Sum of the series will be (19/30)
Partial differentiation is the method of determining a function's partial derivative. By holding the other variable constant, one may use this method to get the partial derivative of a function with respect to one variable.
An equation having an unknown function of two or more variables and its partial derivatives with respect to these variables is known as a partial differential equation. A partial differential equation has the highest-order derivatives as its order. is a partial differential equation of order 2, as an illustration.
Ordinary differential equations, often known as ODEs, are equations for which only one variable's derivatives are considered. Consequently, there is just one independent variable. PDEs are equations that rely on the partial derivatives of a number of distinct variables.
Using partial fractions, we have
[tex]\frac{6}{(n+8)(n+10)}=\frac{A}{n+8}+\frac{B}{n+10}\\\\=\frac{A(n+10)+B(n+8)}{(n+8)(n+10)} \\\\ 6=A(n+8)+B(n+10)[/tex]
Put n=-8,
we have 6=0+2B=>B=3
Put n=-10,
we have 6=-2A =>A=-3
[tex]$$\begin{aligned}& \sum_{n=1}^{\infty} \frac{6}{(n+8)(n+10)}=\sum_{n=1}^{\infty}\left(\frac{3}{n+8}-\frac{3}{n+10}\right) \\& =3 \sum_{n=1}^{\infty} \frac{1}{n+8}-\frac{1}{n+10} \\& =3\left[\left(\frac{1}{9}-\frac{1}{11}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{11}-\frac{1}{13}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)+\ldots\right] \\& =3\left[\frac{1}{9}+\frac{1}{10}\right]=\frac{19}{30}\end{aligned}$$[/tex]
other terms will be cancelled out
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The correct question should be:
Find the sum of the convergent series: [tex]$$\sum_{n=1}^{\infty} 6 /(n+8)(n+10)$$[/tex]
Find the measure of x
Answer:
113°
Step-by-step explanation:
Angles that form a linear pair are supplementary, and thus add to 180°.
Find the product of 2.1n(6n + 3.4).
12.6n + 3.4
8.1n + 3.4
8.1n2 + 7.14n
12.6n2 + 7.14n
ASAP PLEASE
Which point us the coordinate of the image of A under the transformation [0 1 1 0]
(-2,4)
(2,4)
(4,2)
(-4,-2)
Answer:
Step-by-step explanation:
(4, 2)
will you brainlyest?
At some department store, all suits are reduced 20% from the retail price. If a man purchased a suit that originally retailed for 231.20 how much did he save?
well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]
Which algebraic expression is equivalent to the expression below 5(5x + 7) - 6 (4- 2x)
The algebraic expression equivalent to the expression 5(5x + 7) - 6 (4- 2x) is 37x + 11.
What is the equivalent of the expression?Given the expression; 5(5x + 7) - 6 (4- 2x)
We expand and collect like terms.
5(5x + 7) - 6 (4- 2x)
25x + 35 -24 + 12x
We collect like terms
25x + 12x + 35 - 24
37x + 11
Therefore, the algebraic expression equivalent to the expression 5(5x + 7) - 6 (4- 2x) is 37x + 11.
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the probability that an international flight leaving is delay in departing (event D) is .28. The probability that an international flight is a transpacific flight is (event P) is .55. The probability that an international flight leaving the U.S is a transpacific flight and delay is .13. What is the probability that an international flight leaving the United states is delay in departing given that the flight is a transpacific flight?
The probability that an international flight leaving the United states is delay in departing given that the flight is a transpacific flight is 0.7
What is probability?Probability describes the likelihood of an event happening. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not.
The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The probability of an event occurring can be anything between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.
According to the question,
P(D)=0.28
P(P)=0.55
P(D∩P)=0.13
Thus, the required probability,
P(DUP)=P(D)+P(P)-P(D∩P)
=0.28+0.55-0.13
=0.70
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A ship leaves port on a bearing of 36.0° and travels 12.1 mi. The ship then turns due east and travels 6.1 mi. How far is the ship from port, and what is its bearing
The bearing angle exists 53.49°.
