Determine the end behavior of each function.
(a)
p(x) = a(x + b)5(x − c)3
, where a, b, and c are constants and
a < 0
.
p(x) → as x → −∞
p(x) → as x → ∞
(b)
f(x) =
9x2 − 11x + 2
8x2 − 6
f(x) → as x → −∞
f(x) → as x → ∞
(c)
g(x) = 9 + e−6x
g(x) → as x → −∞
g(x) → as x → ∞
Answers
Step-by-step explanation:
(a)
a, b, c are constants and play no role with their value when it goes relative to enormous numbers and to infinity.
but the sign is important.
a < 0, so, it will stay < 0 for all eternity/infinity.
(x + b)⁵ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (the exponent 5 is odd, so a negative value put to an odd power will create a negative result value).
(x - c)³ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (for the same reasons - 3 is an odd number).
x going to -infinity,
p(x) = -×-infinity×-infinity = -infinity
x going to infinity,
p(x) = -×infinity×infinity = -infinity
(b)
the x² terms drown out all other terms with lower x exponent (so, incl. -11x or any constants).
what remains for very, very large x is
9x²/8x² = 9/8 = 1.125
since we have x² terms, it does not matter, if x is positive or negative, the result is always positive.
so, x going to infinity or to -infinity, p(x) is the same again :
p(x) = 9/8 = 1.125
(c)
finally, we have a different result for x going to -infinity or to infinity.
x going to -infinity :
the exponent of e is then -6×-infinity = infinity. and e to the power of infinity is infinity.
p(x) = 9 + infinity = infinity
x going to infinity :
the exponent of e is then -6×infinity = -infinity. and e to the power of -infinity is 1/e to the power of infinity.
and that is 1/infinity. the limit for that is 0.
p(x) = 9 + 0 = 9
Related Questions
ON A HIGHWAY GOING TO YOUR PROVINCE YOU, NOTICE THAT THERE IS A BILLBOARD LOCATED EVERY 1 1/2 KILOMETERS. THERE ARE 14 BILLBOARDS IN THAT HIGHWAY. HOW LONG IS HIGHWAY
Answers
Answer:
The highway is 21 km long.
Step-by-step explanation:
[tex]\frac{1 billboard}{1.5 km} =\frac{14 billboard}{x}[/tex]
x = 21 km
Sixty-five students voted for Jessica. Two times
many students voted for Sierra. How many
students voted
Answers
students voted= 195
Solution :
a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Jessica = 65 student
Sierra = 2 (Sixty-five students voted for Jessica.) = 2(65) = 130
Total number of students = NO of students voted for Jessica +NO of students voted for Sierra
= 65+130
= 195
students voted= 195
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Translate the English phrase into an algebraic expression: the quotient of the sum of a and b and the product of a and b.
Answers
The algebraic expression from the given statement is (a+b)/ab.
Given the statement is the quotient of the sum of a and b and the product of a and b.
In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.
In the given statement the sum of a and b means a+b.
And the product of a and b means ab.
Now, as it is given in the statement that the quotient of the sum of a and b and the product of a and b can be written as
(a+b)/ab.
Hence, the algebraic expression from the given statement "the quotient of the sum of a and b and the product of a and b" is (a+b)/ab.
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-4 + 8 - 5
Please help.
I'm on a knowledge check on ALEKS and my teacher won't help.
Please I've been doing this for almost the whole period.
Answers
Answer:
-1
Step-by-step explanation:
read warriors
by eren hunter.
50 POINTS HELP PLEASE
Graph the system of inequalities. Show at least two points for each inequality. (Lesson 1.08)
Answers
Answer:
54fhuuyfghhhrfbifgifd
Approximate square root 80 by using perfect squares. 80 is between which two perfect squares? What are the square roots of those two perfect squares? What is the approximate value of square root 80?
Answers
By finding square numbers, we will get:
8 < √80 < 9
And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95
How to approximate the square root of 80?
We want to approximate √80, now we need to find two consecutive square numbers such that one is smaller and the other is larger than 80.
We know that:
9*9 = 81
8*8 = 64
Then:
√81 = 9
√64 = 8
So we can see that:
√64 < √80 < √81
Then:
8 < √80 < 9
And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95
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how do i solve this?
