Answer:
Linear pair angle of 40 is
=180-40
=140
If, the two rays are parallel
Therefore, the two rays are parallel and the straight line is transversal
Therefore, (?) angle =140 corrosponding angle
Your answer is 140
If a least-squares regression line fits the data well, what characteristics should the residual plot exhibit? Sketch a well-labeled example
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
\(y=b_1x+b_0\)
There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.
Given a collection of pairs (x,y) of numbers, there is a line \(y=b_1x+b_0\) that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.
\(b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)\)
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
\(y=b_1x+b_0\)
specifying the least squares regression line is called the least squares regression equation.
Example,
Find the least squares regression line for the five-point data set
x = 2 2 6 8 10
y= 0 1 2 3 3.
compute the table,
x y x2 xy
2 0 4 0
2 1 4 2
6 2 36 12
8 3 64 24
10 3 100 30
28 9 208 68 (sum)
\(S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125\)
The regression line is y=0.34375x-0.125
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PLS HELP MEE.. I hv BEEN working on this question for days..i hv to submit it today...
Answer:
Below
Step-by-step explanation:
Working on this for days ? Seriously ??
5 x 10 ^8 = 50 x 10^7
50 x 10^7 + 2 x 10^7 = 52 x 10^7 = 5.2 x 10^8 = 520, 000,000
Pick the form you need.....
Josie combines 6.72 ounces of strawberries with 6.47 ounces of blueberries to make fruit bowls. She pours the fruit equally into 3 bowls, and has 2.57 ounces of fruit left over. How many ounces of fruit are in each bowl?
Josie combines 6.72 ounces of strawberries with 6.47 ounces of blueberries and divides them equally into 3 bowls. There are 2.57 ounces of fruit left over. We need to find the number of ounces of fruit in each bowl.
To find the number of ounces of fruit in each bowl, we need to divide the total amount of fruit by the number of bowls. The total amount of fruit is the sum of the strawberries and blueberries, which is 6.72 + 6.47 = 13.19 ounces.
If we divide 13.19 ounces by 3, we get 4.3967 ounces per bowl. However, we need to consider the fact that there are 2.57 ounces of fruit left over. This means that the 13.19 ounces of fruit cannot be divided equally into 3 bowls.
To distribute the remaining 2.57 ounces of fruit equally among the 3 bowls, we can add 2.57/3 = 0.8567 ounces to each bowl. Adding this amount to the initial division, we get approximately 4.3967 + 0.8567 = 5.2534 ounces per bowl.
Therefore, each bowl contains approximately 5.2534 ounces of fruit.
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How many positive integers less than 100 have a remainder of 3
when divided by 7?
a) 18
b) 13 c) 14 d) 12
Answer:
13
Step-by-step explanation:
We can write the following inequality to find the answer:
7x + 3 < 100 (where x is our answer and x is an integer)
7x < 97
x < 13.86
The largest integer value of x that satisfies this inequality is x = 13 so we know that our answer will be 13.
How do you explain a diameter of 0.00085 inches using scientific notation
Answer:
8.5 \(E^{-4}\) inches
Step-by-step explanation:
Scientific scientific notation is where the super small / super large number is multiplied by a 10 (E) to the power of a number. Here, the number is smaller than 8.5 so our power must be negative. As we are making it four "places" bigger, we use the exponent of -4.
Hope this helps, have a nice day! :D
A standing wave can be mathematically expressed as y(x,t) = Asin(kx)sin(wt)
A = max transverse displacement (amplitude), k = wave number, w = angular frequency, t = time.
At time t=0, what is the displacement of the string y(x,0)?
Express your answer in terms of A, k, and other introduced quantities.
The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.
At time t=0,
the standing wave can be mathematically expressed as
y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.
This means that the displacement of the string is zero at time t=0.
However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.
As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).
The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.
