N/2 + 3
Find the first 5 terms in the sequence...
Answers
Answer:
The first '5' terms of the given sequence
\(\frac{7}{2} , 4 ,\frac{9}{2} ,5,\frac{11}{2}\)
Step-by-step explanation:
Explanation:-
Given that the \(n^{th}\) aₙ = \(\frac{N}{2} + 3\)
first term
Put n=1 ⇒ \(\frac{1}{2} + 3 = \frac{7}{2}\)
second term
Put n=2 ⇒ \(\frac{2}{2} + 3 = 1+3=4\)
Third term
Put n=3 ⇒ \(\frac{3}{2} + 3 = \frac{3+6}{2}=\frac{9}{2}\)
Fourth term
Put n=4 ⇒ \(\frac{4}{2} + 3 = 2+3 =5\)
Fifth term
Put n=5 ⇒ \(\frac{5}{2} + 3 = \frac{5+6}{2}=\frac{11}{2}\)
The first '5' terms of the given sequence
\(\frac{7}{2} , 4 ,\frac{9}{2} ,5,\frac{11}{2}\)
Related Questions
What are the lengths of the major and minor axes of the ellipse?
(x−3)227+(y+4)245=1
Answers
The lengths of the major and minor axis are 4√6 and 4√3.
What is Major and Minor Axis?A point on a curve is described by an ellipse if its location is such that the sum of the distances between its two focal points is a constant.
(x−h)²/ b² +(y- k)² /a² = 1
Given:
(x−3)²/ 27+(y+4)² /45=1
The above equation can be compared to the standard equation of an ellipse
(x−h)²/ b² +(y- k)² /a² = 1
where, (h, k) = coordinates of the center of the ellipse
a = length of the semi major axis
b = length of the semi minor axis
By comparison, we have;
(h, k) = (3, -4)
a = √(24) = 2 x√6
b = √(12) = 2 x√3
and, length of the major axis = 2a
length of the minor axis = 2b
Thus, The length of the major axis is
2x a = 2 × 2 x √6 = 4√6
and, length of the minor axis is
2•b = 2 × 2√3 = 4√3
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Answer: 6sqrt(5) and 6sqrt(3)
Step-by-step explanation:
I took the test and these were the correct answers.
plz help thxxxxxxxxxxxxxxxxxx
Answers
Answer:
slope is positive 2/1
Step-by-step explanation:
Answer:
a) the slope is 2 because the line goes from (4,1) to (5,3)
I d k any of the bonus questions tho sorryyyy
Step-by-step explanation:
LCM [a,b] = 36 HCF [a,b] = 6 find the value of a=b
Answers
All the values that are possible here are (1, 36) (4,9) (9,4), and (36,1).
The possible values of and b are (1, 36) (4,9) (9,4), and (36,1).
Given: The LCM of a and b is 36 and HCF is 1
To find: The values of a and b?
Here is the solution:
The two numbers are a and b.
LCM of a and b is 36.
HCF of a and b is 1
We know that,
product of two numbers = LCM * HCF
= A*B=36*1
i.e = a, b=36,1
in a similar way:
The all-possible values of and b are (1, 36) (4,9) (9,4), and (36,1).
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y=(x-4) ²-2
Find the vertex. How do you do that ?
Answers
Answer:
(4,-2)
Step-by-step explanation:
Going to Desmos and you will see the the graph and you can push on the vertex and see the answer
Solve dy/dx=1/3(sin x − xy^2), y(0)=5
Answers
The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
To solve this differential equation, we can use separation of variables.
First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:
dy/dx = 1/3(sin x − xy^2)
dy/(sin x - xy^2) = dx/3
Now we can integrate both sides:
∫dy/(sin x - xy^2) = ∫dx/3
To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:
∫dy/(sin x - xy^2) = ∫du/(sin x - u)
= -1/2∫d(cos x - u/sin x)
= -1/2 ln|sin x - xy^2| + C1
For the right side, we simply integrate with respect to x:
∫dx/3 = x/3 + C2
Putting these together, we get:
-1/2 ln|sin x - xy^2| = x/3 + C
To solve for y, we can exponentiate both sides:
|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)
|sin x - xy^2| = 1/e^(2C/3 - x/3)
Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.
Case 1: sin x - xy^2 > 0
In this case, we have:
sin x - xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]
Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:
y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5
Squaring both sides and solving for C, we get:
C = 3/2 ln(1/25)
Putting this value of C back into the expression for y, we get:
y = √[(sin x - e^(x/2)/25)/x]
Case 2: sin x - xy^2 < 0
In this case, we have:
- sin x + xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(e^(2C/3 - x/3) - sin x)/x]
Again, using the initial condition y(0) = 5 and solving for C, we get:
C = 3/2 ln(1/25) + 2/3 ln(5)
Putting this value of C back into the expression for y, we get:
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]
So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:
y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5
Note that there is no solution for y when sin x - xy^2 = 0.
