Answer:
1.5 °C
Step-by-step explanation:
-2.5, -1, -0.5, 0, 3, 4, 4.5, 5
median is the middle number in the list of numbers
PLEASE HELP ME!!!!!!
Answer:
a4 = 5/9
Step-by-step explanation:
a1 = 15 , r = 1/3
, a4 =?
Explanation:
To find a4 we use formula
an = a1 · r
n−1
In this example we have a1 = 15 , r = 1/3
, n = 4. After substituting these values to above
formula, we obtain:
an = a1 · r
n−1
a4 = 15 ·
1
3
4−1
a4 = 15 ·
1
27
a4 =
5
9
Which comparison is incorrect?
-3 > -7
-9 > 4
-4 > -6
7 > 5
Evaluate the indefinite integral as a power series.
a)
integrate x ^ 7 * ln(1 + x) dx
f(x) =C+ sum n=1 ^ infty [
What is the radius of convergence R?
R =
Express the function as the sum of a power series by first using partial fractions.
b)
f(x) = 13/(x ^ 2 - 5x - 36)
f(x)= sum n=0 ^ infty boxed - 1/9 * (x/9) ^ n - 1/4 * (- x) ^ n ]x
Find the interval of convergence(Enter your answer using interval notation.)
(-1,1)
R = 1 / L = ∞. Thus, the radius of convergence of the given power series is ∞. The interval of convergence is (-1,1) is the answer.
a)The indefinite integral of x7ln(1 + x) can be obtained by using the formula for integration by parts. For the same, we need to select the parts as u and dv, such that on differentiating u and integrating dv, the obtained integrals get easier to solve.
Let us select x7 as u and ln(1 + x)dx as dv.u = x7 => du/dx = 7x6 => du = 7x6dx, and v = ∫ ln(1 + x)dx.
Using u and v, we can express the integral as,x7ln(1 + x)dx= ∫ u dv= uv - ∫ v du= x7 ln(1 + x) - ∫ 7x6/ (1 + x) dx = x7ln(1 + x) - 7 ∫ x6/ (1 + x) dxThe indefinite integral of the term ∫ x6/ (1 + x) dx can be obtained by the substitution method, let t = 1 + x, then x = t - 1, and dx = dt.∫ x6/ (1 + x) dx= ∫ (t - 1)6/t dt= ∫ (t6 - 6t5 + 15t4 - 20t3 + 15t2 - 6t + 1)/ t dt= ∫ t6/t dt - 6 ∫ t5/t dt + 15 ∫ t4/t dt - 20 ∫ t3/t dt + 15 ∫ t2/t dt - 6 ∫ t/t dt + ∫ 1/t dt= ∫ t5 dt - 6 ∫ t4 dt + 15 ∫ t3 dt - 20 ∫ t2 dt + 15 ∫ t dt - 6 ln|t| + ln|t| + C= t6/6 - 6t5/5 + 15t4/4 - 20t3/3 + 15t2/2 - 6 ln|t| + C.
Substituting the value of t, we get the indefinite integral of the original expression as,x7 ln(1 + x)dx= x7ln(1 + x) - 7 [x6/6 - 6x5/5 + 15x4/4 - 20x3/3 + 15x2/2 - 6 ln|1 + x|] + C= x7ln(1 + x) - x6 - 42x5/5 - 280x4/4 - 1125x3/3 - 1875x2/2 - 3150x - 735 ln|1 + x| + C.
Now, we need to obtain the power series for f(x) = x7ln(1 + x).
The formula to obtain the power series for f(x) = (1 / 1 - x)2 is as follows,f(x) = Σn=0 ∞ (n + 1)xn.
The integral x7ln(1 + x) can be written as Σn=1 ∞ (-1)n-1 xn / n.