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set up the integral for the volume of the solid of revolution rotating region between y = sqrt(x) and y = x around x=2
Plug these into the washer method formula and integrate over the interval [0, 1]:
V =\(\pi * \int[ (2 - x)^2 - (2 - \sqrt(x))^2 ] dx \ from\ x = 0\ to\ x = 1\)
To set up the integral for the volume of the solid of revolution formed by rotating the region between y = sqrt(x) and y = x around the line x = 2, we will use the washer method. The washer method formula for the volume is given by:
V = pi * ∫\([R^2(x) - r^2(x)] dx\)
where V is the volume, R(x) is the outer radius, r(x) is the inner radius, and the integral is taken over the interval where the two functions intersect. In this case, we need to find the interval of intersection first:
\(\sqrt(x) = x\\x = x^2\\x^2 - x = 0\\x(x - 1) = 0\)
So, x = 0 and x = 1 are the points of intersection. Now, we need to find R(x) and r(x) as the distances from the line x = 2 to the respective curves:
R(x) = 2 - x (distance from x = 2 to y = x)
r(x) = 2 - sqrt(x) (distance from x = 2 to y = sqrt(x))
Now, plug these into the washer method formula and integrate over the interval [0, 1]:
V =\(\pi * \int[ (2 - x)^2 - (2 - \sqrt(x))^2 ] dx \ from\ x = 0\ to\ x = 1\)
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A researcher wishes to estimate within $300 the true average amount of money a country spends on road repairs each year. If she wants to be 90% confident, how large a sample is necessary
The researcher needs a sample size of at least 83. To estimate the true average amount of money a country spends on road repairs each year within $300 and be 90% confident, the researcher needs to determine the required sample size.
The formula to calculate the sample size is given by:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score (corresponding to the desired level of confidence)
σ = standard deviation of the population (unknown)
E = maximum allowable error
Since the standard deviation (σ) is unknown, the researcher can use a conservative estimate based on a previous study or assume a worst-case scenario.
Let's assume a worst-case scenario where the standard deviation is $1000. The desired level of confidence is 90% (Z-score = 1.645) and the maximum allowable error (E) is $300.
Substituting these values into the formula:
n = (1.645 * 1000 / 300)^2
n ≈ 9.08^2
n ≈ 82.66
Since the sample size cannot be a fraction, we round up to the nearest whole number. Therefore, the researcher needs a sample size of at least 83 to estimate the average amount of money spent on road repairs with a maximum error of $300 and a confidence level of 90%.
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The coordinates of point T are (0,2). The midpoint os ST is (1,-5). Find the coordinates of point S.
Answer:
...........................................
What is g^4/g^2? Because I am a little confused about it
The quotient rule states that when dividing two powers
that have the same base, subtract their exponents.
Since each of the powers in this problem has a base of g,
we can simplify the expression by subtracting the exponents.
4 - 2 is 2 so our answer is g².
Find the product of 32 and 46. Now reverse the digits and find the product of 23 and 64. The products are the same!
Does this happen with any pair of two-digit numbers? Find two other pairs of two-digit numbers that have this property.
Is there a way to tell (without doing the arithmetic) if a given pair of two-digit numbers will have this property?
Let's calculate the products and check if they indeed have the same value:
Product of 32 and 46:
32 * 46 = 1,472
Reverse the digits of 23 and 64:
23 * 64 = 1,472
As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.
To find two other pairs of two-digit numbers that have this property, we can explore a few examples:
Product of 13 and 62:
13 * 62 = 806
Reversed digits: 31 * 26 = 806
Product of 17 and 83:
17 * 83 = 1,411
Reversed digits: 71 * 38 = 1,411
As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.
For example, let's consider the pair 25 and 79:
A = 2, B = 5, C = 7, D = 9
The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.
Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.
Calculus help please!!! I don’t know what I’m missing (steps are correct but isn’t the correct final answer) :(
The composite function are
u(x) = 2x² - 4x -2 and f(u) = ⁵√u(x)What is a composite function?A composite function is a function which contains another function.
Since we have the function f(x) = ⁵√(2x² - 4x -2) and we want to redefine it as a composite functions u(x) and f(u), where u(x) is a polynomial, we proceed as follows.
Since we have the function f(x) = ⁵√(2x² - 4x -2).
Now since we require u(x) to be a polynomial, u(x) = 2x² - 4x -2
Thus, we have f(x) = ⁵√(2x² - 4x -2)
= ⁵√u(x)
So, f(u) = ⁵√u(x)
So, the composite function are
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In a control chart application, we have found that the grand average over all the past samples of 6 units is X-Double Bar = 25 and R-Bar = 5.
a) Set up X-bar and R Control charts.
A2= 483 D3=0 D4=2.004
.483*5=2.415+25=27.415=UCL
.485*5=25-2.415=22.585=LCL
LCL(R bar)=0
UCL=10.020
b) The following measurements are taken from a new sample: 33, 37, 25, 35, 34 and 32. Is the process still in control?