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Solve each differential equation.
a) dy/dx= x^2y^2−x^2+4y2−4
b) (x-1)dy/dx - xy=e^4x
c) (7x-3y)dx+(6y-3x)dy=0
Answers
Answer:
C
Step-by-step explanation:
there is a line whose slope is 1 and whose y-intercept is -9, what is its equation in slope-intercept form?
Answers
The inverse of a function can be found by ___ the numbers in each ordered pair of the function.interchangingreflectingexponentintercept
Answers
The main answer to your question is "interchanging". To find the inverse of a function, we interchange the numbers in each ordered pair of the function. This means that we switch the x and y values of each point in the function.
For example, if we have a function f(x) = 2x + 3, the ordered pairs would be (1,5), (2,7), (3,9), etc. To find the inverse function, we would switch the x and y values of each point to get ordered pairs such as (5,1), (7,2), (9,3), etc.
The explanation for why we interchange the numbers is that the inverse function "undoes" the original function. If we apply the original function to a number, the inverse function will take us back to the original number. By switching the x and y values, we make sure that the inverse function will undo the original function.
In conclusion, to find the inverse of a function, we interchange the numbers in each ordered pair of the function. This ensures that the inverse function will undo the original function.
Hi! I'm happy to help you with your question.
Main answer: The inverse of a function can be found by interchanging the numbers in each ordered pair of the function.
Explanation: When finding the inverse of a function, you are essentially swapping the input and output values in each ordered pair (x, y) to create a new ordered pair (y, x). This process is called interchanging the numbers in the ordered pair.
Conclusion: To find the inverse of a function, you need to interchange the numbers in each ordered pair of the function, which essentially swaps the input and output values.
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I can’t seem to find the right answer no matter what I try
Answers
Blank2)52cups of lemonade
Blank3) 200 cups of lemonade
Blank4) 64
Blank 1) 4
Blank 2) 5
Blank 3) 14
Blank 4) 1.5
Fill in the missing number. % of 30 = 3
Answers
Answer:
Answer is 10% of 30 = 3
What is the most direct use of a compass in geometric constructions?
A.
to draw congruent angles
B.
to draw arcs of a given size
C.
to draw perpendicular lines
D.
to draw straight lines
Answers
Answer:
B
Step-by-step explanation:
to draw arcs of a given size
Answer:
B. to draw arcs of a given size.
Step-by-step explanation:
its correct on plato :)
Which graphs do not show a constant rate of change? Check all that apply.
On a coordinate plane, a parabola opens down.
On a coordinate plane, a line has a negative slope.
On a coordinate plane, a horizontal line is graphed.
On a coordinate plane, a curve curves downwards.
Answers
Answer:
a horizontal line is graphed
Step-by-step explanation:
It does not change it will always stay at the same y but just different x.
The rate of change/slope is the change in y divided by a corresponding change in x.
Hi. . .
A n s w e r : -
A, and D.
E x p l a n a t i o n :Cause- A, and D do not show the constant rate of the change.
Hope It Helps . . .
Which of these tables represents a function
Answers
W
a system can only be a function if there are no more than one value of y for each value of x. if a value of x is repeated twice or more in a table, it means it is not a function.
Taylor currently earn $24. 00 an hour at her job. Thank to her hard work, her bo i going to give her a 15% raie. How much will he earn each hour after the raie?
Answers
Answer:
Taylor will earn $27.60 after the raise.
Step-by-step explanation:
If you take $24.00 and multiply it by $1.15, your answer should be $27.60. Therefore, this is the answer to your question.
Hopefully this helps, did the best I could!
1) Which of these is a two-step equation?
A) x +9=21
B) x = 11
C) 2x + 9 = 21
Answers
A two-step equation is an equation which needs two steps to solve.
In this case, answer choice "C" is a two-step equation.
2x + 9 = 21. Subtract 9 from both sides
2x = 12. Divide both sides by 2.
x = 6.
Answer choice "B" just gives us the answer.
Answer choice "A" needs only one step to solve the equation.
x + 9 = 21. Subtract 9 from both sides.
x = 12.
The equation with two-step solution is x +9=21.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
A) x+ 9 = 21
Subtract 9 from both side we get
x +9 -9 = 21 -9
x = 12
B) x = 11
C) 2x + 9 = 21
Subtract 9 from both side we get
2x = 12
Divide both side by 2
x = 6.
