Which statement describes the sequence defined by an
n3 +3?
n2-60
O The sequence diverges.
O The sequence converges to a limit of 0.
O The sequence converges to a limit of infinity
O The sequence converges to a limit of - infinity
Answers
Answer:
C
Step-by-step explanation:
To find the statement that describes the sequence, we find it's limit as n goes to infinity.
Doing this, as we get that the limit goes to infinity, we get that the sequence diverges.
Sequence:
\(a_n = \frac{n^3 + 3n}{n^2 - 6n}\)
Limit as n goes to infinity:
Limit of n going to infinity, so we consider just the terms with the highest exponent in the numerator and in the denominator.
\(\lim_{n \rightarrow \infty} a_n = \lim_{n \rightarrow \infty} \frac{n^3 + 3n}{n^2 - 6n} = \lim_{n \rightarrow \infty} \frac{n^3}{3n^2} = \lim_{n \rightarrow \infty} \frac{n}{3} = \frac{\infty}{3} = \infty\)
Thus, the correct answer is that the sequence diverges.
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Related Questions
Relative intensity of 9 decibels is how many times higher than that of 8 decibels
Answers
Answer:
what do you mean by land ?
The intensity of sound is proportional to the square of its amplitude.
Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:
I9/I8 = (10^(9/10))/(10^(8/10))
I9/I8 = 10^(0.1)
I9/I8 = 1.2589
Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
G(x) = x^2 log2x
?
?
?
Answers
Answer:
Differentiate using the power rule where \(d/dx[x^n]=nx^n-1,n=2\)
the derivative would be 2x
Step-by-step explanation:
Slope= -2/5 y-intercept = -3
Please answer ASP!!!!!
Answers
Answer:
the equation would be y=-2/5x-3
Answer:
The answer is y=-2/5x-3
Step-by-step explanation:
Hope this helped, Have a Wonderful Day!!!
\(8x - 4 - 5x \leq 21+5\)
Answers
Answer:
x ≤ 10
Step-by-step explanation:
A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Years of experience Salary
0 $52,000
1 $53,150
2 $54,260
3 $55,285
4 $56,921
5 $57,126
Use the equation for the line of best fit to predict the salary for an employee with 6 years of experience? (Round your answer to the nearest dollar.)
$61,150
$59,672
$58,587
$57,990
Answers
Answer:
Answer down bellow
Step-by-step explanation:
Q's Asked: A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Years of experience Salary
0 $52,000
1 $53,150
2 $54,260
3 $55,285
4 $56,921
5 $57,126
---------------------------------------------------------------------------------------------------------
So based on the chart:
0 $52,000
1 $53,150
2 $54,260
3 $55,285
4 $56,921
5 $57,126
We can see for each year of experience the "Salary" goes up one thousands constantly. And that makes sense bc as you get used to the work u gradually get better meaning u work better and u also get paid better. ehmm... my bad
----------------------------------------------------------------------------------------------------------
So work side of things based on the chart we see the amount the amount change. so from
0 to 1 yr
you will be paid $1,150 more.
and from 1 to 2 yrs you will be paid 1110.
and so on.
So the answer is $58,587And btw i got it right on my test !
~~Wdfads~~Pls like and give brainlest
Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph
Answers
Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.
Uniform acceleration towards the positive direction:
In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.
Uniform acceleration towards the negative direction:
Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.
The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.
Uniform deceleration towards the positive direction:
In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.
The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.
Uniform deceleration towards the negative direction:
Here, the object's velocity decreases in the negative direction, opposing its initial direction.
The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.
In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.
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Pre - Calculus evaluate exponential derivative at a point !
Answers
Answer:
\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)
Step-by-step explanation:
Use Quotient Rule to find f'(x)
\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)
Find f'(1) using f'(x)
\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)
Answer:
\(f'(1)=-\dfrac{9}{e^{3}}\)
Step-by-step explanation:
Given rational function:
\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)
To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.