Based on the given data, the process is out of control.
To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.
For the X-bar chart:
The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:
UCL = 25 + (0.483 * 5) = 27.415
The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:
LCL = 25 - (0.483 * 5) = 22.585
For the R chart:
The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:
UCL = 2.004 * 5 = 10.020
The LCL (Lower Control Limit) for the R chart is 0.
Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.
Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.
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234 inch board is to be cut into three pieces so that the second piece is four times the length of the first piece and the third piece is eight times the length of the first piece find the length of each piece
Let the length of the first piece be "x", second piece be "y" and third piece be "z".
Total length is 234 inches, so we can write:
\(x+y+z=234\)Also,
• Second piece is 4 times the first piece, ,we can write:
\(y=4x\)• Third piece is 8 times the first piece, ,we can write:
\(z=8x\)Substituting these 2 equations into the first equation, we will have an equation in x. Then we solve for x. Shown below:
\(\begin{gathered} x+y+z=234 \\ x+4x+8x=234 \\ 13x=234 \\ x=18 \end{gathered}\)Consequently, we can find y and z >>>>
y = 4x
y = 4(18)
y = 72
and
z = 8x
z = 8(18)
z = 144
Answer
First Piece = 18 inches
Second Piece = 72 inches
Third Piece = 144 inches
Solve the system of linear equations by graphing. need help on these 2
The solution is at (-5, 0)
see the graph below
Explanation:9) To graph the equatios, we would assign values to x and get corresponding values of y
x + y = -5 ...equation 1
-x + 2y = 5 ...equation 2
when x = -6, -5, -4
when x = -6
-6 + y = -5
y = -5 + 6 = 1
when x = -5
-5 + y = -5
y = -5 + 5
y = 0
when x = -4
-4 + y = -5
y = -5 + 4
y = -1
when x = -6
-(-6) + 2y = 5
6 + 2y = 5
2y = 5 - 6
y = -1/2
when x = -5
-(-5) + 2y = 5
5 + 2y = 5
2y = 5-5
2y = 0
y = 0
when x = -4
-(-4) + 2y = 5
4 + 2y = 5
2y = 5-4
y = 1/2
plotting the graph:
The solution of the graph is at the intersection of both lines.
The solution is at (-5, 0)
can someone help with math please. asap (file attached :)
30° = 0.52
150° = 2.68
-220° = -3.34
The polynomial p(x)=x^3-19x-30 has a known factor of (x+2)
Rewrite p(x) as a product of linear factors
Answer:
(x+2) (x+3) (x-5)
Step-by-step explanation:
x³-19x-30 = (x+2) (x²+ax-15) ... x³=x*(1*x²) while -30= (2)*(-15)
x³ + 0*x² - 19x -30 = x³ + (2+a)x² + (2a-15)x -30
2+a = 0
a = -2
x³-19x-30 = (x+2) (x²-2x-15) = (x+2) (x+3) (x-5)
Answer:
\((x + 2)\, (x + 3)\, (x - 5)\).
Step-by-step explanation:
Apply polynomial long division to divide \(p(x)\) by the know factor, \((x + 2)\).
Fill in the omitted terms:
\(\begin{aligned}p(x) &= x^{3}- 19\, x - 30 \\ &= x^{3} + 0\, x^{2} - 19\, x - 30\end{aligned}\).
The leading term of the dividend is currently \(x^{3}\). On the other hand, the leading term of the divisor, \((x + 2)\), is \(x\).
Hence, the next term of the quotient would be \(x^{3} / x = x^{2}\).
\(\begin{aligned}p(x) &= \cdots \\ &= x^{3} + 0\, x^{2} - 19\, x - 30 \\ &= x^{3} + 0\, x^{2} - 19\, x - 30 \\ &\quad - x^{2} \, (x + 2) + [x^{2} \, (x + 2)] \\ &= x^{3} + 0\, x^{2} - 19\, x - 30 \\ &\quad -x^{3} - 2\, x^{2} + [x^{2}\, (x + 2)] \\ &= -2\, x^{2} - 19\, x - 30 \\ &\quad + [x^{2} \, (x + 2)]\end{aligned}\).
The dividend is now \((-2\, x^{2} - 19\, x - 30)\), with \((-2\, x^{2})\) being the new leading term. The leading term of the divisor \((x + 2)\) is still \(x\).