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let w be a subspace, and let s be a spanning set for w. find a basis for w, and calculate dim(w ) for each set s.
a) s= [1 1 -2] [-1 -2 3] [1 0 -1] [2 -1 0]
b) s=[1 2 -1 1] [3 1 1 2] [-1 1 -2 2] [0 -2 1 2]
Answers
To find a basis for the subspace W spanned by set S, we can perform Gaussian elimination on the matrix formed by the vectors in S. The basis vectors will be the non-zero rows in the reduced row-echelon form of the matrix.
a) s = [1 1 -2], [-1 -2 3], [1 0 -1], [2 -1 0]
Let's form a matrix using the given vectors:
```
[1 1 -2]
[-1 -2 3]
[1 0 -1]
[2 -1 0]
```
Perform Gaussian elimination to obtain the reduced row-echelon form:
```
[1 0 -1]
[0 1 -1]
[0 0 0]
[0 0 0]
```
The non-zero rows correspond to the basis vectors:
[1 0 -1] and [0 1 -1].
Therefore, the basis for W is {[1 0 -1], [0 1 -1]}.
The dimension of W (dim(W)) is equal to the number of basis vectors, which in this case is 2.
b) s = [1 2 -1 1], [3 1 1 2], [-1 1 -2 2], [0 -2 1 2]
Let's form a matrix using the given vectors:
```
[1 2 -1 1]
[3 1 1 2]
[-1 1 -2 2]
[0 -2 1 2]
```
Perform Gaussian elimination to obtain the reduced row-echelon form:
```
[1 0 1 0]
[0 1 -1 0]
[0 0 0 1]
[0 0 0 0]
```
The non-zero rows correspond to the basis vectors:
[1 0 1 0], [0 1 -1 0], and [0 0 0 1].
Therefore, the basis for W is {[1 0 1 0], [0 1 -1 0], [0 0 0 1]}.
The dimension of W (dim(W)) is equal to the number of basis vectors, which in this case is 3.
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he quadratic formula is used to solve for x in equations taking the form of a quadratic equation, ax 2
+bx+c=0. quadratic formula: x= 2a
−b± b 2
−4ac
Solve for x in the following expression using the quadratic formula. 2x 2
+29x−6.1=0 Use at least three significant figures in each answer. and x=
Answers
To solve the quadratic equation \(2x^{2} +29x-6.1=0\) using the quadratic formula, we can use the equation. The solutions for the quadratic equation \(2x^{2} +29x-6.1=0\)using the quadratic formula are:
x = (-b ± \(\sqrt{b^{2}-4ac }\)) / (2a)
Given the coefficients:
a = 2
b = 29
c = -6.1
x = (-29 ± \(\sqrt{841+48.8}\)) / 4
x = (-29 ± \(\sqrt{889.8}\)) / 4
Calculating the square root:
x = (-29 ± 29.828) / 4
Now, let's calculate the two possible values for x:
x1 = (-29 + 29.828) / 4 ≈ 0.207 (rounded to three significant figures)
x2 = (-29 - 29.828) / 4 ≈ -14.957 (rounded to three significant figures)
Therefore, the solutions for the quadratic equation \(2x^{2} +29x-6.1=0\)using the quadratic formula are:
x ≈ 0.207 and x ≈ -14.957 (both rounded to three significant figures).
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i dont understand it (7×5)+(6×4)
Answers
59
Step-by-step explanation:
7 × 5 = 35
6 × 4 = 24
35 + 24 = 59
because 4 + 5 is 9 and 3 + 2 is 5
so 59
Answer:
59
Step-by-step explanation:
Follow PEMDAS
P=Parenthesis
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtracting
So, multiply 7 times 5, then add 6 times 4.
35+24=59
What is the volume of a rectangular prism with a base area of 32 cm and a height 7cm
Answers
Answer:
224 cm³
Step-by-step explanation:
Volume = Area of base x height
V = 32 x 7
V = 224 cm³
In this question, all the required information is given so we'll simply have to solve.
\(\large\boxed{\bold{V= \ base \ area× \ height}}\)
Now, substitute the values according to the formula.
\(V= \ 32 × 7\)
\(\large\boxed{\bold{ V= \ 224 \ {cm}^{3}}}\)
The answer is a whole number so we won't have to round off.
Hence, the volume of the given rectangular prism is 224 cubic centimeters.
6. A person can order a new car with a choice of 11 possible
colors, with or without air conditioning, with or without
heated seats, with or without anti-lock brakes, with or
without power windows, and with or without a CD player. In
how many different ways can a new car be ordered in terms
of these options?
A) 352
B) 704
C) 22
D) 176
Answers
Solve the real-world situation by using the substitution method.