\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)
\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)
\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)
Therefore:
\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)
\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)
\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)
To find f'(1), substitute x = 1 into f'(x):
\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)
\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)
\(f'(1)=-\dfrac{9}{e^{3}}\)
Consider this function and its graph. f(x) = tan(3x + pi/4) - 1 Which statement best describes function f?
A. The function is odd.
B. The function is even.
C. There is not enough information to determine whether the function is even or odd.
D. The function is neither even nor odd.
Answers
Answer: D. The function is neither even nor odd.
Step-by-step explanation:
A function f(x) is even if:
f(x) = f(-x) for all x-valies
A function f(x) is odd if:
f(x) = -f(-x) for all x-values.
If there is only one value of x such that the above conditions are false, then the function is neither odd nor even.
In the graph, we can see that:
f( -π/3) = f(π/3)
This would imply that the function is even (at least in that point)
And can also see that as x increases from zero, the value of f(x) increases.
And as x decreases from zero, the graph of f(x) decreases.
So for a point 1 > a > 0, we have that:
f(a) ≠ f(-a)
Then we can conclude that the function is neither even nor odd, the correct option is D.
Answer:
D. The function is neither even nor odd
Step-by-step explanation:
edmentum
Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total number of tickets she sold.
Based on the table, write an equation for the relation between the number hours Gwen worked and the number of tickets she sold.
t = h/23
h = 23t
ht = 23
t = 23h
Answers
The equation that shows the relation between the number of hours worked and tickets sold is t = 23h (fourth option)
What is the equation?Examining the table, it can be seen that the number of tickets sold increases by 23 for every hour that Gwen works.
Tickets sold when Gwen works for 2 hours = 23 x 2 = 46
Tickets sold when Gwen works for 2 hours = 23 x 3 = 69
Because the tickets sold increase by a constant number, the equation would be modelled as a linear function.
Linear equations have the form : a + bx
Ticket sold = (number of hours x ticket sold in the first hour)
t = 23h
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9. In a deck of 52 playing cards what is the probability, as a fraction, of drawing a picture card (A,K,Q,J) replacing it and then drawing either a heart or a diamond?
Answers
Answer:
13/52 or 1/4
Step-by-step explanation:
In a deck of 52 playing cards what is the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9?
So, we have,
n(S) =52
And the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9 is,
n(E) =13 a set of a diamond suit, because a diamond suit has {A, K ,Q ,J ,2,..,9}
Thus, the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9 is
Elena receives $95 per year in simple interest from three investments totaling $2100 . Part is invested at 3%, part at 4%, and part at 5%. There is $1000 more invested at 5% than at 4%. Find the amount invested at each rate.
The amount invested at 3% is $
the amount invested at 4% is $
and the amount invested at 5% is $
Answers
The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.
Let's assume the amount invested at 4% is x dollars.
According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.
So, the amount invested at 5% is (x + $1000).
The total amount invested is the sum of the amounts invested at each rate, which is $2100.
Therefore, we can write the equation:
x + (x + $1000) + (amount invested at 3%) = $2100
Now, we can calculate the amount invested at 3%.
We subtract the sum of the amounts invested at 4% and 5% from the total investment:
(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)
Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:
Simple Interest = Principal × Interest Rate
The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.
According to the problem, the total interest earned is $95.
So we can write the equation:
(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95
Now we can substitute the expression for (amount invested at 3%) and solve for x.
Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.
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Please help last question
Answers
Answer:
1/3x
The point (135,45) as well as all other listed points falls on the line 1/3x=y
Hope this helps! :)
9x + 3 + 8x
Please help
Answers
A 3-gallon bottle of fabric softener costs $51.36. What is the price per cup?