The next term of the quotient would be \((-2\, x^{2}) / x = -2\, x\).
\(\begin{aligned}p(x) &= \cdots \\ &= -2\, x^{2} - 19\, x - 30 \\ &\quad + [x^{2} \, (x + 2)] \\ &=-2\, x^{2} - 19\, x - 30 \\ &\quad - (-2\,x ) \, (x + 2) + [(-2\, x) \, (x + 2)] + [x^{2} \, (x + 2)] \\ &= -2\, x^{2} - 19\, x - 30 \\ &\quad - (-2\, x^{2} - 4\, x) + [(x^{2} - 2\, x)\, (x + 2)] \\ &= -15\, x - 30 \\ &\quad + [(x^{2} - 2\, x)\, (x + 2)]\end{aligned}\).
The dividend is now \((-15\, x - 30)\), with \((-15\, x)\) as the new leading term.
The next term of the quotient would be \((-15\, x) / x = -15\).
\(\begin{aligned}p(x) &= \cdots \\ &= -15\, x - 30 \\ &\quad + [(x^{2} - 2\, x)\, (x + 2)] \\ &=-15\, x - 30 \\ &\quad -(-15)\, (x + 2) + [(-15)\, (x + 2)] + [(x^{2} - 2\, x)\, (x + 2)] \\ &= -15\, x - 30 \\ &\quad -(-15\, x - 30) + [(x^{2} - 2\, x - 15)\, (x + 2)] \\ &= (x^{2} - 2\, x - 15)\, (x + 2)\end{aligned}\).
In other words:
\(\displaystyle \text{$\frac{x^{3} - 19\, x - 30}{x + 2} = x^{2} - 2\, x - 15$ given that $x+2 \ne 0$}\).
The next step is to factorize the quadratic polynomial \((x^{2} - 2\, x - 15)\).
Apply the quadratic formula to find the two roots of \(x^{2} - 2\, x - 15 = 0\):
\(\begin{aligned} x_{1} &= \frac{-(-2) + \sqrt{2^{2} - 4\times 1 \times (-15)}}{2} \\ &= \frac{2 + 8}{2}= 5\end{aligned}\).
\(\begin{aligned} x_{2} &= \frac{2 - 8}{2} = -3\end{aligned}\).
By the factor theorem, the two factors of \((x^{2} - 2\, x - 15)\) would be \((x - 5)\) and \((x - (-3))\). That is:
\(x^{2} - 2\, x -15 = (x + 3)\, (x - 5)\).
Therefore:
\(\begin{aligned}p(x) &= \cdots \\ &= (x^{2} - 2\, x - 15)\, (x + 2) \\ &= (x + 2)\, (x + 3)\, (x - 5)\end{aligned}\).
a radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=15e^(-0,02t) where m(t) is measured in kilograms.
a. Find the mass at time t=3
b. How much of the mass remains after 20 days?
For the given data, a) The mass at the time t = 3 is 14.13 kg. and b) The mass remaining after 20 days is 10.05 kg.
What is radioactive decay?
The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay.
The Radioactive Formula is given by
\(N = N_{0} e^{-\lambda T}\)
Given, \(m(t) = 15e^{-0.02t}\)
where m(t) is measured in kilograms
a) To find the mass at time t=3, then
m(3) = \(15e^{-0.02*3}\) = \(15e^{-0.06}\) = 14.13 kg
Therefore, the mass at the time t=3 is 14.13 kg.
b) To find how much of the mass remains after 20 days,
m(20) = \(15e^{-0.02*20}\) = \(15e^{-0.4}\) = 10.05 kg
Therefore, the mass remaining after 20 days is 10.05 kg.
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a weighted coin has a 0.455 probability of landing on heads. if you toss the coin 27 times, what is the probability of getting heads more than 12 times? (round your answer to 3 decimal places if necessary.)
Using the probability mass function, the probability of getting heads more than 12 times is 0.465.
In the given question,
The probability of landing on heads P(H)=0.455
We toss the coin 27 times. So n=27
We have to find the probability of getting heads more than 12 times.
Then, the probability mass function should be
P(X=x)=
where x=no of heads in 27 tosses.