1. A standard rectangular highway billboard has a perimeter of 124 ft.
The length is 34 ft. more than the width. Let l represent the length
521 + 2w
124
and w represent the width. The system of equations
1 = 34 + w
Find the length and the width.
Answers
Answer:
521 plus 521 is equal to 10000
Which of the following correctly uses exponents to write "6 factors of 2"?
062
26
06.2
12
Please hurry!
Answers
Answer: 2^6
Step-by-step explanation:
First, when we have:
x^n
this means that we are multiplicating x by itself n times.
Now, in this case we have:
6 factors of 2 would mean that we have:
(2)*(2)*(2)*(2)*(2)*(2)
2 multiplied by itself 6 times.
This is equal to:
(2)*(2)*(2)*(2)*(2)*(2) = 2^6
Which of the following three numbers cannot measure of the sides of a triangle?a. 10, 12, 8b. 7, 12, 11c. 9, 9, 9d. 11,6, 3
Answers
The condition on the sides of a triangle is that the sum of any two side lengths must be greater than the third side.
So, if there is any pair of numbers that sum up to less than the third number, those three numbers cannot be measures of the sides of a triangle.
Notice that, for the three numbers given in option d (11, 6, 3), we have:
11 + 6 > 3
11 + 3 > 6
but
6 + 3 = 9
6 + 3 < 11
Therefore, those numbers in option d cannot be measures of the sides of a triangle.
Find p(0),p(1),p(-1) and p(2) of the 3x(x-2)
Answers
Answer:
make x→0
\(p(0)=(0)^{2}-3(0)+2\)
→ \(p(0)=0+0+2\)
→\(p(0)=2\)
\(------\)
Replace x→-1
\(p(-1)=(-1) ^{2} -3 (-1)+2\)
→ \(p(-1)=1-3+2\)
→ \(p(-1)=0\)
\(----------\)
Now make x→2
\(p(2)=(2) ^{2} -3(2)+2\)
→ \(p(2)=4-6+2\)
→ \(p(2)=0\)
\(Answer:-2,0,0\)
\(-----------\)
hope it helps...
have a great day!!
A cone has a volume of 6443.28 cubic millimeters and a radius of 18 millimeters
. What is its height?
Answers
Answer:
not sure if they want 19 or 19.00
One year, the population of a city was 132,000. Several years later it was 149,160.
Find the percent increase.
Answers
Answer: 13%
Step-by-step explanation:
To find the percent increase, first find the increase in figures:
= 149,160 - 132,000
= 17,160 people
Then find the percent increase in this manner:
= Increase / Previous population * 100%
= 17,160 / 132,000 * 100%
= 13%
please help with this :)!
Answers
Answer:
it should be 7
Step-by-step explanation:
Graphs
Question 1: Graphs Consider the function f(x) whose graph is shown below. 4-3-2-1 2 3 4 5 6 7 -2 A) What is the domain and range of f(x)? B) - Draw f(x) and f(x + 3) - 1 on the same graph. • What is
Answers
A) Domain and Range of f(x):
The domain of a function represents all the possible values of x for which the function is defined. From the information provided, it is not clear what the exact domain of the function is. However, assuming that the graph extends indefinitely in both directions, the domain of f(x) is likely to be all real numbers (-∞, +∞).
The range of a function represents all the possible values of f(x) for the given domain. Again, without specific details about the graph, it is difficult to determine the exact range. However, based on the visible portion of the graph, it appears that the range of f(x) lies between the lowest point on the graph and the highest point on the graph.
B) Drawing f(x) and f(x + 3) - 1 on the same graph:
To graph f(x) and f(x + 3) - 1 on the same graph, you would start by plotting the points of the original function f(x). Then, to graph f(x + 3) - 1, you would shift the entire graph of f(x) horizontally by 3 units to the left (since it's x + 3) and vertically down by 1 unit (due to the -1). This transformation reflects the effect of the function f(x + 3) - 1.
By plotting the transformed points, you would be able to see how the graph of f(x + 3) - 1 relates to the function f(x).
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Click on all the values for n that make this inequality true
Answers
8. PROM A limo costs $85 to rent for 3 hours plus a 7% sales tax, What is the total cost
to rent a limo for 6 hours?
Answers
Answer:
181.9 dollars
Step-by-step explanation:
If it costs 85 dollars for 3 hours we want to double that to get the amount for 6 hours which is 170 dollars. This is before sales tax. You can find the amount after sales tax by multiplying 170 by 1.07. You do this because 100 percent of the cost would be 170 times 1, and 7 percent is .07, so if you want 107 percent of the cost you want to do 170 times 1.07. This works because it takes 7 percent of 170 and adds it to the total cost. You could also do this by 170 times .07. Then add the product to 170. 181.9 is the final answer.