A few more problems and then I’m done
Answer:
((c)).g(x) = 3 × 2^x +2..
Find a9 for the geometric sequence 5, –20, 80, ...
Answer:
327680
Step-by-step explanation:
The general formula of the formula for the sequence is 5*(-4)^(n-1). The 9th term will be 5*(-4)^8=327680
I need help ASAP thank you
9514 1404 393
Answer:
C
Step-by-step explanation:
The graph shows two vertical asymptotes, so the relevant function will be zero in the denominator for two different x-values. The only possibility is ...
[tex]F(x)=\dfrac{1}{(x-1)(x+1)}[/tex]
One year, Alex bought an antique car for his birthday. During the first year he owned it, the
value of the car gained 10%. During the second year, the value of the car gained another
15% from the previous year. If the value of the car is now $37,950.00, how much did Alex
originally pay for his car?
Answer:
28462.5
Step-by-step explanation:
During the first year it gained 10% and during his second year he gained 15% so you first add those and you get 25%.
Then you multiply 25% with 37,950.
25/100 * 37950 = 948,750/100
= 9487.5
To get the original amount you subtract 9487.5 from 37,950
37,950 - 9487.5 = 28462.5
So the original amount was 28462.5
The sum of a number x and
eleven
Answer:
what is the sum.
Step-by-step explanation:
Take the sum - 11 =x
There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y ratio is 3:1. What is a possible coordinate?
Answer:
Step-by-step explanation:
Suppose the radius is 1. The parametric equations for the circle are
x = cosθ
y = sinθ
x:y = 3:1
tanθ = ⅓
cosθ = 3/√(1²+3²) = 3/√10
sinθ = 1/√10
The solutions are (3/√10, 1/√10) and (-3/√10, -1/√10).
Find the first, second, third and fourth order Maclaurin polynomials of f(x) =
arctan(x). Draw the graph of f(x) and the four polynomials on the same
diagram. (Sketch by hand or use software.)
#urgent please give me this answer and help me#
The first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:
The first order Maclaurin polynomial is f(x)=xThe second order Maclaurin polynomial is also f(x)=xThe third order Maclaurin polynomial is [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]The fourth order Maclaurin polynomial is also [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]You can see the graph on the attached picture.So let's start by finding the first order maclaurin polynomial:
f(x)=f(0)+f'(0)x
so let's find each part of the function:
f(0)=arctan(0)
f(0)=0
now, let's find the first derivative of f(x)
f(x)=arctan(x)
This is a usual derivative so there is a rule we can use here:
[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]
so now we can find f'(0)
[tex]f'(0)=\frac{1}{(0)^{2}+1}[/tex]
f'(0)=1
So we can now complete the first order Maclaurin Polynomial:
f(x)=0+1x
which simplifies to:
f(x)=x
Now let's find the second order polynomial, for which we will need to get the second derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}[/tex]
so:
[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]
we can rewrite this derivative as:
[tex]f'(x)=(x^{2}+1)^{-1}[/tex]
and use the chain rule to get:
[tex]f''(x)=-1(x^{2}+1)^{-2}(2x)[/tex]
which simplifies to:
[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]
now, we can find f''(0):
[tex]f''(0)=-\frac{2(0)}{((0)^{2}+1)^{2}}[/tex]
which yields:
f''(0)=0
so now we can complete the second order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}[/tex]
which simplifies to:
f(x)=x
Now let's find the third order polynomial, for which we will need to get the third derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}[/tex]
so:
[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]
In this case we can use the quotient rule to solve this:
Quotient rule: Whenever you have a function in the form , then it's derivative is:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
in this case:
p=2x
p'=2
[tex]q=(x^{2}+1)^{2}[/tex]
[tex]q'=2(x^{2}+1)(2x)[/tex]