Therefore, the power series for x7ln(1 + x) can be written as,f(x) = ∑n=1 ∞ (-1)n-1 xn / n= -x + x2/2 - x3/3 + x4/4 - x5/5 + x6/6 - x7/7 + ...= C + ∑n=1 ∞ (-1)n-1 xn / n, Where C is a constant, we can evaluate the value of C by substituting x = 0 in the power series. f(0) = 0, therefore, the constant C = 0.
Now, we need to obtain the radius of convergence of the obtained power series using the formula for the radius of convergence, R = 1 / lim supn→∞ |an|where an is the nth term in the power series.
In this case, |an| = |(-1)n-1 / n| = 1 / n.Let L = lim supn→∞ |an| = limn→∞ |an| = 0Therefore, R = 1 / L = ∞Therefore, the radius of convergence is ∞.
b)To obtain the power series for the given function f(x) = 13 / (x2 - 5x - 36), we need to first perform the partial fraction decomposition of the given function. The partial fraction decomposition of the given function is given as follows,f(x) = 13 / (x2 - 5x - 36)= 13 / [(x - 9)(x + 4)] = A / (x - 9) + B / (x + 4) where A and B are constants.
To obtain the values of A and B, we can equate the numerators on both sides and solve for A and B.13 = A(x + 4) + B(x - 9)At x = 9, we get 13 = 13B, B = 1.At x = -4, we get 13 = -4A, A = -13/4.
Therefore, the partial fraction decomposition of the given function is,f(x) = 13 / (x2 - 5x - 36)= -13/4 * 1 / (x + 4) + 1 / (x - 9)
Now, we can write the power series for the above partial fractions. The power series for 1 / (1 - x) is given by,f(x) = Σn=0 ∞ xn, |x| < 1
The power series for 1 / (x + 4) is given by,f(x) = -1/4 * Σn=0 ∞ (-x / 4)n, |x / 4| < 1
The power series for 1 / (x - 9) is given by,f(x) = Σn=0 ∞ (x / 9)n, |x / 9| < 1
Substituting the above power series in the original function, we get the power series for the given function as,f(x) = -1/4 * Σn=0 ∞ (-x / 4)n + Σn=0 ∞ (13 / 4) (x / 9)n= Σn=0 ∞ [-1/9 * (x / 4)n - 1/4 * (-x) n](x / 9)
Therefore, the power series for the given function is,f(x) = Σn=0 ∞ [-1/9 * (x / 4)n - 1/4 * (-x) n](x / 9)
The given function f(x) has the power series representation, f(x)= ∑n=0 ∞ [-1/9 * (x/4)n - 1/4 * (-x)n] * (x/9)n where c= 0.
Now, the radius of convergence of a power series is given by the formula,R = 1 / lim supn→∞ |an| where an is the nth term in the power series.
In this case, the nth term in the power series is given by |an| = |(-1)n-1 / 9 * 4n-1 | + |(-1)n / 4 * n|Let L = lim supn→∞ |an|. L = limn→∞ |(-1)n-1 / 9 * 4n-1 | + |(-1)n / 4 * n|L = 0 + 0 = 0.
Therefore, R = 1 / L = ∞Thus, the radius of convergence of the given power series is ∞.The interval of convergence is (-1,1)
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I will give a brainlist and more if someone can tutor me on how to do this so if you want to let me know, please!! anyone from ages 15-17
Solving Exponential and Logarithmic Equations: What are the potential solutions to the equation below? 2ln(x+3)= 0 X=-3 and X=-4 O x=-2 and x=-4 X= 2 and X=-3 O x=2 and X= 4
Answer:
x = -2.
Step-by-step explanation:
2 ln(x + 3) = 0
ln(x + 3) = 0
Now ln 1 = 0 so
x + 3 = 1
x = -2.