Answers
Find the students mistake then find the correct x-intercepts for the graph of the function.
Answers
The value of the given equation the value of x : (3 , -10)
What is a quadratic equation in mathematics?Definitions: A quadratic equation is a second-order polynomial equation in some kind of a single variable x ax2+bx+c=0. Because it is a second-order polynomial problem, the fundamental theorem of fundamental algebra guarantees therefore it has at least one solution.
Briefing:the student haven't solved the equation properly he has not expanded the equation:
According to the given data:
The given equation is f(x) = (x - 3)² - 10
(x - 3)² - 10 = 0
this could be expand and write as:
x² + 9 -6x - 10 = 0
x² -6x -1 = 0
The vertex of an up-down facing parabola of the form y=ax^2+bx+c is Xv.
The parabola params are:
a=1, b=-6, c=-1
[tex]\:x_v=-\frac{b}{2a}[/tex]
[tex]x_v=-\frac{(-6)}{2 \cdot 1}[/tex]
Xv = 3
Putting x = 3 to get the value of y
we get:
y = -10
(3 , -10)
The value of the given equation the value of x : (3 , -10)
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The mean height of American women in their late twenties is about 64.5 inches and the standard deviation is about 2.5 inches. The mean height of men the same age is about 68.5 inches, with a standard deviation of about 2.7 inches. If the correlation between the heights of married heterosexual men and their wives is about r=0.5, what is the equation of the regression line of the the husbands height on the wife’s height in young couples?
Answers
Answer:
For married couples in their early 20s, the regression equation and the prediction of a husband's heightEquation: Y'=33.67+0.54*X'
Step-by-step explanation:
Given that
r=0.5x'=64.5Sx=2.5y'=68.5Sy=2.7General regression line equation is:
Y'=a+b*X'
Therefore, the slope of the regression line is equal to the linear correlation coefficient times the difference between the standard deviations of y' and x'.
[tex]b = r\times\frac{S_y}{S_x}[/tex]
[tex]b = 0.5\times\frac{2.7}{2.5}[/tex]
b = 0.54
The mean of the lowered by the slope and mean of x is the intercept with axis y.
[tex]a = y'-b\times x'[/tex]
[tex]a = 68.5-0.54\times 64.5[/tex]
[tex]a = 33.67[/tex]
Now, putting the values of a and b in regression equation
So, we get
Y'=a+b*X'
Equation: Y'=33.67+0.54*X'
Answer:
For married couples in their early 20s, the regression equation and the prediction of a husband's heightEquation: Y'=33.67+0.54*X'
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What is the quotient for 81/-9, -123 divided by -4, -94/-9, and 65 divided by (-5)
Answers
The final answer is -9, -30.75, -13
What is Quotient?
The number resulting from the division of one number by another.
In the given statement is:
What is the quotient for 81/-9
If we divide 81 by -9
The Quotient will be -9
And, come to the next :
-123 divide by -4
The quotient will be -30.75
And, 65 divided by (-5)
The Quotient will be -13
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A control tower observes the flight of an aircraft. At 09:23 the aircraft is 580 km away on a bearing of 043º. At 09:25 the aircraft is 360 km away on a bearing of 016º. What is the speed and the course of the aircraft? (Use a scale of 1 cm to 50 km.)
Answers
The speed and the course of the aircraft is 27465 km/h.
What is an aircraft?A machine or vehicle can fly by obtaining support from the air, and this is how an airplane works. It uses either static lift, dynamic lift provided by an airfoil, or, in certain rare situations, the downward thrust from jet engines to counteract the pull of gravity.
From the figure, let us use cosine formula to calculate the resultant displacement.
B^2 = C^2 + A^2 - 2(A)(C) cosØ
Where C = 580km
A = 360 km
Ø = 153 degree
Substitute all the parameters into the formula
B^2 = 580^2 + 360^2 - 2(360)(580)cos153
B^2 = 466000 - ( - 372084.32 )
B^2 = 466000 + 372084.32
B^2 = 838084.32
Square root both sides
B = 915.5 km
You are told to use a scale of 1 cm to 50 km.
Therefore, B = 915.5/50 = 18.3 cm
The time given are: 09:23 and 09:25.