[tex]q'=4x(x^{2}+1)[/tex]
So when using the quotient rule we get:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
[tex]f'''(x)=\frac{(2)(x^{2}+1)^{2}-(2x)(4x)(x^{2}+1)}{((x^{2}+1)^{2})^{2}}[/tex]
which simplifies to:
[tex]f'''(x)=\frac{-2x^{2}-2+8x^{2}}{(x^{2}+1)^{3}}[/tex]
[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]
now, we can find f'''(0):
[tex]f'''(0)=\frac{6(0)^{2}-2}{((0)^{2}+1)^{3}}[/tex]
which yields:
f'''(0)=-2
so now we can complete the third order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}[/tex]
which simplifies to:
[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]
Now let's find the fourth order polynomial, for which we will need to get the fourth derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}+\frac{f^{(4)}(0)}{4!}x^{4}[/tex]
so:
[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]
In this case we can use the quotient rule to solve this:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
in this case:
[tex]p=6x^{2}-2[/tex]
p'=12x
[tex]q=(x^{2}+1)^{3}[/tex]
[tex]q'=3(x^{2}+1)^{2}(2x)[/tex]
[tex]q'=6x(x^{2}+1)^{2}[/tex]
So when using the quotient rule we get:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
[tex]f^{4}(x)=\frac{(12x)(x^{2}+1)^{3}-(6x^{2}-2)(6x)(x^{2}+1)^{2}}{((x^{2}+1)^{3})^{2}}[/tex]
which simplifies to:
[tex]f^{4}(x)=\frac{12x^{3}+12x-6x^{3}+12x}{(x^{2}+1)^{4}}[/tex]
[tex]f^{4}(x)=\frac{6x^{3}+24x}{(x^{2}+1)^{4}}[/tex]
now, we can find f^{4}(0):
[tex]f^{4}(x)=\frac{6(0)^{3}+24(0)}{((0)^{2}+1)^{4}}[/tex]
which yields:
[tex]f^{4}(0)=0[/tex]
so now we can complete the fourth order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}+\frac{0}{4!}x^{4}[/tex]
which simplifies to:
[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]
you can find the graph of the four polynomials in the attached picture.
So the first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:
The first order Maclaurin polynomial is f(x)=xThe second order Maclaurin polynomial is also f(x)=xThe third order Maclaurin polynomial is [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]The fourth order Maclaurin polynomial is also [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]You can find further information on the following link:
https://brainly.com/question/17440012?referrer=searchResults
The starting line up for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard. There are four forwards and six guards from which to choose the line up. If the starting players are chosen at random, what is the probability that the two brothers will end up in the starting line up
Answer:
0.25 = 25% probability that the two brothers will end up in the starting line up
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the players are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
Matthew plus another forward from a set of 3.
Tony plus another two guards from a set of 5.
So
[tex]D = C_{3,1}C_{5,2} = \frac{3!}{1!2!} \times \frac{5!}{2!3!} = 3*10 = 30[/tex]
Total outcomes:
Two forwards from a set of 4.
Three guards from a set of 6.
So
[tex]T = C_{4,2}C_{6,3} = \frac{4!}{2!2!} \times \frac{6!}{3!3!} = 6*20 = 120[/tex]
What is the probability that the two brothers will end up in the starting line up?
[tex]p = \frac{D}{T} = \frac{30}{120} = 0.25[/tex]
0.25 = 25% probability that the two brothers will end up in the starting line up
Pls helppppp,,,,,.....
Answer:
yall do school right now???and i forgot how to do these sorry
Answer:
18 = 2x-14
or, 2x =18+14
or, 2x =32
or, x=32/2
x=16
2(6x-7)=10
or, 12x-14=10
or, 12x=10+14
or, x=24/12
x=2
_+3=-9 pls help I will give branlyiest
PPPPPLLLLZZZZ HELPPPP
Use the function f(x) = -16x² + 60x + 16 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph
Here we have the quadratic function:
f(x) = -16*x^2 + 60*x + 16
We can see that it is in standard form:
y = a*x^2 + b*x + c
a) First we want to completely factorize the function f(x).
