Sketch each angle in standard position. 120°
Answers
The angle of 120° in standard position refers to an angle that starts from the positive x-axis and rotates counterclockwise. To sketch this angle, you can follow these steps:
1. Begin by drawing a horizontal line to represent the positive x-axis.
2. Mark a point on the x-axis where the angle starts. This will be the initial side of the angle.
3. Starting from the initial side, rotate counterclockwise by 120°. To do this, draw an arc with a radius equal to the desired angle measure. In this case, it would be an arc with a length of 120 units.
4. The final side of the angle is the line segment connecting the initial side to the endpoint of the arc. This line segment is called the terminal side.
5. Label the angle as 120° at the vertex where the initial and terminal sides meet.
Keep in mind that the sketch of the angle should be proportional and accurately represent the angle measure. The angle should open in the counterclockwise direction.
It's important to note that the sketch of the angle should only show the angle itself, without any additional lines or shapes. The focus is solely on representing the angle of 120° in standard position.
Remember, the concept of angles in standard position is used to visualize and understand angles in trigonometry and other mathematical concepts. By sketching these angles, we can better grasp their positions and relationships to other angles and shapes.
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Related Questions
A survey was given to a random sample of 400 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 168 respondents said they were in favor of the plan. Determine a 95% confidence interval for the proportion of people who favor the tax plan, rounding values to the nearest thousandth.
Answers
The standard error of the sample proportion is sqrt[(0.42)(0.58)/400] = 0.032.
Using a 95% confidence level, the critical value is 1.96.
The margin of error is 1.96 * 0.032 = 0.063.
The 95% confidence interval is 0.42 ± 0.063, which is (0.357, 0.483).
Therefore, we can be 95% confident that the true proportion of people who favor the tax plan is between 0.357 and 0.483.
a) Using a 2-year moving average, the forecast for year 6= miles (round your response to the nearest whole number). b) If a 2-year moving average is used to make the forecast, the MAD based on this = miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) c) The forecast for year 6 using a weighted 2-year moving average with weights of 0.40 and 0.60 (the weight of 0.60 is for the most recent period) =3,740 miles (round your response to the nearest whole number). The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.40 and 0.60= miles (round your response to one decimal place). (Hint: You will have only 3 years of matched data.) d) Using exponential smoothing with α=0.20 and the forecast for year 1 being 3,100 , the forecast for year 6=3,468 miles (round your response to the nearest whole number).
Answers
a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.
a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.
b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.
c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.
The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.
d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.
In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.
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2.5 - 5.8n - 4n + 6 =
Answers
Answer:
Simplify: -9.8n + 8.5
Step-by-step explanation:
2.5 - 5.8m - 4n + 6
(-5.8n - 4n = -9.8n)
( 2.5 + 6 = 8.5)
-9.8n + 8.5
Sorry if this isn't what you meant!
I did everything else, I don’t know what correct unit to use though. Can you help me?
Answers
To solve the given problem we will use the equation for the circumference as a function of the radius:
\(C=2\cdot\pi\cdot r^{}\)Substituting the given values, we have:
\(\begin{gathered} C=2\cdot3.14\cdot9\operatorname{cm} \\ C=56.52\operatorname{cm} \end{gathered}\)From the solution developed above, we are able to conclude that the circumference of the given circle is C = 56.52 cm
what is the p-value if, in a two-tailed hypothesis test , z stat = 1.49?
Answers
The p-value for a two-tailed hypothesis test with z stat = 1.49 is approximately 0.136.
What is the significance level of the test if the p-value is 0.136 for a two-tailed hypothesis test with z stat = 1.49?The p-value is the probability of obtaining a test statistic as extreme as the observed result, assuming the null hypothesis is true.
In this case, if the null hypothesis is that there is no significant difference between the observed result and the population mean, then the p-value of 0.136 suggests that there is a 13.6% chance of observing a difference as extreme as the one observed, given that the null hypothesis is true.
In statistical hypothesis testing, the p-value is used to determine the statistical significance of the results. If the p-value is less than or equal to the significance level, typically set at 0.05, then the null hypothesis is rejected in favor of the alternative hypothesis.
In this case, the p-value is greater than 0.05, indicating that we do not have enough evidence to reject the null hypothesis.
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Can someone help, please? Thanks!