The time difference = 25 - 23 = 2 minute
Convert minutes to hours
2 minute = 2/60 = 1/30 hours
Speed = distance/time
Speed = 915.5 ÷ 1/30
Speed = 915.5 × 30
Speed = 27465 km/h
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Daslyn has a piece of rope 2.085 meters long and another piece
2.63 meters long. Which piece can she cut to make a piece that is
2.5 meters long? Explain.
Answers
Answer:
the second piece of rope
Step-by-step explanation:
2.63 ≥ 2.5
2.085≤2.5
Find the area of the figure.
Answers
Answer:
10 x 12 x 9 cm^2
= 1080 cm^2
Answer:
105
Step-by-step explanation:
a = 1/2(bh) + 1/2(bh)
a = 1/2(12)(10) + 1/2 (9)(10)
a= 1/2 (120) + 1/2(90)
a = 60 + 45
a = 105
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
A. four ninths raised to the fourteenth power
B. four ninths raised to the twenty fourth power
C. two thirds raised to the fourteenth power
D. two thirds raised to the twenty fourth power
Answers
Answer:
C. two-thirds raised to the fourteenth
Step-by-step explanation:
Dylan wants to buy a book for 16.95 and a magazine for 4.50
Answers
Dylan needs $ 21.45 for the purchase of both books and the magazine.
Addition refers to the basic operation of mathematics where we find the sum of two or moe numbers.
We are given that:
Dylan wants to buy two things:
1. she wants to buy a book for $ 16.95
2. she wants to buy a magazine for $ 4.50
So, the total money that she needs will be calculated by adding the prices of both the products.
So, by using addition, we get the total money required by Dylan as:
Total money = $ 16.95 + $ 4.50
Total money = $ 21.45
Therefore, we get that, Dylan needs $ 21.45 for the purchase of both books and the magazine.
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Bill’s spelling list is 3 words long at the start of the school year. Each month, his teacher adds 8 words to the list.
Let m represent the number of months since school began and w represent the total number of spelling words.
This relationship can also be shown in a table. Complete the equation that represents between m and w.
Answers
Based on the fact that m represents the number of months and w is the total number of spelling words, the equation that represents the relationship between m and w is w = 8m + 3
How to find the equation?The first thing to find is the slope of the relationship. This can be found as:
= ( 51 - 43) / (6 - 5)
= 8 / 1
= 8
The y-intercept is:
w = 8m + c
43 = 8(5) + c
c = 43 - 40
c = 3
The equation to represent the relationship between m and w is:
w = 8m + 3
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What is the quotient of (−56) ÷ (−4) ÷ 7?What is the quotient of (−56) ÷ (−4) ÷ 7?
Answers
Answer:
98
Step-by-step explanation:
Find the following values for the function
Answers
Answer:
a. -5; b. 4; c. -2.
Step-by-step explanation:
a) f(-3)=3*(-3)+4=-5;
b) f(3)=2*3-2=4;
c) f(0)=2*0-2=-2.
Write an equation in point-slope form of the line
(-7,2); m=2
Answers
Answer: y - 2 = 2(x + 7)
Step-by-step explanation:
Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
y - 2 = 2(x + 7)
If p percent of q is r what percent of r is q
Answers
Answer:
10000/p.
Step-by-step explanation:
r = pq/100
pq = 100r
q = 100r/p
As a percentage of r:
we have P = q * 100/r
P = 100r/p * 100/r
= 10,000r / rp
= 10000/p
Need help with number 6
Answers
Applying the definition of bisection, PR = RQ = 28.5 cm.
What is the Definition of Bisection?When a line segment bisects another line segment, it divides the line into two equal segments. This means the two resultant line segments formed have the same length.
The image below shows the bisection of segment PQ by segment ST at point R, which forms two equal segments, PR and RQ.
This means that the length of segments PR and RQ will be equal to each other.
Given that, PQ = 57 centimeters, therefore:
PR = RQ = 1/2(PQ)
PR = RQ = 1/2(57)
PR = RQ = 28.5 cm
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Algebra Question Help
Answers
Answer:
[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]
Linear function: As x increases by one, y always increases by a constant value. Therefore, the first differences between y-values are the same.Quadratic function: The second differences between y-values are the same.Exponential function: The y-value either increases or decreases by a constant factor.Work out the first differences between the y-values:
[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]
As the first differences are not the same, it is not a linear function.