\(\[f(x)=\begin{cases}\binom{27}{x}(0.455)^x(0.545)^{27-x},&\text{if }x=0,1,2,........,27\\0,&\text{elsewhere}\end{cases}\]\)
So the probability;
P(X>12)=1-P(x≤12)
P(X>12)=1- \(\Sigma_{x=0}^{12}\) P(X=x)
From the binomial table
P(X>12)=1-0.535
P(X>12)=0.465
Hence, the probability of getting heads more than 12 times is 0.465.
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mark sweeney wants to receive a letter grade of a for this course, and he needs to earn at least 90 points to do so. based on the regression equation developed in part (b), what is the estimated minimum number of hours mark should study to receive a letter grade of a for this course? (round your answer to one decimal place.)
Mark needs to invest 5572.24 hours (rounded to one decimal place) of study time in order to achieve an A letter grade in this course.
To determine the estimated minimum number of hours Mark should study, we need to solve for the number of hours such that his predicted score, given by the regression equation from part (b), is at least 90.
The regression equation is as follows: Predicted score = 48.74 + 0.00726(number of hours studied)
Setting the predicted score equal to 90 and solving for the number of hours studied gives:90 = 48.74 + 0.00726 (number of hours studied)
Solving for the number of hours studied gives: number of hours studied = (90 - 48.74)/0.00726= 5572.24
Therefore, Mark should study for 5572.24 hours (rounded to one decimal place) to receive a letter grade of A for this course.
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There are 198,714 people living in Belleville. What is the number of people rounded to the nearest ten thousand?What digit is in the ten thousands place?Which place is used to decide which way to round the ten thousands place?What is the digit in this place?Should you round the number in the ten thousands place up or down?What happens when you round up a 9?What do you do when the value of a place is 10 or more?What is the value of the ten thousands place when the number is rounded to the nearest tenthousand?What is 198,714 rounded to the nearest ten thousand?What is 302,895 rounded to the nearest thousand?What is 7,142 rounded to the nearest ten?Round 24,793 to the nearest hundred.?
198714 to the nearest ten thousand:
\(198714\approx200000\)The digit in the ten thousands place is:
\(9\)Which place is used to decide which way to round the ten thousands place:
The second place from the left
--------------------------------
302895 to the nearest thousand:
\(303000\)7142 to the nearest ten:
\(7140\)24793 to the nearest hundred:
\(24800\)Having trouble,Whats 1/3 (-2/4)
Answer:
-1/6
Step-by-step explanation:
im assuming you meant multiply them? if so then
1 -2 -2 -1
--- * --- = --- = ---
3 4 12 6
or
1/3=4/12 and -2/4=-6/12
4/12*-6/12=-24/144=-1/6
Answer:
-1/6
Step-by-step explanation:
just multiply 1/3x2/4=
and then in front of the answer put the negative sign
Solve the following problems involving oo of the complex plane. (a) (2 pts) Find 23 – 3iz2 +52 – 7 lim 422 – 3i 200 (b) (2 pts) Determine whether 1214 lim 2700 24 exists. If yes, find it; if no, explain why. (c) (4pts) For f(z) 23(2 – 2)3 (z2 + 1)(2 – 3)4 find its residue at oo. (d) (2pts) Use (c) to find the sum of the residues of f(z) at its poles i, -i, 3.
a) The limit as z approaches infinity is 75/(622 – 3i).
b) The limit exists and its value is approximately 0.4456.
c) The residue at infinity for f(z) is 23.
d) The sum of the residues of f(z) at its poles is -23.
a) The limit can be computed by substituting the given values into the expression:
lim(z→∞) (23 – 3iz^2 + 52 – 7)/(422 – 3i + 200)
Simplifying the expression gives:
lim(z→∞) (23 + 52)/(422 – 3i + 200)
= 75/(622 – 3i)
Therefore, the limit as z approaches infinity is 75/(622 – 3i).
b) To determine if the limit exists, we need to evaluate:
lim(z→∞) 1214/(2700 + 24)
Since the denominator approaches infinity as z approaches infinity, and the numerator is a constant value, the limit exists and can be computed as:
lim(z→∞) 1214/(2700 + 24) = 1214/2724 = 0.4456 (rounded to four decimal places).