Answers
Each points can be determine as the ordered pair (x, y) with inequalities;
W ⇒ x ≥ 5 and y < -1
X ⇒ x ≥ 5 and y > 1
Y ⇒ x < -5 and y ≥ 5
Z ⇒ x < -1 and y < -4
Define the term graph?A chart in x-y hub plot is a visual portrayal of numerical capabilities or data of interest on a Cartesian direction framework. The horizontal, or independent, variable is represented by the x-axis, while the vertical, or dependent, variable is represented by the y-axis. To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.
According to the graph each points can be determine with inequalities;
W = (5, -2) ⇒ x ≥ 5 and y < -1
X = (5, 2) ⇒ x ≥ 5 and y > 1
Y = (-6, 5) ⇒ x < -5 and y ≥ 5
Z = (-2, -5) ⇒ x < -1 and y < -4
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∠A and ∠B are complementary. If ∠A= 32 find m∠B.
Answers
Answer:
Your answer is 58
Step-by-step explanation:
This is true because complementary means both angles add to 90 degrees. So if you know one is 32 then you subtract 90-32 which will give you 58 (angle B).
Answer: 58
Step-by-step explanation: Complementary means adds up to 90 degrees. So you would just do 90 minus 32 and get 58.
I may be wrong- I don't know for sure. I am a little rustly on this.
Find the measure of each side indicated. Round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
to find x we can use tangent function
tan 31= x/9
0.60=x/9
x=0.60*9=5.4 choice B
The measure of x side.
We have given a right angle triangle whose angle A=31 degrees and two sides that is x and 9.
We have to determine the value of x.
Therefore we use here the trigonometric ratio
What is the tan ratio?\(tan\theta=\frac{opposite side}{adjacent side}\)
Therefore we get
tan 31= x/9
tan(31)=0.60
0.60=x/9
Isolate the x
x=0.60*9
x=5.4
Therefore option B is correct.
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the value of a car is $20,000. it loses 10.3% of its value each year. write an exponential function to determine the value of the car in t years.
Answers
To model the decrease in the value of the car over time, we can use an exponential function of the form:
V(t) = V(0) * e^(-rt)
where:
V(0) is the initial value of the car (in this case, $20,000).
r is the annual rate of depreciation, expressed as a decimal (in this case, 0.103).
t is the number of years since the car was purchased.
Plugging in the given values, we get:
V(t) = $20,000 * e^(-0.103t)
This is the exponential function that models the value of the car in t years.
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Match each expression with its value. −9 7 −2 Undefined h( 3.999 ) h(4) h(4.0001) h(9)
Answers
The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.
Let's match each expression with its corresponding value:
Expression: -9
Value: -9
Expression: 7
Value: 7
Expression: -2
Value: -2
Expression: Undefined
Value: Undefined
Expression: h(3.999)
Value: Undefined
Expression: h(4)
Value: 8
Expression: h(4.0001)
Value: Undefined
Expression: h(9)
Value: Undefined
Now let's explain the reasoning behind each value:
The expression -9 represents the number -9, so its value is -9.
Similarly, the expression 7 represents the number 7, so its value is 7.
The expression -2 represents the number -2, so its value is -2.
When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.
For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.
The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.
Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.
Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.
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What are the steps to understanding this problem as well as the answers.
Answers
Step-by-step explanation:
1
\( \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{3 - 4i}{25} = \frac{ 3}{25} - \frac{4i}{25} \)
2)
\( \frac{1}{3 - 4i} \times \frac{3 + 4i}{3 + 4i} = \frac{3 + 4i}{25} = \frac{ 3}{25} + \frac{4i}{25} \)
3)
1+0i
4)
\( \frac{3 - 4i}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{ - 7 - 24i}{25} = - \frac{7}{25} - \frac{24i}{25} \)
5)
3 - 4i
6)
\( \frac{3 + 4i}{3 - 4i} \times \frac{3 + 4i}{3 + 4i} = \frac{ - 7 + 24i}{25} = - \frac{7}{25} + \frac{24i}{25} \)
Which of the following statements is not true about chi-square distributions? The mean decreases as the degrees of freedom increase. OPG? < 0) = 0 O PU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1 There are an infinite number of chi-square distributions, depending on degrees of freedom. They are always skewed to the right Previous Only saved at 4:44pm
Answers
The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.
Is it true that the mean of a chi-square distribution decreases as the degrees of freedom increase?In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.
The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.