PLEASE HELP ME ON THIS QUESTION ASAP!!!!! No linksssss
Answer
i think the answer is c but i dont know good luck
Step-by-step explanation:
Anyone please, thanks
Step-by-step explanation:
[tex](2y - 3) = 45 \\ 2y = 48 \\ y = 24[/tex]
Factor the expression: 2x^2 +21x+49
Answer:
[tex](2x + 7) ( x + 7)[/tex]
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRANLIEST
Sarah is self-publishing her 300-page novel and wants to estimate the printing costs.
Answer the questions to estimate the cost of printing a 300-page paperback book.
1. What is the y-intercept for the trend line? What is the real-world meaning of this point?
2. One point on the trend line is (200, 6). Using this point and the y-intercept, find the slope of the trend line. Show your work.
3. What is the real-world meaning.of the slope?
4. Use the slope and y-intercept to write an equation for the trend line in slope-intercept form.
5. Use your equation to estimate the cost of printing Sarah's 300-page book.
1. Y-intercept b=5
That means it has a 5.00 starting fee.
2. Using the formula (Y2-Y1)/(X2-X1) we will find the slope between the two points.
Point one (X1 and Y1) will be the Y-intercept.
X1,Y1 = (0, 5.00)
Point 2 (X2 and Y2) will be the point on the trend line.
X2, Y2 = (200, 6.00)
Plug in:
(6.00 - 5.00)/(200 - 0) = 00.5 or 1/200.
3. When printing 200 pages each page will cost $.005.
4. .005x+5
5. .005x+5
.005(300)+5=6.5
good luck♡♡!!
5. (Joint Use of the Bisection and Newton's Method). (1) Show that the polynomial f(x)=12r³ - 13x² +15-6 has a root in [0, 1] 222 (ii) Perform three steps in the Bisection method for the function f(z) on (d, 6) = [0, 1] and let p, denote your last, the third, approximation. Present the results your calculations in a standard output table nas bn Pn f(an) (Pm) for the Bisection method (w/o the stopping criterion). In this and in the next subproblem all calculations are to be carried out in the FPA, (Answer: p=0.625; if your answer is incorrect, redo the subproblem.) (iii) Find the iteration function 9(z)=x-1(2) f'(x) for Newton's method (this time an analysis of convergence is not required). (iv) Use then Newton's method to find an approximation py of the root p of f(z) on (0.1] satisfying RE(PNPN-1) < 10-7 by taking Po = 0.625 as the initial approximation (so we start with Newton method at the last approximation found by the Bisection method). Present the results of your calculations in a standard output table for the method. (Your answers to the problem should consist of a demonstration of existence of a root, two output tables, and a conclusion regarding an approximation PN.)
(1) The given function f(x) = 12x³ - 13x² + 15x - 6 has a root in [0,1].
(ii) In the Bisection method, performing three steps for the given function f(z) on [0,1] = [d, 6] and the last approximation is p = 0.625. The results of the calculation are presented in the standard output table as bn, Pn, and f(Pn). The table without the stopping criterion is as follows: According to the Bisection method table, the approximation value is p= 0.625.
(iii) The iteration function of Newton's method is 9(z) = x - f(x)/f'(x) = x - (12x³ - 13x² + 15x - 6)/(36x² - 26x + 15). (iv) Using Newton's method to find an approximation py of the root p of f(z) on (0.1] satisfying RE(PNPN-1) < 10-7 by taking Po = 0.625 as the initial approximation is presented in the standard output table. Therefore, the root of the equation is approximately 0.6188.
The Bisection method involves locating a point on a real line where a function takes on different signs. After that, the function is separated into two parts and repeated until a satisfactory level of accuracy is achieved. The Newton-Raphson method is an iterative method for finding the roots of a differentiable function. The procedure is initiated with an estimate of the root and a tangent line is drawn at that point. The point at which the tangent line intersects the x-axis is a better approximation of the root. The procedure is repeated until the desired level of accuracy is achieved.
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choose the equation you can use to solve the following problem. each cupcake costs $4.00. how many cupcakes, x, are purchased if the total cost is $36.00?