How to estimate the bearing angle of a ship?A bearing of 36° corresponds to the corresponding angle of
θ = 90 -36 = 54°
The (x, y) values for the position of the ship after achieving its first heading exist:
[tex]x_1[/tex] = 12.1 Cos 54° = 7.11 m
[tex]y_1[/tex] = 12.1 Sin 54° = 9.78 m
Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore
[tex]x_2[/tex] = 6.1 mi
[tex]y_2[/tex] = 0 mi
To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:
Δx [tex]= x_1+x_2[/tex]
= 7.11 mi + 6.1 mi = 13.21 mi
Δy [tex]=y_1+y_2[/tex]
= 9.78 mi + 0 mi = 9.78 mi
[tex]$r=\sqrt{(x_{total})^2+(y_{total})^2}[/tex]
[tex]=\sqrt{(13.21mi)^2+(9.78mi)^2}[/tex]
= 16.43 mi
The direction of the displacement vector exists given by
tan θ = Δy/Δx
θ = arc tan (Δy/Δx)
= arc tan (9.78/13.21)
= 36.51°
The question requested for the bearing angle, which exists just this angle subtracted from 90°:
90° - 36.51° = 53.49°.
Therefore, the bearing angle exists 53.49°.
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true or false, [tex]\pi[/tex] only used to determine the area of a circle?
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer: A = JIH
B = GJH
C = GH
D = 300
E = 60
Step-by-step explanation:
A) <JIH is a inscribed angle
B) GJH is a major arc
C) GH is a minor arc
D) m GH = m<GFh = 60
Find the vertex, focus and diretrix of x^2+4x-12y=-64
It needs to be in (x-h)^2=4p(y-k) form
Vertex of the equation is (-2, 5)
Focus of the equation is (-2, 8)
Directrix of the equation is 2
What is a Quadratic curve?
A quadratic curve is a parabolic curve is a graph of the points which define a quadratic function. It shows how a function behaves in the cartesian plane.
Quadratic curve may bend upwards, or downwards depending on the gradient of the curve.
Analysis:
setting the equation in the form, [tex]x^{2}[/tex] +4x -12y = -64 in the form [tex](x-h)^{2}[/tex] = 4p(y-k)
Firstly we take -12y to the right hand side
[tex]x^{2}[/tex] +4x = 12y - 64
Making the left hand side a perfect square expression, we square both sides with -2
[tex]x^{2}[/tex] +4x + [tex](2)^{2}[/tex] = 12y -64 + [tex](2)^{2}[/tex]
[tex](x+2)^{2}[/tex] = 12y -60
[tex](x+2)^{2}[/tex] = 12(y - 5)
comparing with the other equation
-h = , h = -2, -k = - 5 k = 5, 4p = 12, p = 3
Vertex is (h, k) = (-2, 5)
Focus is (h, k+p) = (-2, 5+3) = (-2, 8)
Directrix is y = k-p = 5 - 3 = 2
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The nurse must give a patient 9 milligrams of a medication. If the tables are 2 milligrams each, how many tablets are needed?
Answer:
4.5 tablets.
Step-by-step explanation:
We just divide 9 by 2.
13. The tablets needed is 4 and a half.
14. There are 10 half-gram doses available from the 5 gram vials of medication.
15. Pat's heart beats approximately 58.5 times in 3/4 of a minute.
Given are words problems based on the mixed numbers:
13. To determine the number of tablets needed, we divide the total dosage required by the dosage per tablet.
In this case, the nurse needs to administer 9 milligrams of medication, and each tablet contains 2 milligrams.
So, the number of tablets needed is:
9 milligrams / 2 milligrams per tablet = 4.5 tablets
Hence, the tablets needed is 4 and a half.
14. If the pharmacy has 5 gram vials of medication, we can calculate the number of 1/2 gram doses available by dividing the total amount of medication by the dose size.
The total amount of medication in grams is 5 grams.