Regarding the other statements:
The statement "OPG? < 0) = 0" is true. The probability of a chi-square random variable being less than zero is always zero, as chi-square values are non-negative.The statement "OPU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1" is true. As the degrees of freedom increase, the right-tail probability of a chi-square distribution also increases.The statement "There are an infinite number of chi-square distributions, depending on degrees of freedom" is true. The number of chi-square distributions is infinite because the degrees of freedom can take any positive integer value.The statement "They are always skewed to the right" is generally true. Chi-square distributions tend to be skewed to the right, especially when the degrees of freedom are small.In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.
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consider the following code snippet: vector vect data(90); vect data.pop_back; what is the size of the vector vectdata after the given code snippet is executed? group of answer choices 89 2 88 90
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The vector vectdata will retain its original size of 90, and none of the provided answer choices (89, 2, 88, 90) are correct.
The code snippet you provided has a syntax error. The correct syntax to call the pop_back function on a vector is vectdata.pop_back(), with parentheses at the end. However, in the given code, the parentheses are missing, causing a compilation error.
Assuming we fix the syntax error and call the pop_back() function correctly, the size of the vector vectdata would be reduced by one. The pop_back() function removes the last element from the vector. Since the vector was initially created with a size of 90 using vector vectdata(90), calling pop_back() will remove one element, resulting in a new size of 89.
However, in the given code snippet, the missing parentheses make the line vectdata. pop_back an invalid expression, preventing the code from compiling successfully. Therefore, the vector vectdata will retain its original size of 90, and none of the provided answer choices (89, 2, 88, 90) are correct.
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The continuous random variable V has a probability density function given by: 6 f(v) = for 3 ≤ ≤7,0 otherwise. 24 What is the expected value of V? Number
Answers
The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.
The PDF of V is defined as:
f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.
The expected value of V, denoted as E(V), can be calculated as:
E(V) = ∫v * f(v) dv
To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.
E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.
E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].
E(V) = (0.25) * [(49 / 2) - (9 / 2)].
E(V) = (0.25) * (40 / 2).
E(V) = (0.25) * 20.
E(V) = 5.
Therefore, the expected value of the continuous random variable V is 5.
The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
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Vertex of -2x2-16+3
Answers
Rewrite the equation in vertex form.
Tap for fewer steps...
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−
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-
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2
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x
+
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Set
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Find the inverse of the following matrix,
if it exists.
[ -1 0 1]
A = [ 2 2 0]
[ 1 0 1]
Answers
Inverse of the given matrix is
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
the matrix in question is
−1 0 1
2 2 0
1 0 1
now, we are given that inverse of the matrix exists.
A⁻¹ = adjoint of A/|A|
The determinant of the matrix A is:
det(A) = (-1) [(2)(1) - (0)(0)] - 0 [(2)(1)-(0)(1)] + 1 [(2)(0) - (2)(1)] = -4
The adjoint of the matrix A is:
2 2 −2
0 −2 −2
−2 −2 −2
Therefore, the inverse of the matrix A is:
A⁻¹ = 1/(-4) [2 2 −2]
[0 −2 −2]
[−2 −2 −2]
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
So, the inverse of the matrix A is:
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
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The diameter of a circle is 69 yards. The circle's circumference is about ___ yards. Use 3.14 for π.
Answers
The circumference of circle is ,
\(C=2\Pi r\)where r is the radius of circle.
The diamteter of circle is , 69 yards
Convert into radius,
\(d=2r\)\(69=2r\)\(r=\frac{69}{2}\)Substitute the radius in the circumference formula.
\(C=2\times3.14\times\frac{69}{2}\)\(C=3.14\times69\)\(C=216.66\text{ yards.}\)Hence the circumference of circle is 216.66 yards.
A chameleon is looking for prey. Let positive numbers represent the elevation of prey above the chameleon and
negative numbers represent the elevation of prey below the chameleon
The chameleon spots a fly at 4 m and a grasshopper at - 6 m.
What does an elevation of Om represent in this situation?
Choose 1 answer.
The elevation of the fly
The elevation of the chameleon
The elevation of the grasshopper
Report a problem
Stuck? Watch a video or use a hint.