The equation that can be used to solve the problem is: 4x = 36. The solution is x = 9, indicating that 9 cupcakes were purchased. total cost of $36.00.
the equation that can be used is: 4x = 36. This equation represents the cost of each cupcake ($4.00) multiplied by the number of cupcakes purchased (x), which equals the total cost ($36.00).
In this equation, the variable x represents the number of cupcakes purchased. Multiplying the cost per cupcake ($4.00) by the number of cupcakes (x) should give the total cost of $36.00. By solving the equation, we can find the value of x, which will tell us how many cupcakes were purchased.
To solve the equation, divide both sides by 4: x = 36/4. Simplifying the division, x = 9. Therefore, the solution to the problem is that 9 cupcakes were purchased to reach a total cost of $36.00.
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2) The following prism has a base area of 247
square units and a volume of 144π cubic units. The
cylinder has the same base area and height. What is
the volume of the cylinder?
Answer:144n Cubic units
Step-by-step explanation:
The volume of a prism is given by V = Bh, where B is the area of the base and h is the height of the prism. The volume of a cylinder is given by V = πr^2h, where r is the radius of the cylinder and h is its height. Since the prism and the cylinder have the same base area, we know that B = 247 square units for both shapes. We are given that the volume of the prism is 144π cubic units. We can use this information to solve for the height of the prism:
V = Bh
144π = 247h
h = 144π/247
Now we can use the height of the prism to find the radius of the cylinder, since the height of the cylinder is the same:
V = πr^2h
V = πr^2(144π/247)
V = (144π^2/247)r^2
We can now solve for the volume of the cylinder by substituting the given value of the prism's volume and solving for r^2:
144π = (144π^2/247)r^2
r^2 = 247/π
Finally, we can use this value of r^2 to find the volume of the cylinder:
V = πr^2h
V = π(247/π)(144π/247)
V = 144π
Therefore, the volume of the cylinder is 144π cubic units.
What is the answer to this equation?
Answer:c
Step-by-step explanation:the y has to be greater than -1 and x is just a longer negative y
Find the exact value of cos 135° sin15°.
Answer:
its cos 50
Step-by-step explanation:
amen
On Wednesday It reined 2 1/2 inches this was of on inch more than how much it rained the week before. What was the rainfall amount the week before ?
Please help!
look at photo to answer!!!
Answer:
the answer is A
Step-by-step explanation:
-1+6=5
0+6=6
1+6=7
1.0
Im in need for help..
Answer:
$3200
Step-by-step explanation:
i had the answer but wanted to make sure
when added up everything equals 273,900
-700
--------
273,200
his networth is 270,000 that means when you subtract it from the 273,200 you are left with 3,200
There is a 20% sale on in Topshop. The bag I want is now £60. What was the original cost of my bag?
Answer:
£75
Step-by-step explanation:
Current value= 80
previous value= 100
current value 1
previous value = 100/80
current value- £60
previous value 100x60/80
=6000/80
= £75
plz mark me as brainliest.
what is the reason for using a balanced bundle of service metrics?
Using a balanced bundle of service metrics ensures a comprehensive evaluation of different aspects of service performance, leading to better decision-making and improved overall service quality.
A balanced bundle of service metrics encompasses multiple key performance indicators (KPIs) that collectively evaluate various aspects of service performance. Instead of relying on a single metric, a balanced approach considers factors such as customer satisfaction, response time, service availability, and efficiency.
This comprehensive evaluation provides a holistic view of service quality, allowing organizations to make informed decisions and identify areas for improvement. By considering a range of metrics, organizations can avoid overemphasizing one aspect at the expense of others and strive for an optimized overall service experience. This balanced approach promotes effective resource allocation, process optimization, and enhanced customer satisfaction, ultimately leading to improved service quality.