To find the number of 1/2 gram doses available, we divide the total amount of medication (5 grams) by the dose size (1/2 gram):
5 grams / (1/2 gram) = 5 grams x (2/1 gram)
= 5 x 2 = 10 doses.
Therefore, there are 10 half-gram doses available from the 5 gram vials of medication.
15. To calculate how many times Pat's heart beats in 3/4 of a minute, you can use a simple proportion:
1 minute = 78 beats
3/4 minute = ? beats
Let's solve for the number of beats in 3/4 of a minute:
Number of beats in 3/4 minute = (3/4) x 78
= 0.75 x 78
= 58.5
So, Pat's heart beats approximately 58.5 times in 3/4 of a minute. Since you can't have half a heartbeat, the closest whole number is 58 beats.
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Which of the following expressions does sin(x + y) - sin(x - y) simplify to?
O2(sin x)(sin y)
O2(sin x)(cos y)
O2(cos x)(cos y)
O 2(cos x) (sin y)
The answer choice which sin(x + y) - sin(x - y) simplifies to is; 2(cos x)(sin y).
Which of the following expressions does sin(x + y) - sin(x - y) simplify to?It follows from the task content that the expression given in the task content can be simplified by trigonometric identities as follows;
sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy -cosxsiny)
= 2cosxsiny.
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he graphs of y = 3x and y = 3x are shown below.
In general, how does the growth of y = 3x compare to the growth of y = 3x?
The function y = 3x is growing slower than y = 3x.
The function y = 3x is growing faster than y = 3x.
The functions y = 3x and y = 3x are growing at the same rate.
The function y = 3x is growing slower than y = 3x.
The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.
Which answer choice correctly compares the growth of the graphs?The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.
Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.
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Choose the equation that matches
the graph.
a.y = 3x - 2
b. y = 3x-2
c. y = 3x+2
d. y = 3x + 2
e. y = (1/3)x-2
Answer:
it matches with equation a
what is the equation for -2(5x+8)
Answer:
Step-by-step explanation:
-10x-16
Answer:
distribute the -2 so your answer is -10x-16
Step-by-step explanation:
Find the area of the triangle with sides 40, 50, and 60.
The area of the triangle is 1000 unit square
What is the area of a triangle?
The area of a triangle is half the base multiplied by the height
The formula is given as;
Area = 1/2 × b × h
From the information given, the base is given as 50 and the height is 40
Area = 1/ 2 × 50 × 40
Area = 1/ 2 × 2000
Area = 1000 unit square
Thus, the area of the triangle is 1000 unit square
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a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons
Answer: 30 miles
Work Shown:
2 in : 6 mi
5*2 in : 5*6 mi
10 in : 30 mi
Sets J and F are defined as follows.
J= {c,e,f}
F={g,k,j}
Answer each part below. Write your answer in roster form or as 0.
Find the intersection of J and F.
FInd the union of J and F.
The value of J ∩ F = ∅
The value of J ∪ F = {c, e, f, g, k, j}
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Sets J and F are defined as follows;
J = {c, e, f}
F = {g, k, j}
Now,
Since, Sets J and F are defined as follows;
J = {c, e, f}
F = {g, k, j}
Hence, The value of J ∩ F = {c, e, f} ∩ {g, k, j}
= ∅
The value of J ∪ F = {c, e, f} ∪ {g, k, j}
= {c, e, f, g, k, j}
Thus, The value of J ∩ F = ∅
The value of J ∪ F = {c, e, f, g, k, j}
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Which statement most clearly shows an example of ethos? There is nothing more important than making sure everyone has access to a quality education. O Today, too many recent college graduates are struggling to secure a job in their field of study. O As the CEO of a major technology company, I am constantly making tough hiring decisions. O While a college education isn't everything, it does make a difference on a job application. Mark this and return Save and Exit Next Submit
The statement that most clearly shows an example of ethos is C. As the CEO of a major technology company, I am constantly making tough hiring decisions.
What is an ethos statement?An ethos statement establishes the credibility, knowledge, and good moral character of the speaker or writer.