Answers
Answer:
$1.07
Step-by-step explanation:
16 cups per gallon
16*3=48cups
51.36/48=1.07
Please help me! Here is screenshot attached
Answers
Answer:
x = 2
Step-by-step explanation:
hope that helps....
all points having an x-coordinate of 1 whose distance from the point (-3,-6) is 5
Answers
Answer:
\(They'll \: be \: on \: the \: circle:\)
\((x+3)^2+(y+6)^2=25\)
\(x=1\)
\((y+6)^2=9\)
\(y + 6 = 3\)
\(y = -3\)
\((1,-3)\)
\(y + 6 = -3\)
\(y = -9\)
\((1,-9)\)
Step-by-step explanation:
\(Thank \: you!!!!!!\)
on : to show More... Then click on √x to enter your answers using the Math Equation editor. Question 5 A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = − 16t² +64t + 3. What is the height of the stump? O 3 ft -3 ft O 16 ft O 64 ft ◄ Previous 1 pts M Next ▸
Answers
The height of the stump is 3 ft.
The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.
In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:
h(0) = -16(0)² + 64(0) + 3
Since any term multiplied by zero is zero, we can simplify further:
h(0) = 0 + 0 + 3
Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.
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A square has an area of 56 units, find the length of the side in simplest form. Has to be an Improper fraction.
Answers
The length of the side of the square in simplest form is 2sqrt(14).
The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.
We are given that the area of the square is 56 units, so we can set up the equation:
\(56 = s^2\)
To solve for s, we can take the square root of both sides of the equation:
sqrt(56) = \(sqrt(s^2)\)
We can simplify the square root of 56 by factoring it:
sqrt(56) = sqrt(222*7) = 2sqrt(14)
So, we have:
2sqrt(14) = s
This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).
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What is the quotient of (-55) divide by 5?
Answers
Answer:
11
Step-by-step explanation:
✨Answer:✨
-11
✨Step-by-step explanation:✨
-55 ÷ 5 = -11
(Just take the negative sign away and divide)
L=10 inches and A=40 square inches, solve A=lw
Answers
Answer:
w=4
Step-by-step explanation:
\(A=lw\)
\(40= (10)w\)
\(\frac{40}{10} = \frac{10}{10}w\\w=4\\\)
During a trip, Amy had to take two different trains. Her first train traveled for 3 hours, and the second
train traveled for 4 hours. Combined, the trains traveled 625 miles.
If the equation 3m + 4n = 625 represents this situation, which statements are true regarding this
equation?
Select two that apply.
The variable m in the equation represents the speed of the first train.
The variable m in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the first train.
The variable m in the equation represents the number of hours Amy traveled on the
first train.
The variable n in the equation represents the number of hours Amy traveled on the
second train.
Answers
Answer:
Let's solve for m.
3m + 4n = 625
Step 1: Add -4n to both sides.
3m + 4n + −4n = 625 + −4n
3m = −4n + 625
Step 2: Divide both sides by 3.
3m/3 = 4n + 625/3
m = -4/3 n + 625/3
C) The variable m in the equation represents the number of hours Amy traveled on the
first train.
D) The variable n in the equation represents the number of hours Amy traveled on the
second train.
25% OFF! The original price of an apple tart is $20. How much will Manny pay if he buys it during the sale?
Answers
Answer:
15 dollars
Step-by-step explanation:
Because it is 25% off you multiply the original cost(20) by 75$: 20*75%=15
If you apply the changes below to the quadratio parent function, f(x) = x2
what is the equation of the new function?
• Shift 1 unit right.
• Vertically stretch by a factor of 5.
• Reflect over the x-axis.
Answers
Answer:
\(f(x) = -5(x+1)^2\)
Step-by-step explanation:
We are given the following function:
\(f(x) = x^2\)
Shift 1 unit right.
Shifting a function a units to the right is finding f(x+a). So
To shift one unit right:
\((x+1)^2\)
Vertically stretch by a factor of 5.
To vertically stretch by a factor of 5, we multiply the function by 5. So
\(5(x+1)^2\)
Reflect over the x-axis.
To reflect over the x-axis we multiply the function by -1. So
\(f(x) = -5(x+1)^2\)
How can u find a geometry-big circle mAB=56 mBC=59 mCD=63 mDE=63 mEF= 31
Answers
To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.