Answers
In ΔABC, if m∠CAD = 29°,what
is CAB
Answers
Step-by-step explanation:
in any traingle the sum of all the angle is 180°.
if u have given two angle then use
x+,(known angle1)+(known angle2)=180°
or x=180°-{(known angle1)+known angle2)
[where 'x' is unknown angle]
Determine whether each given expression is equivalent to 6 x 4 1/2 or is not equivalent by checking the appeopriate box in the table below
А 6 x 4 + 2
B 6x5-1/2
C 6x4+6x1/2
D 6 x 5-6x1/2
Answers
the function f(x)=1/2x+3/2 is used to complete this table.
which statements are true if the given function? check all that apply.
f(-1/2)= -2
f(0)=3/2
f(1)= -1
f(2)= 1
f(4)=7/2
Answers
9514 1404 393
Answer:
f(0)=3/2f(4)=7/2Step-by-step explanation:
You can read f(0) = 3/2 from the table. The slope is 1/2, so f(4) will be 1 more than f(2): f(4) = 7/2.
Find the derivative of
\(y = \frac{3}{2x ^{2} } \)
at the point
\((1. \frac{3}{2} )\)
Answers
Answer:
\(\displaystyle y'(1, \frac{3}{2}) = -3\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)FunctionsFunction NotationTerms/CoefficientsExponential Rule [Rewrite]: \(\displaystyle b^{-m} = \frac{1}{b^m}\)Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
\(\displaystyle y = \frac{3}{2x^2}\)
\(\displaystyle \text{Point} \ (1, \frac{3}{2})\)
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Rewrite]: \(\displaystyle y = \frac{3}{2}x^{-2}\)Basic Power Rule: \(\displaystyle y' = -2 \cdot \frac{3}{2}x^{-2 - 1}\)Simplify: \(\displaystyle y' = -3x^{-3}\)Rewrite [Exponential Rule - Rewrite]: \(\displaystyle y' = \frac{-3}{x^3}\)Step 3: Solve
Substitute in coordinate [Derivative]: \(\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1^3}\)Evaluate exponents: \(\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1}\)Divide: \(\displaystyle y'(1, \frac{3}{2}) = -3\)Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
for each model, choose categorical or numeric for the explanatory and response variables. for simple linear regression, the explanatory variable is
Answers
For simple linear regression, the explanatory variable is numeric.
What is simple linear regression?Simple linear regression is a statistical method that allows researchers to understand the relationship between two continuous variables. A simple linear regression model is used to represent the relationship between a dependent variable (Y) and an independent variable (X) by making a linear equation of the form
Y = a + bX, where a is the constant, and b is the regression coefficient.
In simple linear regression, the explanatory variable is of numeric type. This statistical method involves the use of two numeric variables, namely the explanatory (independent) variable and the response (dependent) variable, which are analyzed to establish a linear relationship between them.
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An analogue clock is gaining three minutes 24 hour. If you set the correct time 6pm on Saturday ,when will it show the correct time again?
Answers
Therefore, The day and time the analogue clock will be correct again is 6 PM on Wednesday.
Analogue clock calculation.
To determine when the analogue clock will show the correct time again, we can calculate the time it takes to reach 12 hours which is 720minutes. that is half a day.
Time to gain 720 minutes = 720 minutes/1/8 minute per hour.
720 * 8 = 5760 hours.
Since there are 24 hours in a day we can divide it by 24 hours.
5760/24 = 240 days.
Starting from 6 PM on Saturday, we will add 240 days to know when the time will be correct again.
Therefore, The day and time the analogue clock will be correct again is 6 PM on Wednesday.
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help me please TT,,,,,
Answers
Answer:
The value of ∠A is 62° ⇒ c
The value of ∠B is 54°⇒ d
Step-by-step explanation:
In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.
In Δ ABC
∵ The measure of the exterior angle at the vertex C = 116°
∵ The opposite interior angles to vertex C are ∠A and ∠B
∵ m∠A = (3x - 13)°
∵ m∠B = (2x + 4)°
→ By using the rule above
∴ (3x - 13) + (2x + 4) = 116
→ Add the like terms in the left side
∵ (3x + 2x) + (-13 + 4) = 116
∴ 5x + -9 = 116
∴ 5x - 9 = 116
→ Add 9 to both sides
∵ 5x - 9 + 9 = 116 + 9
∴ 5x = 125
→ Divide both sides by 5
∴ x = 25
→ To find the measures of angle A and B substitute x in their
measures by 25
∵ m∠A = 3(25) - 13 = 75 - 13
∴ m∠A = 62°
∴ The value of ∠A is 62°
∵ m∠B = 2(25) + 4 = 50 + 4
∴ m∠B = 54°
∴ The value of ∠B is 54°
Penny gets £8 pocket money. She is given an increase of £3. (a) Write down £3 as a fraction of £8
Answers
Answer:
£3/£8 = 37.5/100 = 3/8.