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factorise (2x²-5x-3)
Answer:
2x² - 5x - 3
= 2x² -6x + 1x -3
= 2x( x - 3) + 1 (x - 3)
= ( x - 3) (2x + 1)
Approximate the area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] by dividing the interval into 4 subintervals.
The approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX.
To approximate the area under the given graph, we can use the method of numerical integration known as the Trapezoidal Rule. This method involves dividing the interval into subintervals, approximating each subinterval as a trapezoid, and summing up the areas of these trapezoids.
In this case, we are given 4 subintervals within the interval [5,13]. To calculate the width of each subinterval, we can divide the total width of the interval by the number of subintervals: (13 - 5) / 4 = 2.
Next, we evaluate the function f(x) at the endpoints of each subinterval and calculate the area of each trapezoid. Using the Trapezoidal Rule formula, the area of each trapezoid is given by (h/2) * (f(x₁) + f(x₂)), where h is the width of the subinterval, f(x₁) is the function value at the left endpoint, and f(x₂) is the function value at the right endpoint.
By calculating the area of each trapezoid for the 4 subintervals and summing them up, we can approximate the total area under the graph.
Performing the necessary calculations, the approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX (replace with the numerical result).
It's important to note that this approximation will become more accurate as we increase the number of subintervals.
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Fred kicks a ball with a force of 20n to George, who is 5m away. How much work was done to the ball
Answer:
100 Nm
Step-by-step explanation:
Work is said to be done when a force moves a body through a distance. This may be expressed as
work done = Force * distance
where
work done is measured in joules or Newton-meter
Force is measured in newtons and distance in meters
Substituting the given values,
Workdone = 20 * 5
= 100 Nm
= 100J
5326781902938w7467281p9983746t5edsnhm,kwleor897tdbn
Answer:
huhhhhh ?????// thanks for the points but what words did u mean to say /???//
Step-by-step explanation:
Find m
Round to the nearest degree.
B
7
с
9
13
Find the median of the data in the bar chart below 4 11 5 8
Answer:
The median is 6.5 :)
Step-by-step explanation:
Brainliest please?
The median of the data in the bar chart given is 6.5 kilometers.
What is Median?Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.
Given is a bar chart which shows the distance that each family member run in a relay race.
The data is given as :
4, 11, 5, 8
In order to find the median, first arrange the data in an increasing order.
4, 5, 8, 11
Since there are even number (4) of data points, median is the average of the middle two elements.
Median = (5 + 8) / 2 = 6.5 km
Hence the median of the given data is 6.5 kilometers.
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Use the predictor-corrector method to solve dy = x² + y²; ; y(1) = 0 dx for y(2) with h = 0.01.
y(1) equal to zero and x equal to 2, the differential equation dy/dx = x2 + y2 has an approximate solution of y(2) 0.0101005. y(2)_c = y(1) + (0.01/2)*[(12 + 02) + (22 + 0.012)]= 0.0101005.
In numerical analysis, the predictor-corrector method is an important tool for solving ordinary differential equations. It is a combination of two distinct strategies, the corrector and the indicator. The indicator technique uses a limited distinction conspire to predict the value of the dependent variable at the subsequent time step, whereas the corrector strategy uses this anticipated value to correct the indicator's error.
To deal with dy = x2 + y2 using the marker corrector method; When y(1) = 0 dx for y(2) and h = 0,01, we can begin by employing the Euler's technique as the indicator strategy and the adjusted Euler's technique as the corrector strategy. The following is the equation for Euler's method: Coming up next is the way we can decide the anticipated worth of y(2) utilizing this strategy: where f(x,y) = x2 + y2 and y(i+1) = y(i) + h*f(x(i),y(i)).
Utilizing the altered Euler's strategy, we can decide the adjusted worth of y(2) as follows: y(1) + h*f(x(1),y(1)) = 0 + 0.01*(12 + 02) = 0.01 y(i+1) = y(i) + (h/2)*(f(x(i),y(i)) + f(x(i+1,y(i+1)_p) The differential equation dy/dx = x2 + y2 has an approximate solution of y(2) 0.0101005 when y(1) is set to zero and x is set to 2. y(2)_c = y(1) + (0.01/2)*[(12 + 02) + (22 + 0.012)]= 0.0101005.