To do it, we first need to find the roots of f(x).
Remember that for a generic quadratic equation:
a*x^2 + b*x + c = 0
whit roots x₁ and x₂, the factorized form is:
a*(x - x₁)*(x - x₂)
And the roots are given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:
[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*(-16)*16} }{2*(-16)} = \frac{-60 \pm 68}{-32}[/tex]
So the two roots are:
x₁ = (-60 + 68)/-32 = -0.25
x₂ = (-60 - 68)/-32 = 4
Then the factorized form is:
f(x) = -16*(x - 4)*(x + 0.25)
B) We already found the roots, which are:
x₁ = -0.25
x₂ = 4
These are the x-intercepts:
(-0.25, 0) and (4, 0)
C) We can see that the leading coefficient is negative.
This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.
D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.
If you want to learn more about this topic, you can read:
https://brainly.com/question/22761001
I need help completing this answer are you available
Answer:
Step-by-step explanation:
plz help me with this question
What is one important role that ocean waters have in heating Earth?
absorb and transport solar energy
transport nutrients and waste
create and emit solar energy
wear away rock and soil
also support me on on ubute SadSpade4679
Answer:
The ocean absorbs heat energy from the sun
Step-by-step explanation:
Yw :)
Answer:
The ocean absorbs heat energy from the sun.
Step-by-step explanation:
what is the mean of this graph?
Answer:
Step-by-step explanation:
Mean: sum of terms/ number of terms
4 + 2 + 3 + 1 + 1 + 5 = 16
Numbr of terms = 6
16/6 = 2.66
Answered by g a u t h m a th
Answer:
2 2/3
Step-by-step explanation:
The mean is the average of the values
The values on the graph are 4, 2, 3, 1, 1, and 5
Average is sum/number of values
4+2+3+1+1+5=16
16/6=2 2/3
What is the area of this figure?
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
For a 13-person team, how does the actual weekly labor cost compare to the targeted labor cost?
The actual labor cost is $600 over the targeted labor cost.
Given that,
Work done by each person per week = 40 hours
Required labor hours per week = 600 hours
No. of workers in the team = 13
To find,
Actual weekly labor cost = ?
Procedure:
Actual weekly labor cost = No. of workers * no. of hours performed by them
[tex]= 13 * 40[/tex]
[tex]= 520 hours[/tex]
Given that,
[tex]Regular rate = $ 15.00 per hour[/tex]
[tex]Overtime rate = $ 22.50 per hour[/tex]
Thus,
Actual labor cost = (regular hours worked * regular rate) + (overtime * overtime rate)
[tex]= (520 * 15) + ([600 - 520] * 22.50)[/tex]
[tex]= $ 7,800 + $ 1,800[/tex]
[tex]= $ 9600[/tex]
Targeted Labor cost = $ 9,000 per week
Thus, option C i.e. the actual labor cost is $ 600 over the targeted labor cost.
Learn more about 'Labor Cost' here:
brainly.com/question/5427701
Find median of given data : 6,6,7,8,11,19,6
Answer:
Median =7
Mean = 9
Mode = 6
Step-by-step explanation:
Have a gr8 day!
Answer:
the median is 7
Step-by-step explanation:
6,6,6,7,8,11,19
7 is the middle number
Find the area of the figure.
A =
Is it m, m2, or m3
Answer:
348 m^2
Step-by-step explanation:
The figure is made up of a rectangle 24 m by 12 m, and a triangle with a 24 m base and a 5 m height.