Therefore, the limit exists and its value is approximately 0.4456.
c) To find the residue at infinity for the function f(z), we need to consider the coefficient of 1/z in the Laurent series expansion of f(z) around z = ∞. Since the function f(z) has a finite number of poles, we can rewrite it as:
f(z) = (23(2 – 2)3)/(z^2 + 1)(2 – 3)4
As z approaches infinity, the dominant term in the denominator is z^2. Therefore, the residue at infinity is 23(2 – 2)3/(2 – 3)4 = 23(1)/(1) = 23.
d) The sum of the residues of f(z) at its poles i, -i, and 3 is equal to the negative of the residue at infinity. Therefore, the sum of the residues is -23.
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How do you simplify square roots.
Answer:
Simplifying a square root just means factoring out any perfect squares from the radicand, moving them to the left of the radical symbol, and leaving the other factor inside the radical symbol. If the number is a perfect square, then the radical sign will disappear once you write down its root.
determine the intercepts of the line
Answer:
x-intercepts(-7,0)
y-intercepts(0,-2)
Step-by-step explanation:
Step-by-step explanation:
The x-intercept is (-7,0)
The y-intercept is (0,2)
Factor completely
x^2+11x+24
Answer:
\((x+8)(x+3)\)
Step-by-step explanation:
\(x^2+11x+24\\\\=(x+s_1)(x+s_2)\\\\and\:we\:have\:that\\\\s_1+s_2=11\\\\s_1s_2=24\\\\so\:by\:guessing\:we\:can\:say:\\\\s_1=8\\\\s_2=3\\\\=(x+8)(x+3)\)
Esh deposits $3500 in an account that
earns 3.75% interest each year. After the
first year, Esh has $3631.25 in the account.
After the second year, Esh has $3767.42 in
the account, and after the third year Esh has
$3908.70 in the account.
Answer:
Compound interest
Step-by-step explanation:
The question requires us to determine if the interest earned is a simple or compound interest
Simple interest = amount deposited x time x interest rate
Future value with compounding = A( 1 + r)^n
A = amount deposited
r = interest rate
n = time
We would calculate the simple interest and the future value in year 2
Simple interest in year 2 = $3500 x 0.0375 x 2 = 262.50
Future value in 2 years with a simple interest = 262.50 + 3500 = $3762.50
Future value in year 2 with compounding = 3500 x (1.0375)^2 = $3767.42
The value provided in year 2 with compounding matches that provided in the question. Thus, it is compounding of interest that is done
Subtract (x² + 5x – 6) – (3x^2 – 7x + 1).
What is the difference?
Give expressions for the following(a) 4 added to 3 times y(b) 7 less than twice t(c) p divided by 3(d) (-10) multiplied by x(e) 9 subtracted from w
Expressions are mathematical statements that contain variables, numbers, and operations.
(a) The expression for 4 added to 3 times y is 3y + 4
(b) The expression for 7 less than twice t is 2t - 7
(c) The expression for p divided by 3 is p/3
(d) The expression for (-10) multiplied by x is -10x(e)
The expression for 9 subtracted from w is w - 9
In this question, we were given five expressions to simplify. After performing the required arithmetic operations, the expressions can be simplified to 3y + 4, 2t - 7, p/3, -10x, and w - 9.
These expressions are useful in solving mathematical problems and finding solutions to equations.
It is important to understand how to construct and manipulate mathematical expressions to be able to solve problems that require algebraic thinking.
Expressions are mathematical statements that contain variables, numbers, and operations.
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The positive angle between 0 and 2 in radians that is coterminal with the angle −143 in radians is
The positive angle between 0 and 2 radians that is coterminal with the angle −143 radians is 1.057 radians, which is equal to 59.8°.
To find the positive angle in radians that is coterminal with −143 radians, we must first convert the negative angle to its equivalent positive angle. The angle −143 radians is equivalent to the angle 2π - 143 radians. We can calculate this by using the formula 2π + x = 2π - |x|, where x is the given angle. In this case, x = −143. Applying this formula, we get 2π + (−143) = 2π - |−143| = 2π - 143. This is the equivalent positive angle of the given negative angle. To find the positive angle that is coterminal with the positive angle we just found, we must subtract it from 2π until we get a value that is between 0 and 2π. To do this, we subtract 2π - 143 from 2π until we get a value that is between 0 and 2π. After subtracting 2π - 143 from 2π multiple times, we get the result 1.057 radians, which is equal to 59.8°. Therefore, the positive angle between 0 and 2 radians that is coterminal with the angle −143 radians is 1.057 radians.
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