Step-by-step explanation:
To write £3 as a fraction of £8, we can use the following formula:
Part/Whole = Percent/100
In this case, the whole is £8 and the part is £3, so we have:
£3/£8 = x/100
To solve for x, we can cross-multiply:
£3 * 100 = £8 * x
300 = 8x
x = 300/8
x = 37.5
Therefore, £3 is equivalent to 37.5% of £8. We can also write this as a fraction:
£3/£8 = 37.5/100 = 3/8.
In Minnesota you he morning temp was -20 degrees by mid morning it decreased by 6 1/4 what was the final temp
Answers
Answer:
-26.25 degrees
Step-by-step explanation:
1. Given that the initial temperature in Minnesota was -20 degrees and it decreased by 6 1/4, we can translate it into an expression: -20 - 6.25.
2. Now, all we have to do is solve the expression:
-20 - 6.25-26.25Therefore, the final temperature is -26.25 degrees.
Determine whether the given limit leads to a determinate or indeterminate form. HINT [See Example 2.]
lim x→+[infinity] 4−x
Evaluate the limit if it exists. (If you need to use [infinity] or −[infinity], enter INFINITY or −INFINITY, respectively. If the limit does not exist, enter DNE.)
If the limit does not exist, say why. (If the limit does exist, so state.)
Answers
we can still express its behavior as x approaches positive infinity by stating that the limit is equal to -∞.
To determine whether the given limit leads to a determinate or indeterminate form, we must first examine the limit as x approaches positive infinity:
lim (x→+∞) (4-x)
As x becomes infinitely large, the expression (4-x) becomes increasingly negative, approaching negative infinity. Since the limit approaches a specific value, in this case, -∞, it is considered a determinate form.
The given limit, lim (x→+∞) (4-x), is a determinate form because as x approaches positive infinity, the expression (4-x) becomes increasingly negative, ultimately approaching negative infinity.
The limit of the given expression, lim (x→+∞) (4-x), is a determinate form and evaluates to -∞. about existence, the limit does not exist in the conventional sense, as it does not approach a finite value. However, we can still express its behavior as x approaches positive infinity by stating that the limit is equal to -∞.
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find the length of the equiangular spiral r=e^theta for e^theta for 0
Answers
The lenth of equiangular spiral is L = √2 ∫[0, π/4] e^(u) du= √2 [e^(π/4) - e^0]= √2 [e^(π/4) - 1]≈ 1.1736a.
An equiangular spiral is a kind of spiral that forms a constant angle with its tangent at any point. It has the polar equation r = a * e^(kθ), where a and k are constants, k determines the spiral’s steepness, and a is the distance between the two arms of the spiral at θ = 0.
To find the length of the equiangular spiral r = e^(θ) for 0 < θ < π/4, we'll use the formula for the arc length of a curve in polar coordinates. The formula is given by:
L = ∫[a, b] √(r² + (dr/dθ)²) dθ
To evaluate the integral, we first need to find the derivative of r, which is:
dr/dθ = e^(θ)The integrand then becomes:
√(r² + (dr/dθ)²) = √(e^(2θ) + e^(2θ)) = e^(θ) √2The integral becomes:
L = ∫[0, π/4] e^(θ) √2 dθWe can evaluate the integral using integration by substitution. Let u = θ, then du = dθ, and the integral becomes:
L = √2 ∫[0, π/4] e^(u) du= √2 [e^(π/4) - e^0]= √2 [e^(π/4) - 1]≈ 1.1736a
We can find the length of the equiangular spiral by using the formula for the arc length of a curve in polar coordinates which is given by:
L = ∫[a, b] √(r² + (dr/dθ)²) dθ.
The derivative of r is:
dr/dθ = e^(θ).The integrand then becomes:
√(r² + (dr/dθ)²) = √(e^(2θ) + e^(2θ)) = e^(θ) √2. The integral becomes:
L = ∫[0, π/4] e^(θ) √2 dθ.
We can evaluate the integral using integration by substitution. Let u = θ, then du = dθ, and the integral becomes:
Thus, the L = √2 ∫[0, π/4] e^(u) du= √2 [e^(π/4) - e^0]= √2 [e^(π/4) - 1]≈ 1.1736a.
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Which one of these shapes is not like the others? Explain what makes it
different by representing each width and height pair with a ratio.
А
B
C
Answers
Answer: C
Step-by-step explanation: because you it has the greatest with an ration is 4 by 8