Work out the second differences:
[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]
As the second differences are not the same, it is not a quadratic function.
Work out if the second differences have a common ratio:
[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]
[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]
As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.
General form of an exponential function:
[tex]y=a(b)^x[/tex]
where:
a is the y-intercept.b is the base (growth/decay factor) in decimal form.The y-intercept is the value of y when x = 0.
From inspection of the table, the y-intercept is ⁷/₃.
Therefore:
[tex]a = \dfrac{7}{3}[/tex]
[tex]b = \dfrac{1}{3}[/tex]
Substitute the found values of a and b into the formula to create an exponential function that models the given data:
[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
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I need solution to this question tutor
Answers
Answer:
x=3 and y=
Step-by-step explanation:
Answer:
x=5 and y any number
Step-by-step explanation:
The sum of 8 and three times a number is 41
Answers
Answer:
x=11
Step-by-step explanation:
let number =x
(8+3x)=41
group like terms
3x=41-8
3x=33
divide both side by the coefficient of x
3x/3=33/3
x=11
TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested
Answers
A person who wants to get in shape goes to a local gym that advertises 62 training sessions for $1109. Find the cost of 94 training sessions.
Answers
The cost of 94 training sessions is $1681.3.
A unit means one thing. A unit rate means the rate of something. Write this as a ratio with a denominator of 1. For example, if you ran 70 meters in 10 seconds, you ran an average of 7 meters in 1 second. A ratio of 70 yards in 10 seconds and 7 yards in 1 second are both rates, but 7 yards in 1 second is a unit rate. The unitary method is a method of finding the value of one unit and then finding the value of the required number of units.Suppose you go to the market to buy six apples. The shopkeeper told you that he sells 10 apples for 100 rupees. In this case, the apple is the unit and the apple price is the value.
62 training sessions for $1109
1 session = 1109/62
94 sessions = (1109/62) * 94
= $1681 .3
The cost of 94 training sessions is $1681.3.
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Find the value of x. Then find the missing angle measures of the polygon.
x = ?
5x degrees = ?
2x degrees = ?
Answers
Answer:
x = 22.5
2x = 45
5x = 112.5
Step-by-step explanation:
The sum of all internal angles in a triangle is 180 degrees. This can be expressed as the following:
x + 5x + 2x = 180
Combine the like terms:
8x = 180
Divide both sides by 8 to find the value of x:
x = 180/8
Simplify:
x = 22.5
Multiply by 2 to get 2x:
2x = 22.5 * 2
2x = 45
Multiply by 5 to get 5x:
5x = 22.5 * 5
5x = 112.5
Verify the answer is correct by taking all the obtained values and ensuring they sum to 180:
22.5 + 45 + 112.5 = 180
The tables below show some inputs and outputs of functions f and h.
Evaluate
Oh
Answers
The value of the composite functions, (h ° f)(1) = 0.5.
How to Solve Composition of Functions?Given the function, (h ° f)(1), this means h(f(1)) as a composition of functions.
Using the table given for the function, f(x), f(1) = -1.
This means that, to find (h ° f)(1) = h(f(1)), we would find the value of h(x) in the table where x = -1.
Thus, from the table for h(x), when x = -1, h(-1) = 0.5.
Therefore, the value of the composite functions, (h ° f)(1) = 0.5.
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What is 27x45 and can you explain it
Answers
Answer:
1215
Step-by-step explanation:
You have to multiply the smallest number with the largest number; then add the zero along with the numbers being multiplied; then add each number until you get the right answer
Translate and solve: 82 less than a is at least −82.
Give your answer in interval notation.
Answers
The interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).
We are given an expression that:
82 is less than a which is at least - 82.
This expression can also be written as:
- 82 < a and a > 82
where a is any variable that can take any value according to the expression.
This can also be written as:
- 82 < a < 82
In interval form, it will be written as:
( -82, 82)
"()" brackets are used as -82 and 82 are not included in the interval.
Therefore, we get that, the interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).
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