A = LW + bh/2
A = 24 m * 12 m + (24 m)(5 m)/2
A = 288 m^2 + 60 m^2
A = 348 m^2
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
Answer:
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
If you have 2 distinct black playing cards and 2 distinct red playing cards, how many ways can you arrange the four cards given that the red cards can never be next to each other
Answer:
I'm not 100% on the interoperation of this question...
are the two red cars out of a 52 card deck and you can try all the combinations of two red and black cards ????
for this answer i will assume that you have 4 coins two nickels and 2 quarters
and the question is " how many ways can you arrange the four coins given that the nickels can not be next to the quarters"
in that case I think the answer is 8
Step-by-step explanation:
1- N1 Q1 N2 Q2
2- N1 Q2 N2 Q1
3- N2 Q1 N1 Q2
4- N2 Q2 N1 Q1
5- Q1 N2 Q2 N1
6- Q2 N2 Q1 N1
7- Q1 N1 Q2 N2
8- Q2 N1 Q1 N2
[tex]2\cdot \left(\left(2\:choose\:1\right)\:\cdot \:\left(2\:choose\:1\right)\right)[/tex]
Question 2 of 10
Which pair of functions are inverses of each other?
O A. f(x) = i +15 and g(x) = 12x - 15
O B. f(x) = - 10 and g(x) = 2410
O C. f(x) = y3x and g(x) = (3) 3
O D. f(x) = 11x- 4 and g(x) = 4
SUBMIT
Answer:
option c f(x)=-10and g(x)=2410
Geometry please help me need help I don’t know how to do it
Answer:
A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)
A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)
Step-by-step explanation:
first everything is shifted down 8 units (x,y-8), so we get A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)
then you multiply by -1 A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)
The minimum point of the graph y = 2x^2 + 2x +1 is located at:
Answer:
A
Step-by-step explanation:
By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)
Complete the function table.
Answer:
B
Step-by-step explanation:
The function given is f(n) = n-3. Plug in n=0 and you will get an output - 3. Plug in n=2 and you will get an output - 1. Hence table B is the answer .
04.10 Which statement about the graph is true? CO 7 E 5 4 3 2 1 2 3 4 5 6 7 8 x The graph shows a proportional relationship because it is a line, and the difference between each point is the same. The graph shows a proportional relationship because it is a line, and each x-value is a multiple of 2. The graph does not show a proportional relationship because each point written as a ratio gives a different value. O The graph does not show a proportional relationship because a line that increases by 1 in the y-value cannot have a constant of proportionality.
Answer:
c
Step-by-step explanation:
cheese is rotten milk
Find the area of the circle. Use 3.14 for tt. d = 6 ft A = [?] ft2 A=Tr2
d=6ft
According to formula A=πr²
first we need 'r'
Hence,
as, r=d/2
r=6ft/2
r=3ft
A=πr²
A=3.14(3ft)²
A=3.14×9ft²
A=28.26ft²
Find the solutions of the quadratic equation x2 + 7x + 10 = 0.
Question 13 options:
A)
x = 2, 5
B)
x = –2, –5
C)
x = –7, –3
D)
x = 7, 3
Answer:
Step-by-step explanation:
x² + 7x + 10 = 0
x = [-7 ± √(7² - 4·1·10)]/(2·1) = [-7 ± √9[/2 = [-7 ± 3]/2 = -2, -5
What is the slope of the line that passes through the points (10,8) and (-15,18)?
Write your answer in simplest form.
Answer:
I believe it is 2/5 fraction
Answer:
-2/5
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 18-8)/(-15-10)
= 10/-25
= -2/5
A small boat can travel at 28 per hour how many hours will it take to go across the bay that is 56 miles wide
Answer:
2 hours
Remember that time = distance/rate
The distance you need to cover is 56 miles, while you go 28 miles per hour. Using these, we get this:
time=56/28
time=2
So it will take two hours to go across a 56 mile wide bay at 28 mph.
Step-by-step explanation:
What is the common difference for this arithmetic sequence?
-6,-1,4,9,14,...
A. 6
B. 4
C. 5
D. 3
SUBMIT
Answer:
5 is the answer to your question
Step-by-step explanation:
the numbers are increasing by +5