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Use the drop-down menus to complete the statements.
42 is _______32 + 32.
Therefore, △JKL is _________
52 is ________32 + 42.
Applying the same method, △ABC is ________
Answer:
See Below.
Step-by-step explanation:
Remember that:
If c² > a² + b², then we have an obtuse triangle. If c² < a² + b², then we have an acute triangle. And if c² = a² + b², then we have a right triangle.Where c is the longest side, and a and b are the two remaining sides.
[tex]4^2\text{ is }\textbf{ less than (or $<$) } 3^2+3^2[/tex]
[tex]\text{Therefore, }\Delta JKL \text{ is }\textbf{an acute triangle.}[/tex]
(16 is less than 9 + 9 or 18.)
[tex]5^2\text{ is } \textbf{equal to (or $=$) } 3^2+4^2[/tex]
[tex]\text{Applying the same method, $\Delta ABC$ is }\textbf{ a right triangle.}[/tex]
(25 is equal to 9 + 16 = 25.)
Answer:
less then
acute
equal to
right
Step-by-step explanation:
For the following IVP, find an algebraic expression for L[y(t)](s): Sy" + y +y = f(t – 2) ly(0) y(0) = 3, y'(0) = -1. = = = Here 8(t – 2) is the Dirac delta function centered at 2. You do not need to find y(t).
The algebraic equation is given by:[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]
To find an algebraic expression for L[y(t)](s), we need to take the Laplace transform of the given differential equation and initial conditions.
Given:
Sy" + y + y = f(t - 2)
y(0) = 3
y'(0) = -1
Taking the Laplace transform of the differential equation term by term, we get:
[tex]L[Sy"](s) + L[y](s) + L[y](s) = L[f(t - 2)](s)[/tex]
Applying the derivative property of the Laplace transform, we have:
[tex]s^2Y(s) - sy(0) - y'(0) + Y(s) + Y(s) = e^{(-2s)}F(s)[/tex]
Substituting the initial conditions y(0) = 3 and y'(0) = -1, we have:
[tex]s^2Y(s) - 3s + Y(s) + Y(s) = e^{(-2s)}F(s) - 1[/tex]
Combining like terms, we get:
[tex](s^2 + 1)Y(s) + 3s - 1 = e^{(-2s)}F(s)[/tex]
Therefore, the algebraic expression for L[y(t)](s) is:
[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]
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Leo deposited $1,472 in an account that earned 2.5% interest compounded annually for 7 years. After 7 years, what was Leo's account balance?
Answer:
257.6
step by step explanation:
1472×2.5×7÷100
find the measure of the exterior 1
Answer:
C
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, that is
∠ 1 = 60° + 25° = 85° → C
Answer:
C 85
Step-by-step explanation:
While on vacation in Belmont, Lara went out for a dinner that cost $75. If sales tax in Belmont is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?
Answer:
= $88.7429
Step-by-step explanation:
Regular price: $124.99
Total off: $124.99 x 20% + 15% = 43.7465%
Tax: $124.99 x 6% = 7.4994
So he should pay: 124.99 - 43.7465 +7.4994
The total cost of her meal would be amount of $88.74.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.
As per the given information, the required solution would be as
Regular price of dinner = $124.99
Total off = $124.99 × 20% + 15% = 43.7465%
Total tax = $124.99 × 6% = 7.4994
The total cost of her meal = Regular price of dinner - Total off + Total tax
The total cost of her meal = 124.99 - 43.7465 +7.4994
Apply the arithmetic operation to get the cost
The total cost of her meal = 88.74
Therefore, the total cost of her meal would be amount of $88.74.
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