The use of ethos is meant to sound fair or to demonstrate credibility, expertise, education, or pedigree.
Thus, an example of ethos is when this CEO claims they constantly make tough hiring decisions.
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8.
Find the arc length of a central angle of 7pi/3 in a circle whose radius is
3inches
[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{3}\\ r=3 \end{cases}\implies s=(3)(\frac{7\pi }{3})\implies s=7\pi \implies s\approx 21.99~in[/tex]
Which of the following equation(s) has/have slope zero?
a. x = 2
b.y = -3
c. y = 5x+2
d. x+ 5 = 0
O Both a and c
Only c
O Only b
O Both a and d
Answer:
b, only b
y = -3 has zero slope.
Step-by-step explanation:
Only a horizontal line has zero slope. A horizontal line's equation is given in the form: "y equals a number" So y=-3 is horizontal with zero slope.
Vertical lines have undefined slope. This is not the same as zero. Vertical lines have an equation in the form x= anumber. Above in the answer choices, choice a and d are both vertical with undefined slope and are not the correct answer. Choice c has slope 5, because that is the number beside the x in the form y=mx+b where m is the slope. So choice c is also not the answer.
Only choice b has zero slope.
Does this graph represent a function? Why or why not?
bryan brought 8/10 gallon of water on a hiking trip.he drank 4/10 gallon of water.how much water is left
The amount of water left is 4/10 gallons
Difference of fractionsFractions are written as a ratio of two integers
Given the following parameters
Amount of gallon bought = 8/10 gallons
Amount he drank = 4/10
Determine the amount left
Amount left = 8/10 -4/10
Amount left = 4/10 gallons
Hence the amount of water left is 4/10 gallons
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Can someone help me with this plss
Answer:
6. Quadrant four
7. Quadrant three
8. Quadrant one
Step-by-step explanation:
These questions give you points to graph and then asks which quadrants they are graphed in. Here is a visual.
D. 12:28
es 22. The label on a box of cereal states that it
contains 6 servings. If there are 7.5 cups in
the box, how many cups of cereal are there
per serving?
In the following diagram, line m is parallel to line n and line q intersects the parallel lines at
Answer:
108°
Step-by-step explanation:
We know for a theorem that A = B, so:
4x + 28 = 2x + 68
Isolating the x:
2x = 40
x = 20
Now let's plug in the equation for A:
4(20) + 28 = 108°
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
In the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.
A quadratic equation is a polynomial of degree 2, in a single variable x.
The standard form of a quadratic equation is ax² + bx + c = 0.
The quadratic formula is used to find the solution(s)/root(s) of this equation.
The quadratic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Thus, identifying the values of a, b, and c, is the first step in using the quadratic formula to find a solution(s)/root(s) to a quadratic equation.
In the question, we are asked to find the values of a, b, and c, in the given quadratic equation - 3x² - 5x + 9 = 0.
To find the values of a, b, and c, we compare the given equation, to the standard form of a quadratic equation, ax² + bx + c = 0.
On comparing, we get a is the coefficient of x², that is, a = -3.
On comparing, we get b is the coefficient of x, that is, b = -5.
On comparing, we get c is the constant term, that is, c = 9.
Thus, in the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.
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The provided question is incomplete.
The complete question is:
"Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
- 3x² - 5x + 9 = 0
A. a = 5, b = 9, c = 0B. a = 3, b = 5, c = 9C. a = −3, b = −5, c = 9D. a = −5, b = 9, c = 0."CAB SOMEONE HELP ME ASAP PLS
Write the measure of minor arc CE as the sum of the measures of minor arcs.
please open the attached image
The function that will have a horizontal asymptotes are function B, C and D
Horizontal asymptotes of a functionA function is said to have a horizontal asymptotes of the degree of the numerator is less or equal to that of the denominator.
From the rational expression given, the function A and E wil have no horizontal asymptotes since the power of the numerator is greater abd equal to the denominator,
The function that will have a horizontal asymptotes are function B, C and D
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