We are given the following measures:
\(\sf\:m\angle AB = 56 \\\)
\(\sf\:m\angle BC = 59 \\\)
\(\sf\:m\angle CD = 63 \\\)
\(\sf\:m\angle DE = 63 \\\)
\(\sf\:m\angle EF = 31 \\\)
To find the measure of the geometry-big circle, we add up these measures:
\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)
Substituting the given values:
\(\sf\:56 + 59 + 63 + 63 + 31 \\\)
Simplifying the expression:
\(\sf\:272 \\\)
Therefore, the measure of the geometry-big circle is 272.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
\(1 + 1 = 1 + 1\)is this correct ?
Answers
how can i turn a repeating decimal to a fraction
Example
we have
0.33333333...
Let
x=0.3333...
10x=3.33333...
Subtract
10x-x
9x=3.3333...-0.333...
9x=3
solve for x
x=3/9
Simplify
x=1/3
the fraction is 1/3
Solve the equation.
- 3(2x - 3) = -6x + 9
Solution:
Answers
Pls help maths problem
Answers
The function's input value is \(2\), and the result is \(-11\), making LHS identical to RHS.
What does the word value also mean?The words value and cherish are frequently used interchangeably. Value suggests that something is rated highly for its inherent value even if all of these terms imply "to keep in high estimation." our friendship is valued.
What is values so crucial?Like a barometer, values give our lives purpose and direction. Whatever is happening in our life, our values may point the way forward and guide our decision-making. Values are crucial for maintaining our mental health since they are closely related to our identity.
\(x*-7+3=-11\)
Put the value of \(x\)
\(x=2\)
Then
\(2*-7+3=11\)
\(-14+3=11\)
\(L.H.S.=R.H.S.\)
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The Two sets A and B are said to be disjoint sets if A n B=_____
Answers
The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
What does it mean for two sets to be disjoint?Disjoint sets are a pair of sets that do not share any elements. For instance, sets A=2,3 and B=4,5 are not connected sets.When two sets don't share elements, they are considered disjoint sets. In other words, the null set will result if we find the intersection of two sets. The process is straightforward; two sets are given in this procedure.When using a disjoint set union, it is possible to add new sets, combine existing sets, and check whether two sets of elements are the same in almost real-time.The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
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Multiply the polynomials (y −5)(2y+ 3)
Answers
Answer:
(-3 + -2y)(5 + -1y) = 0
Step-by-step explanation:
Simplifying
(y + -5)(2y + 3) = 0
Reorder the terms:
(-5 + y)(2y + 3) = 0
Reorder the terms:
(-5 + y)(3 + 2y) = 0
Multiply (-5 + y) * (3 + 2y)
(-5(3 + 2y) + y(3 + 2y)) = 0
((3 * -5 + 2y * -5) + y(3 + 2y)) = 0
((-15 + -10y) + y(3 + 2y)) = 0
(-15 + -10y + (3 * y + 2y * y)) = 0
(-15 + -10y + (3y + 2y2)) = 0
Combine like terms: -10y + 3y = -7y
(-15 + -7y + 2y2) = 0
Solving
-15 + -7y + 2y2 = 0
Solving for variable 'y'.
Factor a trinomial.
(-3 + -2y)(5 + -1y) = 0
Hope this helps :)
Questions in picture
Answers
A:
For the first graph the equation would be y=25x with y being the cost and x being the number of yards. Then put 40 for x so it is y=25(40) and solve.
The answer for graph is 1000
For the second table it costs 490 dollars to move 20 yards and 40 is double of 20 so double the cost.
The answer for table is 980
B:
The rate of change for graph is y=25x and that means for every yard shipped you pay 25 dollars
The rate of change for table is whatever the cost divided by the number of yards is i can't see the numbers
C:
In the first question the graph is 1000$ and the table is 980$ so the table would be cheaper