 10^3[/tex]
Add the numbers:
[tex]\implies (5.5) \times 10^3[/tex]
[tex]\implies 5.5\times 10^3[/tex]
Therefore, we have added the coefficients and kept the power of 10.
[tex]\hrulefill[/tex]
To multiply in Scientific Notation, you must multiply the coefficients and add the powers of 10.
Example expression:
[tex]2.3 \times 10^3 \times 3.2 \times 10^3[/tex]
Collect like terms:
[tex]\implies 2.3 \times 3.2 \times 10^3 \times 10^3[/tex]
Multiply the numbers (coefficients):
[tex]\implies 7.36 \times 10^3 \times 10^3[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 7.36 \times 10^{(3+3)}[/tex]
[tex]\implies 7.36 \times 10^{6}[/tex]
Therefore, we have multiplied the coefficients and added the powers of 10.
[tex]\hrulefill[/tex]
To divide in Scientific notation, you must divide the coefficients and subtract the powers of 10.
Example expression:
[tex]\dfrac{8.6 \times 10^6}{2.15 \times 10^2}[/tex]
Collect like terms:
[tex]\implies \dfrac{8.6}{2.15} \times \dfrac{10^6 }{10^2}[/tex]
Divide the numbers (coefficients):
[tex]\implies 4\times \dfrac{10^6 }{10^2}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]
[tex]\implies 4\times 10^{(6-2)}[/tex]
[tex]\implies \implies 4\times 10^{4}[/tex]
Therefore, we have divided the coefficients and subtracted the powers of 10.
use the definition of taylor series to find the taylor series, centered at c, for the function. f(x)
The taylor series (centered at c) for the function f(x) = 1/x, c = 1 is f(x) = 1 - (x-1) - (x-1)^2 + (x-1)^3 + ...
The Taylor series is a representation of a function as an infinite sum of terms that involve the function's derivatives evaluated at a particular point. The Taylor series centered at a point c for a function f(x) is given by:
f(x) = f(c) + f'(c)(x-c)/1! + f''(c)(x-c)^2/2! + f'''(c)(x-c)^3/3! + ...
In this case, we want to find the Taylor series centered at c=1 for the function f(x) = 1/x. We can start by finding the derivatives of f(x):
f'(x) = -1/x^2
f''(x) = 2/x^3
f'''(x) = -6/x^4
f''''(x) = 24/x^5
We can then evaluate these derivatives at c=1 to get:
f(1) = 1/1 = 1
f'(1) = -1/1^2 = -1
f''(1) = 2/1^3 = 2
f'''(1) = -6/1^4 = -6
f''''(1) = 24/1^5 = 24
Substituting these values into the Taylor series formula, we get:
f(x) = 1 - (x-1) - (x-1)^2 + (x-1)^3 + ...
This is the Taylor series centered at c=1 for the function f(x) = 1/x. It represents an approximation of the function in the neighborhood of x=1. By adding more terms to the series, we can improve the accuracy of the approximation.
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Complete question is:
Use the definition of Taylor series to find the taylor series (centered at c) for the function. f(x) = 1/x, c = 1.
what is the distance between the points (-9, 4)and(3,-12) ? a. 12 units b. 16 units c. 20 units d. 28 units
Answer:
20 units
Step-by-step explanation:
Point 1 (-9, 4)
Point 2 (3, -12)
Distance Formula
d=√((x2-x1)²+ (y2-y1)²)
d=√((3+9)²+ (-12-4)²)
d=√(12²+ (-16)²)
d=√(144+ 256)
d=√400
d=20
Answer the question below: *
The area of a playground is 108 yd². The width of the playground is 3 yd longer than its length. Find the
length and width of the playground.
•length = 9 yards, width = 12 yards
•length = 12 yards, width = 15 yards
•length = 12 yards, width = 9 yards
•length= 15 yards, width = 12 yards
Solving a system of equations we the length and width of the playground is length = 9 yards, width = 12 yards
How to find the length and the width?Remember that the area of a rectangle of length L and width W is:
Area = L*W
Here we know that the area is 108 square yards, and we know that he width is 3 yards longer than the length, then we can write a system of equations:
W =L + 3
108 = L*W
Replacing the first equation into the second one we will get:
108 = (L + 3)*L
108 = L² + 3L
Then we have the quadratic equation:
L² + 3L - 108 = 0
Using the quadratic formula we get the solutions:
[tex]L = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]
We only care for the positive solution, which is:
L = 9
Then the width is:
W = L + 3 = 9 + 3 = 12
Then the correct option is:
•length = 9 yards, width = 12 yards
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If f(7) = 9 and f’(7) = 3, estimate f(7.3).
Answer:
[tex]f(7.3)\approx9.9[/tex]
Step-by-step explanation:
Use point-slope form
[tex]y-y_1=m(x-x_1)\\y-9=3(x-7)\\y-9=3x-21\\y=3x-12[/tex]
[tex]f(7.3)=3(7.3)-12=21.9-12=9.9[/tex]
If f(a)=a squared plus 7 for all real values of a, which of the following are possible values of a: square root of 5, square root of 7 or 100 times the square root of 3
100 times the square root of 3 is also a possible value of a for this function.
What is a square root?In mathematics, the square root of a non-negative real number "a" is a non-negative real number that, when multiplied by itself, gives the original number "a". It is denoted by the symbol "√".
According to question:We can substitute each of the given values into the function f(a) = a² + 7 to determine if they are possible values of a.
Substituting the square root of 5:
f(√(5)) = (√(5))² + 7 = 5 + 7 = 12
So, the square root of 5 is not a possible value of a for this function.
Substituting the square root of 7:
f(√(7)) = (√(7))² + 7 = 7 + 7 = 14
So, the square root of 7 is a possible value of a for this function.
Substituting 100 times the square root of 3:
f(100√(3)) = (100√(3))² + 7 = 30000 + 7 = 30007
So, 100 times the square root of 3 is also a possible value of a for this function.
Therefore, the possible values of a for the given function are:
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NEED HELP ASAP Writing Quadratics From A Table
Answer: In the table x part, it increases from -2 all the way to 4. In the table y part, it decreases from 17 to -1, but then increases back from -1 to 17.
7. Complete the comparison: 17>?
O A. 18
O B. 17
O C. 39
O D. 1
O Mark for review will be highligh
Answer: 39
39 is the only answer option greater than 17
PLEASE HELP ME ON THIS QUESTION
0-24- Tally (1)
25-49 Tally (4)
50-74 Tally (5)
75-99 Tally (2)
The rate at which a rumor spreads through a town of population N can be modeled by the equation dt/dx = kx(N−x) where k is a constant and x is the number of people who have heard the rumor. (a) If two people start a rumor at time t=0 in a town of 1000 people, find x as a function of t given k=1/250. (b) When will half the population have heard the rumor?
(a) The function x as a function of t is t = 250ln(499x/998)
(b) Half the population will have heard the rumor approximately 109.86 units of time after it was started.
(a) To solve the differential equation dt/dx = kx(N−x), we can separate the variables and integrate
dt/dx = kx(N−x)
dt/(N-x) = kx dx
Integrating both sides, we get
t = -1/k × ln(N-x) - 1/k × ln(x) + C
where C is the constant of integration.
To find C, we can use the initial condition that two people start the rumor at t=0, so x=2:
0 = -1/k * ln(N-2) - 1/k * ln(2) + C
C = 1/k * ln(N-2) + 1/k * ln(2)
Substituting C back into the equation, we get:
t = -1/k * ln(N-x) - 1/k * ln(x) + 1/k * ln(N-2) + 1/k * ln(2)
Simplifying, we get
t = 1/k * [ln((N-2)x/(2(N-x)))]
Substituting k=1/250 and N=1000, we get:
t = 250ln(499x/998)
(b) We want to find the time t when half the population has heard the rumor, so x = N/2 = 500. Substituting this into the equation we obtained in part (a), we get
t = 250ln(499(500)/998) = 250ln(249/499)
t ≈ 109.86
Therefore, half the population will have heard the rumor approximately 109.86 units of time after it was started.
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